The notion of oriented set is the basic elementary concept of the theory of changeable sets. The main motivation for the introduction of changeable sets was the sixth Hilbert problem, that is, the problem of mathematically rigorous formulation of the fundamentals of theoretical physics. In the present paper the necessary and sufficient condition of the existence of one-point time on an oriented set is established. From the intuitive point of view, one-point time is the time associated with the evolution of a system consisting of only one object (for example, from one material point). Namely, it is proven that the one-point time exists on the oriented set if and only if this oriented set is a quasi-chain. Also, using the obtained result, the problem of describing all possible images of linearly ordered sets is solved. This problem naturally arises in the theory of ordered sets.

In order to deal with imprecision, ambiguity, and uncertainty in data analysis, Pawlak introduced rough set theory in 1982. This paper aims to expand the scope of basic set theory developed by presenting the notions of δP-upper and δP-lower approximations, that are based on the notion of δP-open sets, we additionally examine a few of their fundamental characteristics.

Decomposed fuzzy sets are the resent extension of intuitionistic fuzzy sets by incorporating functional and dysfunctional points of views to the definition of membership functions. This paper extends the Technique of Order Preference Similarity to the Ideal Solution (TOPSIS) method to the Decomposed Fuzzy TOPSIS (DF TOPSIS) method and applies it to a multi-criteria risk-based supplier selection problem under fuzziness. DF TOPSIS involves finding a positive ideal solution and a negative ideal solution and measuring the distance of each alternative to these solutions. The final ranking is obtained based on the proportion of distances to the positive and negative ideal solutions. The developed DF TOPSIS method incorporates the accuracy and consistency of expert judgments, enhancing the decision-making process. A sensitivity analysis is also presented in order to show the robustness of the obtained rankings by DF TOPSIS.

In this paper, a geometric model is introduced for Neutrosophic data problem for the first time. This model is based on neutrosophic sets and neutrosophic relations. Neutrosophic control points are defined according to these points, resulting in neutrosophic Bézier curves.

In the dynamic arena of healthcare research, where the complexities of data often rival the intricacies of biological systems, the ability to model and analyze such multifaceted datasets is crucial. This comprehensive review delves into the evolution and application of Soft Sets and their extensions, including HyperSoft Sets, SuperHyperSoft Sets, IndetermSoft Sets, IndetermHyperSoft Sets, and TreeSoft Sets, in healthcare claims data analysis. These extensions address intricate challenges in data analysis, offering versatile frameworks for managing uncertainty and indeterminacy inherent in healthcare claims data. By exploring their definitions and applications, this review elucidates how these mathematical tools have evolved and their significance in advancing healthcare research and enhancing data analysis methodologies. Real-world examples underscore the implications of these tools, emphasizing their pivotal role in facilitating informed decision-making and knowledge discovery in healthcare. The review systematically examines various case studies and research findings to illustrate the practical utility of Soft Set extensions. Detailed analyses of real-world scenarios highlight advancements in processing complex healthcare data. The conclusions drawn from this analysis indicate that the adoption of Soft Sets and their extensions can significantly improve the accuracy and efficiency of healthcare data analysis, ultimately contributing to better healthcare outcomes and more informed policy-making. Future research directions are also discussed, suggesting further potential applications and developments in this field.

This study aims to elucidate a soft computing approach for quantitative assessment of the scoring grade or rubrics for students in an outcome based education system. The intended approach resorts to a fuzzy membership based assessment of the different parameters of the scoring system, thereby yielding a novel and humanly assessment technique. The selection of the membership functions is based on the human behavior so as to make a realistic representation of the scoring strategy. The novelty of the proposed strategy lies in assigning fuzzy membership based weighted scores instead of simply assigning score bands to rubric categories, as is performed in normal rubrics based assessment. Comparative results demonstrated on a case study of Indian education scenario reveal the effectiveness of the proposed strategy over other fuzzy membership and normal rubrics based assessment procedures.

For the symmetrical mixture model and mixture test area, the lattice point set is used to partition, and then the corresponding test statistics can be constructed. In this paper, we first proposes the partition methods under the lattice point sets and obtains several sub-simplexes without common interior points. Furthermore, we present the method for constructing a uniform design on the simplex using the center points of these sub-simplexes. The designs satisfy the uniformity of maximum distance deviation and provide good results for the mean square error deviation. Finally, the uniformity test on the mixture region is considered and illustrated by examples.

Several specific types of generalized sets of a generalized topological space have been defined and investigated for various purposes from time to time in the literature of topological spaces. Our recent research in the field of a new class of generalized sets of a generalized topological space is reported herein as a starting point for more generalized classes.

In this paper, we scrutinize the axiomatic system of effect algebras which is given by D. J. Foulis and M.K. Bennett in the paper Effect Algebras and Unsharp Quantum Logics. We prove that this axiomatic system consists of independent axioms. To do this, we construct some models to indicate the indepence of each axiom. Therefore none of these axioms can be reduced when constructing any effect algebra. As a result, any algebra is an effect algebra if and only if it verifies (E1)-(E4) axioms.

The entropy of the partition generated by an n-tone music scale is proposed to quantify its regularity. The normalized entropy relative to a regular partition, and its complementary, here referred to as the bias, allow to analyze various conditions of similarity between an arbitrary scale and a regular scale. Interesting particular cases are scales having limited bias because their tones are distributed along interval fractions of a regular partition. The most typical case in music concerns partitions associated with well-formed scales generated by a single tone h. These scales are maximal even sets that combine two elementary intervals. Then, the normalized entropy depends on the number of tones as well as the relative size of both elementary intervals. When well-formed scales are refined, several nested families stand out with increasing regularity. It is proven that a scale of minimal bias, i.e. with less bias than those with fewer tones, is always a best rational approximation of log2h.

Attribute reduction is a core technique in the rough set domain and an important step in data preprocessing. Researchers have proposed numerous innovative methods to enhance the capability of attribute reduction, such as the emergence of multi-granularity rough set models, which can effectively process distributed and multi-granularity data. However, these innovative methods still have many shortcomings, such as how to deal with complex constraints and how to perform multi-angle effectiveness evaluations. Based on the multi-granularity model, this study proposes a new method of attribute reduction, namely using multi-granularity neighborhood information gain ratio as the measurement criterion. This method combines both supervised and unsupervised perspectives, and by integrating multi-granularity technology with neighborhood rough set theory, constructs a model that can adapt to multi-level data features. This model can select the optimal granularity level or attribute set according to the requirements. Finally, the proposed method is experimented with on 15 UCI datasets against six other attribute reduction algorithms. The experimental outcomes, upon analysis and comparative review, substantiate the reliability and consistency of the attribute reduction approach introduced in this study.

The purpose of this research article is to provide a comprehensive method that allows the evaluation of the public transportation in their different transport lines that offer in Ciudad Juárez, Chihuahua. This study presents a description of the public transport system as part of the literature review that describes an appropriate model based on the more outstanding publications about urban mobility and public transportation for passengers’ as well as success cases published which serves as a starting point to check the actual state of the public transportation system based on the Pythagorean Fuzzy CODAS to analyze and evaluate the alternatives through criteria that defines the general performance. The integration of these methods provides an adequate methodology for decision-making concerning urban planning and mobility to detect and improve the performance of criteria not considered within sustainable urban mobility plans.

Complete digraphs are referred to in the combinatorics literature as tournaments. We consider a family of semi-simplicial complexes, that we refer to as ``tournaplexes'', whose simplices are tournaments. In particular, given a digraph G, we associate with it a ``flag tournaplex'' which is a tournaplex containing the directed flag complex of G, but also the geometric realisation of cliques that are not directed. We define several types of filtrations on tournaplexes, and exploiting persistent homology, we observe that flag tournaplexes provide finer means of distinguishing graph dynamics than the directed flag complex. We then demonstrate the power of these ideas by applying them to graph data arising from the Blue Brain Project's digital reconstruction of a rat's neocortex.

Type-2 fuzzy sets were introduced by L. Zadeh aiming at modelling some settings in which fuzzy sets (usually called type-1 fuzzy sets) are not sufficient to reflect certain uncertainty degrees - loosely speaking, they are fuzzy sets whose membership degrees are ordinary fuzzy sets. On the other hand, fiber bundles are topological entities of extreme importance in Mathematics itself and many other scientific areas, like Physics (General Relativity, Field Theory etc.), finance modelling, and statistical inference. The present work introduces a conceptual link between the two ideas and conjectures about the potential mutual benefits that can be obtained from this viewpoint.As an objective and usable product of the presented ideas, it is described a framework for defining type-2 fuzzy hedges, proper to operate on interval type-2 fuzzy sets.

Most of the research in data mining concentrated on finding the positive associations that exist in frequent patterns. Frequent patterns have no bearing on the time duration and, therefore, lose interestingness. The Regularity of an itemset is related to the time at which the transaction occurred and the time distance between the transactions. Frequent Regular item sets can be generated considering the Frequency and the Regularity of the occurrence of the Item Sets. The frequent and regular Item sets will be so huge that they cannot be handled in real time. The count of Frequent and regular item sets gets reduced drastically when the properties “closed” and “Maximality” are applied. Finding negative associations among such patterns are important in the field of medicine. Many drugs administered to cure some diseases have counter reactions leading to many other diseases. Negative associations among the mined patterns are important as they reveal significant contradictions frequently among medical drugs administered by medical practitioners to cure some diseases. This paper proposes a method that mines medical databases to find regular, frequent patterns applied with closed and maximal properties and find negative associations among those patterns. The proposed algorithm is accurate to 98% and performs 9% more efficiently than the other algorithms presented in the literature.

The challenging issues of Computer Network and Databases are not only the intrusion detection but also the reduction of false positive and increase of detection rate. In any intrusion detection system, anomaly detection mainly focuses on modeling the normal behavior of the users and detecting the deviations from normal behavior which are assumed to be potential intrusions or treat. Several techniques have already been successfully tried for this purpose. However, the normal and suspicious behavior are hard to predict as there is no precise boundary differentiat-ing one from another. Here rough set theory and fuzzy set theory come into the picture. In this article, a hybrid approach based on rough set theory and intuitionistic fuzzy set theory is pro-posed for the detection of anomaly. The proposed approach is a classification approach which takes the advantages of softness properties both rough and fuzzy set theory to deal with uncer-tainty in the dataset. The algorithm classifies the data instances in such a way that they can be expressed using natural language. The experimental results with a real world dataset and a syn-thetic dataset show that the proposed algorithm has normal true positive rates of 91.989% and 96.99% and attack true positive rates of 91.289% and 96.29% respectively

This paper provides a comprehensive analysis of food security in Sudan by adopting a unique approach of Hesitant Fuzzy Entropy (HFE) analysis to discern the key determinants influencing food security levels and aligning the findings with the Integrated Food Security Phase Classification (IPC) framework. The research utilized a dataset comprising 32 crucial variables related to food security assessment. Employing entropy values, weight coefficients, heatmaps, and scatterplots, the analysis aimed to unravel the intricate distribution of food security levels among Sudanese individuals in our study area. The study reveals that approximately 26% of the Sudanese population in our study region is poised to experience food security, with an additional 24% categorized as marginally food secure. Moreover, an estimated 35% are expected to confront moderate food insecurity, while 15% are projected to face severe food insecurity between January and June 2024. Anticipations for the period from January 2024 to June 2024 project more than 15 million individuals to encounter IPC Phase 3 and fall under moderately or severely food insecure levels. These findings emphasize the urgent need for both short-term humanitarian aid and long-term strategies to address Sudan's deepening food insecurity crisis.

Quantitative and qualitative fuzzy measures have been proposed to hesitant fuzzy sets (HFSs) from different points. However, few of the existing HFSs fuzzy measures refer to the grey relational analysis (GRA) theory. Actually, the GRA theory is very useful in the fuzzy measure domain, which has been developed for such the intuitionistic fuzzy sets. Therefore, in this paper, we apply the GRA theory to the HFSs and interval-valued hesitant fuzzy sets (IVHFS) domain. We propose the HFSs grey relational degree, HFSs slope grey relational degree, HFSs synthetic grey relational degree and IVHFSs grey relational degree, which describe the closeness, the variation tendency and both the closeness and variation tendency of HFSs and closeness of IVHFSs, respectively, greatly enriching the fuzzy measures of HFSs. Furthermore, with the help of the TOPSIS method, we develop the grey relational based MADM methodology to solve the HFSs and IVHFSs MADM problems. Finally, combined with two practical MADM examples about energy policy selection with HFSs information and emergency management evaluation with IVHFSs information, we obtain the most desirable decision results, and compared with the previous methods, the validity, effectiveness and accuracy of the proposed grey relational degree for HFSs and IVHFSs are demonstrated in detail.

The article presents a methodology for modeling the impact of factors of both on-farm activity and environmental factors on the resulting indicators of an international company. The dataset includes the company's profit, revenue, valuation, share price, and market share from 2012 through 2022. This empirical period is optimal for such a type of modeling. Modeling the impact of carbon emissions factors on the resulting indicators is considered based on complex systems theory. Endogenous model variables include indicators of the development of the international company. Predefined model variables reflect the influence of both the external environment and internal factors on the development indicators of an international company. An approach of picture fuzzy rough sets based on time series of endogenous and exogenous variables can provide an opportunity to analyze and consider the consequences of feedback changes in the systems of which they are a part. Based on the results of the analysis of the model construction, it is concluded that picture fuzzy rough sets can be an excellent way to model interdependent social processes.

Ability of quantitative structure – property / activity relationships (QSPRs/QSARs) to serve for epistemological processes in natural sciences is discussed. Some weirdness of QSPR/QSAR state-of-art are listed. There are some contradictions in the research results in this area. Sometimes, these should be classified as paradoxes or weirdness. These points often are ignored. Here these are listed and briefly commented. In addition, hypothesises on the future evolution of the QSPR/QSAR theory and practice are suggested.

Lung nodule segmentation in CT images and its subsequent volume analysis can help determinethe malignancy status of a lung nodule. While several efficient segmentation schemes have beenproposed, only a few studies evaluated the segmentation’s performance for large nodules. In thisresearch, we contribute a semi-automatic system which is capable of performing robust 3-D segmen-tations on both small and large nodules with good accuracy. The target CT volume is de-noisedwith an anisotropic diffusion filter and a region of interest is selected around the target nodule ona reference slice. The proposed model performs nodule segmentation by incorporating a mean in-tensity based threshold in Geodesic Active Contour model in level sets. We also devise an adaptivetechnique using image intensity histogram to estimate the desired mean intensity of the nodule.The proposed system is validated on both lung nodules and phantoms collected from publicly avail-able diverse databases. Quantitative and visual comparative analysis of the proposed work withthe Chan-Vese algorithm and statistic active contour model of 3D Slicer platform is also presented.The resulting mean spatial overlap between segmented nodules and reference nodules is 0.855, themean volume bias is 0.10±0.2 ml and the algorithm repeatability is 0.060 ml. The achieved resultssuggest that the proposed method can be used for volume estimations of small as well as large-sizednodules.

In this paper, we propose a new covering-based set in which the lower and the upper approximation operations are defined by neighborhood systems. We discuss this new type of covering-based set systematically in two steps. First, we study the basic properties of this covering-based set, such as the properties of normality, contraction, and monotone. Second, we discuss the relationship between the new type of covering-based set and the other ten sets proposed.

In this paper, we propose a new covering-based set in which the lower and the upper approximation operation are defined by neighborhood systems. We discuss this new type of covering-based set systematically in two steps. First, we study the basic properties of this covering-based set, such as the properties of normality, contraction, and monotone. Second, we discuss the relationship between the new type of covering-based set and the other ten sets proposed.

This study focuses on a new class of functions called sub-b-s-preinvex, that is a generalization of sub-b-s-convex and preinvex functions, and discusses some of their properties. A new sub-b-s-preinvex programming is introduced and the sufficient conditions of optimality under this type of function is established.

We present a new method for assessing the strength of fuzzy rules with respect to a dataset, based on the measures of the greatest energy and smallest entropy of a fuzzy relation. Considering a fuzzy automaton (relation) in which A is the input fuzzy set and B the output fuzzy set, the fuzzy relation R1 with greatest energy provides information about the greatest strength of the input-output and the fuzzy relation R2 with the smallest entropy provides information about uncertainty of the relationship input-output. We consider a new index of the fuzziness of the input-output based over R1 and R2. In our method this index is calculated for each pair of input and output fuzzy sets in a fuzzy rule. A threshold value is set for choosing the most relevant fuzzy rules with respect to the data.

This paper introduces an innovative framework for the integration of artificial empathy into robot swarms to enhance communication and cooperation. The proposed model relies on fuzzy state vectors to represent the knowledge and environment of individual agents, accommodating uncertainties in the real world. Utilizing similarity measures, the model compares states, enabling empathetic reasoning for synchronized swarm behavior. A practical application example demonstrates the model’s efficacy in a robot swarm striving for a common goal. The evaluation methodology involves the Open Source Physical-based Experimentation Platform (OPEP), emphasizing empirical validation in real-world scenarios. The paper proposes a transitional environment that allows automated and repeatable execution of experiments on a swarm of robots using physical devices.

Several life contingency agreements are based on the assumption that policyholders have impaired life expectancy attributable to factors such as lifestyle, social class, or preexisting health issues. Quantifying two crucial variables, augmented death probabilities and the discount rate of projected cash flows, is essential for pricing such agreements. Information regarding the correct values of these parameters is subject to vagueness and imprecision, which further intensifies if impairments must be considered. This study proposes modelling mortality and interest rates using a generalization of fuzzy numbers (FNs), known as intuitionistic fuzzy numbers (IFNs). Consequently, this paper extends the literature on life contingency pricing with fuzzy parameters, where uncertainty in variables, such as interest rates and death probabilities, is modelled using FNs. While FNs introduce epistemic uncertainty, the use of IFNs adds bipolarity to the analysis by incorporating both positive and negative information regarding actuarial variables. Our analysis focuses on two agreements involving policyholders with impaired life expectancy: determining the annuity payment in a substandard annuity and pricing a life settlement over a whole life insurance policy. In particular, we emphasize modelling interest rates and survival probabilities using triangular intuitionistic fuzzy numbers (TIFNs) owing to their ease of interpretation and implementation.

In this paper we introduce the concept of Nano Beta Closure, Nano Beta Interior and study the relationship between them also study some of their properties. Based on these notions we introduced the topological Approach to Decision Making and Its Application in the Medical Field" which describes the use of topological methods in decision-making, specifically through the utilization of nano beta closure and nano beta interior. These mathematical tools are applied in the medical field to improve diagnostic accuracy and aid in treatment planning. The authors demonstrate the effectiveness of this approach through a case study on the diagnosis of Chronic Kidney. The results show that the topological approach using nano beta closure and nano beta interior provides a reliable and accurate method for medical decision-making. Finally, we introduce a medical application for disease groups patients of with chronic kidney. To identify the main causative agent of kidney disease. where using this approach, the medical team can identify the specific areas of the kidney that are affected by the infection, as well as the extent of damage and any potential complications. This information is used to create an individualized treatment strategy that is customized to meet the specific requirements of the patient. and medical history. We write an algorithm that can be a helpful tool for doctors to utilize in diagnosing infection disease Chronic Kidney infections. By utilizing this approach, clinicians can provide accurate diagnoses, develop effective treatment plans, and ultimately improve patient outcomes. finally, we show that fractals hold significant importance in future nano topological generation of the human factor. Their unique properties and self-similar patterns offer insights into the complex organization of biological systems and provide a foundation for designing advanced Nanosystems.

Βottom-up management in catchment scale is deemed as the determinant way to avoid the conflict of the water users through the participation of stakeholders, strategy co-shaping and solutions co-creation. Water management cannot be one-dimensional but demands cross sectoral coop-eration. Usually, the difficulty lies in proper stakeholder training and their opinion inclusion, using a quantifiable manner in water management. The Laspias River watershed occupies an area of 221.8 km2, belonging to the River Basin District of Thrace and it is characterized by intense agricultural and industrial activity. Complying with the augmented water needs and pollution loads by respecting stakeholders’ opinion, this research aims to utilize a hybrid intuitionistic fuzzy multi-criteria-based methodology. It is a common difficulty to deal with supplier selection in resources management since it is a typically decision-making problem encompassing multiple (several conflicting) criteria, on which stakeholder’s opinions are usually imprecise and in a rather qualitative form. Therefore, the proposed method provides the mathematical tool to move into more comprehensive decisions with the public involvement. The weights are produced based on the stakeholder’s opinion. The alternatives’ ranking is achieved based on the fuzzified intuition-istic version of Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS) and problems’ mitigation solutions’ hierarchy is achieved.

The evolutionary origin of the genome remains elusive. Here, I hypothesize that its first iteration, the protogenome, was a multi-ribozyme RNA. It evolved, likely within liposomes (the protocells) forming in dry-wet cycling environments, through the random fusion of ribozymes by a ligase and was amplified by a polymerase. The protogenome thereby linked, in one molecule, the information required to seed the protometabolism (a combination of RNA-based autocatalytic sets) in newly forming protocells. If this combination of autocatalytic sets was evolutionarily advantageous, the protogenome would have amplified in a population of multiplying protocells. It likely was a quasispecies with redundant information, e.g., multiple copies of one ribozyme. As such, new functionalities could evolve, including a genetic code. Once one or more components of the protometabolism were templated by the protogenome (e.g., when a ribozyme was replaced by a protein enzyme), and/or addiction modules evolved, the protometabolism became dependent on the protogenome. Along with increasing fidelity of the RNA polymerase, the protogenome could grow, e.g., by incorporating additional ribozyme domains. Finally, the protogenome could have evolved into a DNA genome with increased stability and storage capacity. I will provide suggestions for experiments to test some aspects of this hypothesis.

In this paper we address one of the most important topics in the field of Social Networks Analysis: the community detection problem with additional information. That additional information is modeled by a fuzzy measure that represents the possibility of polarization. Particularly, we are interested in dealing with the problem of taking into account the Polarization of nodes in the community detection problem. Adding this type of information to the community detection problem makes it more realistic, as a community is more probably to be defined if the corresponding elements are willing to maintain a peaceful dialogue. The polarization capacity is modeled by a fuzzy measure based on the JDJpol measure of polarization related to two poles. We also present an efficient algorithm for finding groups whose elements are no polarized. Hereafter, we work in a real case. It is a network obtained from Twitter, concerning the political position against the Spanish government taken by several influential users. We analyze how the partitions obtained change when some additional information related to how polarized that society is, is added to the problem.

Several specific types of ordinary and generalized separation axioms of a generalized topological space have been defined and investigated for various purposes from time to time in the literature of topological spaces. Our recent research in the field of a new class of generalized separation axioms of a generalized topological space is reported herein as a starting point for more generalized classes.

Assembly theory provides a promising framework to explain the complexity of systems such as molecular structures and the origins of life, with broad applicability across various disciplines. In this study, we explore and consolidate different aspects of assembly theory by introducing a simplified toy model to simulate the autocatalytic formation of complex structures. This model abstracts the molecular formation process, focusing on the probabilistic control of catalysis rather than the intricate interactions found in organic chemistry. We establish a connection between probabilistic catalysis events and key principles of assembly theory, particularly the probability of a possible construction path in the formation of a complex object, and examine how the assembly of complex objects is impacted by the presence of autocatalysis. Our findings suggest that autocatalysis tends to favor longer consecutive construction sequences in environments with low catalysis probability, while this bias diminishes in environments with higher catalysis probabilities, highlighting the significant influence of environmental factors on the assembly of complex structures.

Along with the economic growth, the companies must contribute to social progress and promote environmental sustainability in equal harmony. Sustainable human resource management (SHRM) strategies make it possible to attain the economic, social and environmental goals of a firm. In this regard, a survey method is discussed using the literature review and online questionnaire to identify the main factors/indicators during the SHRM evaluation of manufacturing firms in India. Uncertainty is commonly occurred in the assessment of SHRM factors. As a generalized version of fuzzy sets, single-valued neutrosophic set (SVNS) has been demonstrated as a valuable tool to illustrate the indeterminate, inconsistent and uncertain data of realistic decision-making problems. Considering the idea of SVNSs, this study develops a hybrid multi-criteria group decision-making (MCGDM) approach for assessing the SHRM of manufacturing firms under uncertainty settings. For this purpose, an SVN-alternative ranking order method accounting for two-step normalization (AROMAN) is proposed based on VIFI-score function-based decision experts’ (DEs’) weighting tool and integrated criteria weight-determining model to solve the MCGDM problems with fully unknown DEs and criteria weights. In this regard, we develop new SVN-distance measure to compute the degree of difference between SVNSs. Some examples are presented to demonstrate the efficacy of developed measure over the existing ones. In addition, new criteria weight-determination model is presented with the integration of objective weights through IVIF-distance measure-based model and subjective weights through ranking comparison (RANCOM) tool on SVNSs. The proposed ranking method is applied to an empirical study of SHRM assessment for manufacturing firms in India, which shows its applicability and feasibility. In this study, the evaluation criteria are characterized into social, environmental and economic aspects with DE’s opinions. Comparative and sensitivity analyses are made to show the strength and steadiness of presented approach. This study provides an innovative MCGDM analysis framework, which makes a significant contribution to the SHRM assessment problem under indeterminate, inconsistent and uncertain setting.

This work aims to generate some types of M_(j )–neighborhoods. Relationships among these M_(j )-neighborhoods and some other types of neighborhoods are discussed. Additionally, M_(j )-lower, M_(j )-upper approximations and M_(j )-accuracy in terms of M_(j )-neighborhoods are presented. Their properties, with some examples, are investigated. Finally, We addressed the comparisons among M_(j )approach and other approaches.

Work done by us shows that rough topology is a good tool for dealing with things that happen in the real world. The concept of ”basis” has been used to show out the deciding elements of the recent outbreak of COVID-19 that was reported all over the world.

This paper analyzes the potential strategies for a bank merger from a Sustainable Development Goals (SDG) perspective, focusing on three key criteria: profitability, market share, and service quality. In the short-term, the merged bank should prioritize optimizing financial performance through cost management, revenue stream identification, and risk management practices. Market share expansion can be achieved through targeted customer acquisition and retention efforts, market research, and competitive analysis. Service quality can be enhanced through improved customer service, efficient complaint resolution processes, and leveraging technology. These short-term plans align the merged bank's operations with the identified criteria and promote responsible banking practices that contribute towards the SDGs. In the long-term, the merged bank should focus on diversifying revenue streams, expanding its customer base, and optimizing cost structure. Long-term strategies should include establishing a strong brand presence, customer loyalty programs, and continuous improvement in service quality. The paper emphasizes the importance of monitoring progress, making necessary adjustments, and aligning with SDGs for sustained profitability and long-term success in the marketplace. The findings of this study provide valuable insights for banks considering a merger and highlight the significance of considering SDGs in their strategic planning.

Increasingly, systems biology is gaining relevance in basic and applied research. The combination of computational biology with wet lab produces a synergy that results in an exponential increase in knowledge of biological systems. The study of microorganisms such as Staphylococcus epidermidis RP62A enables the researcher to understand better its metabolic network, which allows the design of effective strategies to treat infections caused by this species or others. S. epidermidis is the second cause of infection in patients with joint implants, so treating its proliferation seems vital for public health. There are different approaches to the analysis of metabolic networks. Flux Balance Analysis (FBA) is one of the most widespread streams. It allows the study of large metabolic networks, their structural properties, the optimization of metabolic flux, and the search for intervention strategies to modify the state of the metabolic network. This work presents the validation of the Staphylococcus epidermidis RP62A metabolic network model elaborated by Díaz-Calvo et al.. Then, we elaborate further on the network analysis’s essential reactions, classifying them. Finally, we introduce some proposals to intervene in the network and design knock-outs.

We consider partition functions, in the form of state sums, and associated probabilistic measures for aperiodic substrates described by model sets and their associated tiling spaces. We propose model set tiling spaces as microscopic models for small scales in the context of quantum gravity. Model sets possess special self-similarity properties that allow us to consider implications on large and observable scales from the underlying (non-ergodic) dynamics. In particular we consider the implication of the underlying aperiodic substrate for the well known problem of time in quantum gravity, and propose a correspondence between small and large scales, the so-called ergodic correspondence, that addresses the emergence of matter properties and spacetime structure. In the process we find a possible bound in the mass spectrum of fundamental particles.

In a generalized topological space Tg = (Ω, Tg), ordinary interior and ordinary closure operators intg, clg : P (Ω) −→ P (Ω), respectively, are defined in terms of ordinary sets. In order to let these operators be as general and unified a manner as possible, and so to prove as many generalized forms of some of the most important theorems in generalized topological spaces as possible, thereby attaining desirable and interesting results, the present au- thors have defined the notions of generalized interior and generalized closure operators g-Intg, g-Clg : P (Ω) −→ P (Ω), respectively, in terms of a new class of generalized sets which they studied earlier and studied their essen- tial properties and commutativity. The outstanding result to which the study has led to is: g-Intg : P (Ω) −→ P (Ω) is finer (or, larger, stronger) than intg : P (Ω) −→ P (Ω) and g-Clg : P (Ω) −→ P (Ω) is coarser (or, smal ler, weaker) than clg : P (Ω) −→ P (Ω). The elements supporting this fact are reported therein as a source of inspiration for more generalized operations.

This paper formulates the performance evaluation of cloud services as a multicriteria group decision making problem, and presents a fuzzy multicriteria group decision making method for evaluating the performance of cloud services. Interval-valued intuitionistic fuzzy numbers are used to model the inherent subjectiveness and imprecision of the performance evaluation process. An effective algorithm is developed based on the technique for order preference by similarity to ideal solution method and the Choquet integral operator for adequately solving the performance evaluation problem. An example is presented to demonstrate the applicability of the proposed fuzzy multicriteria group decision making method for solving the multicriteria group decision making problem in real world situations.

A review on planar printed structures that are based on Matryoshka-like geometries is presented. These structures use the well-known principle of Matryoshka dolls that are successively nested inside each other. The well-known advantages of the planar printed technology and of the meandered nested Matryoshka geometries are combined to generate miniaturized, multi-resonance and/or wideband configurations. Both metal and complementary slot structures are considered. Closed and open configurations are analyzed. The working principles are explored do get physical insight of their behavior. Low cost and single layer applications as frequency selective surfaces, filters, antennas, and sensors, in the microwave frequency region, are reviewed. Potential future research perspectives and new applications are discussed.

Supply Chain Management (SCM) encompasses a wide variety of decision-making problems that affect business and supply chain performance as a whole. Since most of these problems involve uncertainty and hesitation on the part of Decision Makers (DMs), various studies have emerged recently that present SCM applications of techniques based on Hesitant Fuzzy Linguistic Term Sets (HFLTSs) and HFLTS extensions. Given the relevance of this subject and the lack of literature review studies, this study presents a systematic review of HFLTS and HFLTS extension applications to SCM decision-making problems. In order to answer a set of research questions, the selected papers have been classified in accordance with a group of factors that are pertinent to the origins of these studies, SCM, HFLTSs, and decision-making. The results demonstrate that the Source and Enable processes have been studied with greater frequency, while the most common problems have to do with supplier selection, failure evaluation, and performance evaluation. The companies of the automotive sector and Sustainable SCM and Green SCM strategies predominate in the analyzed studies. Even though most of the studies use techniques based on HFLTSs, we have identified applications of seven distinct HFLTS extensions, with Double Hierarchy Hesitant Fuzzy Linguistic Term Sets and Probabilistic Linguistic Term Sets being the most utilized. The identification of gaps in the literature presents avenues for future studies focused on innovative applications, integrations of techniques, comparisons of techniques, group decision-making, and validation procedures for new models. The results of this study offer a panorama of the state of the art in regard to this subject and can help researchers and practitioners develop new studies which involve the use of methods that employ HFLTSs and HFLTS extensions in SCM decision-making problems.

Unification based upon the generalisation of proper time is proposed as a comprehensive framework to account for the fundamental structure of matter, in a manner contrasting with the more familiar approach based on extra dimensions of space. The elementary properties of matter to be incorporated include the Standard Model of particle physics together with a source for the dark sector and a coherent formalism for quantum gravity. We elaborate upon the manner in which all such material phenomena and empirical properties as distributed in an extended 4-dimensional spacetime can be encompassed within, and derived from, the continuous flow of time alone via a generalised arithmetic form for infinitesimal intervals of proper time. This approach will also be compared and contrasted with the basic structure of causal set theory as a means of demonstrating how it is possible to construct a full physical theory essentially from elements of time alone, as explicitly developed from the most elementary level. The conception of time as utilised and elucidated in this theory, with emphasis upon the causal continuum properties and as the basis for unification, will be clarified.

This work is mainly focused on improving the differential evolution algorithm with the utilization of shadowed and general type 2 fuzzy systems to dynamically adapt one of the parameters of the evolutionary method. In this case, the mutation parameter is dynamically moved during the evolution process by using a shadowed and general type-2 fuzzy systems. The main idea of this work is to make a performance comparison between using shadowed and general type 2 fuzzy systems as controllers of the mutation parameter in differential evolution. The performance is compared with the problem of optimizing fuzzy controllers for a D.C. Motor. Simulation results show that general type-2 fuzzy systems are better when higher levels of noise are considered in the controller.

In a generalized topological space T_g = (Ω, T_g) (T_g-space), the g-topology T_g : P (Ω) −→ P (Ω) can be characterized in the generalized sense by specifying the generalized open, generalized closed sets (g-T_g-open, g-T_g-closed sets), generalized interior, generalized closure operators g-Intg, g-Cl_g : P (Ω) −→ P (Ω) (g-T_g-interior, g-T_g-closure operators), or generalized derived, generalized coderived operators g-Der_g, g-Cod_g : P (Ω) −→ P (Ω) (g-T_g-derived, g-T_g-coderived operators), respectively. For very many T_g-spaces, the δ^th-iterates g-Der_g^(δ), g-Cod_g^(δ) : P (Ω) −→ P (Ω) of g-Der_g, g-Cod_g : P (Ω) −→ P (Ω), respectively, defined by transfinite recursion on the class of successor ordinals are also themselves g-T_g-derived, g-T_g-coderived operators for new g-topologies in the generalized sense on Ω. Thus, the use of novel definitions of g-T_g-derived, g-T_g-coderived operators g-Der_g, g-Cod_g : P (Ω) −→ P (Ω), respectively, based on a very clever construction, together with their δ^th-iterates g-T_g-operators g-Der_g^(δ), g-Cod_g^(δ) : P (Ω) −→ P (Ω), defined by transfinite recursion on the class of successor ordinals, will give rise to novel generalized g-topologies on Ω. The present authors have been actively engaged in the study of g-T_g-operators in T_g-spaces. The study of the essential properties and the commutativity of novel definitions of g-T_g-interior and g-T_g-closure operators g-Int_g, g-Cl_g : P (Ω) −→ P (Ω), respectively, in T_g has formed the first part, and the study of the essential properties and sets of consistent, independent axioms of novel definitions of g-T_g-exterior and g-T_g-frontier operators g-Ext_g, g-Fr_g : P (Ω) −→ P (Ω), respectively, has formed the second part. In this work, which forms the last part on the theory of g-T_g-operators in T_g-spaces, the present authors propose to present novel definitions and the study of the essential properties of g-T_g-derived and g-T_g-coderived operators g-Der_g, g-Cod_g : P (Ω) −→ P (Ω), respectively, and their δ^th-iterates, and the notions of g-T_g-open and g-T_g-closed sets of ranks δ in T_g-spaces.

The eyes are the sense organs through we view the world around us, and the cornea is the transparent layer which covers the outer, visible part of the eye. It is known that the gene expression of corneal endothelium depends on age. And the expressed genes of the endothelium of cornea for pediatric samples is different than that of the adult samples. The purpose or objective of this study was to characterize human corneal endothelial cell (HCEnC) gene expression and differential gene expression and to detect the expressed genes mapped to chromosomal loci associated with some corneal endothelial dystrophies. Both upregulated and downregulated genes were analyzed. For this purpose, total RNA was isolated from ex vivo corneal endothelium taken from six pediatric and five adult corneas. The complementary DNA was hybridized to the Affymetrix GeneChip 1.1 ST array. The data analysis was performed using the Enrichr software for both upregulated and downregulated genes. These are described in more detail in the results and discussion section. This study uses bioinformatics tools to identify and analyse gene sets present in the transcriptome of the corneal endothelium, and tries to find out and observe the relation of the aging effect on the corneal endothelium gene expression. The human subjects had participated voluntarily and informed consent was obtained from all before carrying out any testing procedure. Proper guidelines from the hospital ethical committee were also followed and no harmful chemicals were used on the participants. This study simply aims to raise some awareness of the given topic among the local people so that they are better able to take informed choices about their health in the near future, and also so that they seek medical help when necessary and have no inhibitions in doing so.

More than fifty million people over the age of fifty have osteoporosis issues due to low bone mass, disease contribution, and not exercising continuously. Certain most important risk factors and causes of osteoporosis contain age, gender, hormones, visits to inexperienced doctors, and certain medical conditions. In this manuscript, we diagnosed certain frank operational laws under the availability of complex intuitionistic fuzzy (CIF) information. Furthermore, using the evaluated operational laws, we pioneered the theory of CIF frank weighted averaging (CIFFWA), CIF frank ordered weighted averaging (CIFFOWA), CIF frank hybrid averaging (CIFFHA), CIF frank weighted geometric (CIFFWG), CIF frank ordered weighted geometric (CIFFOWG), CIF frank hybrid geometric (CIFFHG) operators, and described their beneficial and valuable results with certain useful properties. Moreover, we aim to evaluate the most dangerous type of osteoporosis based on their symptoms, causes, and risk factors using diagnosed approaches. Finally, to enhance the worth of the evaluated operators, we compare the diagnosed result with certain prevailing results and illustrated their geometrical representation with the help of MATLAB.

We define the notions of strong and strict recurrency for actions of countable ordered groups on $\sigma$-finite non atomic measure spaces with quasi-invariant measures. We show that strong recurrency is equivalent to non existence of weakly wandering sets of positive measure. We also show that for certain p.m.p ergodic actions the system is not strictly recurrent, which shows that strong and strict recurrency are not equivalent.

In a generalized topological space Tg = (Ω, Tg), generalized interior and generalized closure operators g-Intg, g-Clg : P (Ω) −→ P (Ω), respectively, are merely two of a number of generalized primitive operators which may be employed to topologize the underlying set Ω in the generalized sense. Generalized exterior and generalized frontier operators g-Extg, g-Frg : P (Ω) −→ P (Ω), respectively, are other generalized primitive operators by means of which characterizations of generalized operations under g-Intg, g-Clg : P (Ω) −→ P (Ω) can be given without even realizing generalized interior and generalized closure operations first in order to topologize Ω in the generalized sense. In a recent work, the present authors have defined novel types of generalized interior and generalized closure operators g-Intg, g-Clg : P (Ω) −→ P (Ω), respectively, in Tg and studied their essential properties and commutativity. In this work, they propose to present novel definitions of generalized exterior and generalized frontier operators g-Extg, g-Frg : P (Ω) −→ P (Ω), respectively, a set of consistent, independent axioms after studying their essential properties, and established further characterizations of generalized operations under g-Intg, g-Clg : P (Ω) −→ P (Ω) in Tg.

In the present work we study the properties of geodesic sub-$ (\alpha,b,s) $-preinvex functions on Hadamard manifolds and establish some basic properties in both general and differential cases. Further, we study sufficient conditions of optimality and proved some new inequalities under geodesic sub-($ \alpha,b,s $)-preinvexity.

Supplier selection is one of the most important multi criteria decision making (MCDM) problems for decision makers in competitive market. Organizations of today’s world are seeking new ways to reduce negative effects of their organizations to the environment and to reach a greener system. At this point, green supplier selection concept has gained great importance with its ability on incorporating environmental or green criteria into the classical supplier selection practices. Therefore, in this study, it is aimed at proposing a multi-phase MCDM model based on Best-Worst Method (BWM) and interval type-2 fuzzy technique for order preference by similarity to ideal solution (TOPSIS). A case study in a plastic injection molding facility in Turkey is performed to show the applicability of the proposed integrated methodology. The paper ensures insights into the decision making, methodology, and managerial implications. Results of the case study are examined and suggestions for future research are provided.

The paper presents an adaptation of numerical solution of first order linear differential equation in fuzzy environment. The numerical method is re-established and studied with fuzzy concept to estimate its uncertain parameters whose values are not precisely known. Demonstrations of fuzzy solutions of the governing methods are carried out by the approaches, namely Modified Runge Kutta method and Runge Kutta Merson method. The results are compared with the exact solution which is found using generalized Hukuhara derivative (gH-derivative) concepts. Additionally, different illustrative examples and an application in industry of the methods are also undertaken with the useful table and graph to show the usefulness for attained to the proposed approaches.

Suppose n ∈ N. We wish to meaningfully average ‘sophisticated’ unbounded sets (i.e., sets with positive n-d Hausdorff measure, in any n-d box of the n-d plane, where the measures don’t equal the area of the boxes). We do this by taking the most generalized, satisfying extension of the expected value, w.r.t the Hausdorff measure in its dimension, on bounded sets which takes finite values only. As of now, I’m unable to solve this due to limited knowledge of advanced math and most people are too busy to help. Therefore, I’m wondering if anyone knows a research paper which solves my doubts.

Fermatean fuzzy sets (FFSs) are a versatile tool for handling uncertain problems and have shown great effectiveness in practical applications. However, many existing Fermatean fuzzy similarity measures exhibit counter-intuitive situations, making it challenging to accurately measure the similarity or difference between FFSs. To address this issue, several similarity and distance measures for FFSs are proposed, inspired by the Tanimoto similarity measure. The properties of the proposed measures are also explored, along with several comparative examples with existing measures for FFSs, which illustrate their superior performance in processing fuzzy information from FFSs. The proposed measures have effectively overcome the counter-intuitive challenges posed by many existing measures and significantly outperforms existing measures in differentiating different FFSs. Furthermore, we demonstrate the practical applicability of the proposed measures in solving pattern recognition, medical diagnosis and multiple-attribute decision-making problems.

This article introduces ten similarity measures that utilize cosine and cotangent functions to compare (m,n)-rung orthopair fuzzy sets, this a super class of q-rung orthopair fuzzy sets. Further, we applied our established weighted similarity measures to medical diagnosis, pattern recognition,and building material problems and also presented the comparison between established measures with the existing cosine and cotangent measures of q-rung orthopair, pythagorean and intuitionistic fuzzy sets. Lastly, we considered a numerical example that demonstrates the effective and scientific application of these similarity measures in plant leaf disease classification. Furthermore, we present graphical interpretations to demonstrate the effectiveness of our established measures.

In the present paper, based on the ideas of Algerian physicist M.E. Hassani, the generalized Hassani spatio-temporal transformations in real Hilbert space are introduced. The original transformations, introduced by M.E. Hassani, are the particular cases of the transformations, introduced in this paper. It is proven that the classes of generalized Hassani transforms do not form a group of operators in the general case. Further, using these generalized Hassani transformations as well as the theory of changeable sets and universal kinematics, the mathematically strict models of Hassani kinematics are constructed and the performance of the relativity principle in these models is discussed.

A new model for risk assessment of urban rainstorm disasters, based on information diffusion method and variable fuzzy sets (IDM-VFS) was proposed. In addition, an integrated index system of urban rainstorm risk was established. In the proposed model, IDM was employed to calculate the classification standards of urban rainstorm risk levels, then the VFS was adopted to assess the dangerousness, sensitivity, vulnerability and comprehensive risk of urban rainstorm disasters. In the present study, the urban rainstorm risk of Jiangsu province was evaluated with the proposed model. The results show that Wuxi, Changzhou, Nanjing and Suzhou have higher dangerousness, due to sustained rainfall and strong rainfall intensity in short duration; Wuxi, Changzhou and Nanjing have higher sensitivity because of lower disaster resistance ability; and Wuxi and Suzhou have higher vulnerability because these cities have higher potential losses in face of urban rainstorm disasters. The comprehensive risk zoning map of urban rainstorm shows apparent regional characteristics: the northwestern cities have lower risk than the southern cities. Moreover, most cities of the Jiangsu province are of the moderate urban rainstorm risk level. The results are consistent with the actual situation of Jiangsu province, and the study can provide some decision-making references for the urban rainstorm management.

Currently, Pythagorean fuzzy sets (PFSs) have been widely applied in various fields due to their substantial advantages in expressing and dealing with uncertainty. However, measuring the similarity and difference between PFSs effectively remains an unresolved issue. Inspired by Tanimoto similarity, we propose a novel set of similarity and distance measures for PFSs. We delve into the theoretical properties of the proposed measures and compare it with existing PFSs measures. Numerous numerical examples validate their rationality and effectiveness. Furthermore, our experimental findings suggest that in contrast to existing measures, the introduced measures successfully circumvent various counter-intuitive issues encountered by current measures, and yield more pronounced outcomes in the discrimination of different fuzzy sets. This enhances the uniqueness and superiority of our measures. Finally, we developed two decision models based on the proposed measures and validated their applicability in three applications.

Suppose for n∈ ℕ, set A⊆ℝⁿ and function f∶A→ℝⁿ. If set A, using the Hausdorff outer measure, is measurable in the sense of Carathèodory; we want to find an extension of the expected value, w.r.t the Hausdorff measure, that's unique, finite and "natural" (defined on §2.3 & §2.4) for all f in a prevalent subset of ℝᴬ. The issue is current extensions of the expected value are finite for all functions in only a shy subset of ℝᴬ. The reason this issue wasn't resolved is mathematicians have not thought of the problem, focusing on application rather than generalization. Despite the lack of potential use, we'll attempt to solve the problem by defining a choice function---this shall choose a unique set of equivalent sequences of sets (Fₖ***) , where the set-theoretic limit of Fₖ*** is the graph of f; the measure Hʰ is the ℎ-Hausdorff measure, such for each k∈ℕ, 0 < Hʰ(Fₖ***) < +∞; and (fₖ*) is a sequence of functions where {(x,fₖ*(x))∶x∈ dom(Fₖ***)}=Fₖ***. Thus, the extended expected value of or E**[f,Fₖ***] is: ∀(ε>0)∃(N∈ℕ)∀(k∈N)(k≥N⇒1/Hʰ(dom(Fₖ***))∫dom(Fₖ*** )fₖ* dHʰ - E**[f,Fₖ***]<ε ) which should be unique, finite, and "natural" (defined on §2.3 & §2.4) for all f in a prevalent subset of ℝᴬ. Note we guessed the choice function using computer programming but we don’t use mathematical proofs due to the lack of expertise in the subject matter. Despite this, the biggest use of this research is the extension of the expected value is finite for "almost all" functions: this is easier to use in application when finding the "average" of functions covering an infinite expanse of space.

Product Design is getting nowadays new challenges on developing new products, since the industry is in a rush to introduce products into the marketplace, where customers demand products faster, cheaper, and free of failures. In the meantime, global companies are always trying to improve their Product Design process to get advantages over their competitors using proven tools like FEMA and mixing methodologies like Fuzzy theories with FMEA. Even today using all this tools and combination of methodologies there is a gap to address and it is required a robust risk analysis solving current issues in the electronic industry. This document aims to reveal a novel integrated method, where Failure Mode and Effect Analysis, Pythagorean Fuzzy Sets and Dimensional Analysis are cohesive into a model that minimize the uncertainty of the ranking and prioritization over the Failure Mode and Effect Analysis execution, helping to identify risks within an accurate grade over possible failures in the Product Design process. A real practical example is used to show the proposed method, where it is identified a robust methodology integration and solid and results using a sensitivity analysis.

A multi-server parallel system dispatches the incoming job, which contains kn tasks into n servers. A job is considered to be computed if all the tasks associated with the job are processed. One job’s tasks can be encoded into at least kn “replicas” such that the job is considered to be served if any kn replicas finishing computation. In this paper, we analyze the random scheduling policy of a multi-server computing system under discrete time model in terms of Quality of Exponent (QoE), which is defined as the probability exponent that a typical job can be computed within a given number of time slots. We let kn/n be a constant. Assuming that any task of any job can be randomly dispatched by a “scheduler” to any server, and computing each task takes exactly one time slot. We divide the calculation of probability exponent into two parts, exponent of numerator and exponent of denominator. For the denominator, we give the almost exact exponent using Lagrange multiplier method, while for the numerator, an upper bound of the numerator’s exponent is provided. In addition, we also express the exponent in terms of information theoretical quantities and reconsider both of exponents in the context of large deviation theory.

Several specific types of generalized maps of a generalized topological space have been defined and investigated for various purposes from time to time in the literature of topological spaces. Our recent research in the field of a new class of generalized maps of a generalized topological space is reported herein as a starting point for more generalized classes.

We assume that the current mathematical knowledge K is a finite set of statements from both formal and constructive mathematics, which is time-dependent and publicly available. Any theorem of any mathematician from past or present belongs to K. The set K exists only theoretically. Ignoring K and its subsets, sets exist formally in ZFC theory although their properties can be time-dependent (when they depend on K) or informal. In every branch of mathematics, the set of all knowable truths is the set of all theorems. This set exists independently of K. Algorithms always terminate. We explain the distinction between algorithms whose existence is provable in ZFC and constructively defined algorithms which are currently known. By using this distinction, we obtain non-trivial statements on decidable sets X⊆N that belong to constructive and informal mathematics and refer to the current mathematical knowledge on X. This and the next sentence justify the article title. For any empirical science, we can identify the current knowledge with that science because truths from the empirical sciences are not necessary truths but working models of truth from a particular context. The feature of mathematics from the article title is not quite new. Church's thesis, which is known from the beginning of computability theory, is based on the observation that the currently known computable functions are recursive, where the notion of a computable function is informal. It proves that the predicate of the current mathematical knowledge slightly increases the intuitive mathematics. For a set X⊆N whose infiniteness is false or unproven, we define which elements of X are classified as known. No known set X⊆N satisfies Conditions (1)-(4) and is widely known in number theory or naturally defined, where this term has only informal meaning. (1) A known algorithm with no input returns an integer n satisfying card(X)<ω ⇒ X⊆(-∞,n]. (2) A known algorithm for every k∈N decides whether or not k∈X. (3) No known algorithm with no input returns the logical value of the statement card(X)=ω. (4) There are many elements of X and it is conjectured, though so far unproven, that X is infinite. (5) X is naturally defined. The infiniteness of X is false or unproven. X has the simplest definition among known sets Y⊆N with the same set of known elements. We prove that the set X={n∈N: the interval [-1,n] contains more than 29.5+(11!/(3n+1))∙sin(n) primes of the form k!+1} satisfies Conditions (1)-(5) except the requirement that X is naturally defined. 501893∈X. Condition (1) holds with n=501893. card(X∩[0,501893])=159827. X∩[501894,∞)={n∈N: the interval [-1,n] contains at least 30 primes of the form k!+1}. If we add to X some set W satisfying 14≤card(W)≤23, then the following statements hold: X does not satisfy Condition (1), 159827+14≤card(X), the above lower bound is currently the best known, card(X)<ω ⇒ card(X)≤159827+23, the above upper bound is currently the best known, X satisfies Conditions (2)-(5) except the requirement that X is naturally defined. Analogical statements hold, if we add to X the set ⋃_{x∈N, x divides 99!} {k∈N: k-501894 is the x-th element of P(n^2+1)}, where P(n^2+1) denote the set of primes of the form n^2+1. For a non-negative integer n, let θ(n) denote the largest integer divisor of 10^{10^{10}} smaller than n. Let κ:N→N be defined by setting κ(n) to be the exponent of 2 in the prime factorization of n+1. The set X={n∈N: (θ(n)+κ(n))^2+1 is prime} satisfies Conditions (1)-(5) except the requirement that X is naturally defined. Condition (1) holds with n=0^{10^{10}}. We present a table that shows satisfiable conjunctions of the form #(Condition1)∧ (Condition 2)∧#(Condition 3)∧(Condition 4)∧#(Condition 5), where # denotes the negation ¬ or the absence of any symbol. No set X⊆N will satisfy Conditions (1)-(4) forever, if for every algorithm with no input, at some future day, a computer will be able to execute this algorithm in 1 second or less. The physical limits of computation disprove this assumption.

Warren Weaver, writing about the function that science should have in mankind’s developing future, ideas and ideals, proposed to classify scientific problems into ‘problems of simplicity’, ‘problems of disorganised complexity’, and ‘problems of organised complexity’ — the huge complementary class to which all biological, human, and social problems belong. Problems of simplicity have few components and variables and have been extensively addressed in the last 400 years. Problems of disorganised complexity have a huge number of individually erratic components and variables, but possess collective regularities that can be analysed by resourcing to stochastic methods. Yet, problems of organised complexity do not yield easily to classical or statistical treatment since interrelations among phenomenon elements change during its evolution alongside commonly used state variables, affecting behaviour and outcome. Moreover, organisation, the focal point in this complementary class, is still an elusive concept despite the gigantic efforts undertaken since a century ago to tame it. This paper addresses the description, representation and study of phenomena in the ‘problems of organised complexity’ class. Grounded on relational mathematical constructs, a theoretical framework providing operational definitions and schemes for formally modelling organisations and interaction of organisations is introduced. This framework extends the general systems’ concept and provides a novel perspective for addressing organised complexity phenomena as a collection of interacting organisations.

Swift and diligent resilience response is mandatory in sustainable geo-distributed ecosystems. The real-time geo-spatial resilience requires agility in millions of parallel and distributed data processing tasks on data acquired from regional condition monitoring(RCM) systems. These tasks include expiditous resolution of complex sustainability conflict sets, promptly anomalies characterization in chaos sets, and resilience response uniqueness. This work is an archetype of a paragon geo-resilience support system(GRSS) for regional sustainability using a novel melioration in DADO production machine. The proposed expert system capitalized the synergic strengths of RETE, TREAT, LEAPS and GATOR networks was designed and implemented as a synthetic DADO machine(SDM). The generic architecture of DADO machine was improved in this work by enrichment in rule set conditions and solution set for regional scale resilience rule set conditions. The condition left-hand side(LHS) X equal to the solution set 2X for right-hand side (RHS) was the goal achieved by working memory(WM) optimization and conflict resolution strategy(CRS) in alpha and beta networks rules. A round-trip time of 80.2 seconds for first event response set using 1492 segment size and sequence number 360,000 with maximum packets at a single geospatial structure was 21 packets/sec was a noticeable landmark in this work. LEAPS and Concurrent-read algorithm for GATOR cluster networks in the proposed synthetic DADO machine architecture was the overall implementation that enabled urban scale resilient system practically possible on physical SHM deployment.

In 1999, Molodtsov initiated the theory of soft sets as a new mathematical tool for dealing with uncertainties in many fields of applied sciences. In 2011, Shabir and Naz introduced and studied the notion of soft topological spaces, also defining and investigating many new soft properties as generalization of the classical ones. In this paper, we introduce the notions of soft separation between soft points and soft closed sets in order to obtain a generalization of the well-known Embedding Lemma to the class of soft topological spaces.

This text deals with exploring random solutions for generalized nonlinear variational inequality problems. Using the Fan-KKM theorem and Aumann's measurable selection theorem, we are able to prove the existence and uniqueness of random solution sets under the conditions of monotonicity and convexity. Additionally, we use Minty's lemma to demonstrate the compactness and convexity of the random solution sets.

We propose that quarks and gluon flux tubes emerge from networks of standing vacuum waves. Each unbound nucleon, in its ground state, may be electromagnetically modeled as massless quantized charge on two pairs of orbiting arcs. Each charge arc is associated with a superposition of radially-oriented vacuum fundamental harmonics. These quantum superpositions of radial waves are coupled to nucleon mass-energy. The charge arcs orbit on the two surfaces of a spindle torus with polar charge-exclusion zones. These ground-state models of unbound nucleons may be interpreted as pairs of virtual Möbius bands. The optimal triangular Möbius band may explain proton uniqueness. These unbound proton and neutron models are shown to be precisely connected via a parameter dependent on neutron mass and the sum of the up and down bare quark masses. Due to this precise connection, and the relatively high experimental precision of proton magnetic moment, neutron magnetic moment is calculated about two orders of magnitude more precisely than the most accurate experiments to date. This quantum network-based approach to modeling unbound low-energy nucleons calculates several other measurable parameters.