1. Introduction

2. Literature Review

2.1. Definition of indicators

The humanitarian supply chain is a process of moving materials from the supply side to the demand side that involves multiple relevant participants and relief providers in a complex internal and external environment. In this research, after conducting an extensive literature review and consulting with humanitarian supply chain experts using the Delphi method, and considering various factors, an index system for the assessment of resilience is constructed from the following aspects: 1. organizational involvement, 2. reliability, 3. agility, 4. cost factors, and 5. service quality, described as follows.

2.1.1. Organizational involvement

Humanitarian supply chains are different from commercial supply chains in that they have the characteristics of not being profit driven and instead, focused on being relief-oriented. At the same time, humanitarian relief may be led by governmental organizations, NGOs or UN relief organizations, and involves many other participants including the affected community members. Therefore, unlike previous supply chains in which suppliers were selected through market mechanisms, the selection of suppliers in humanitarian supply chains requires the joint participation of the government and the market [15].

Active government involvement (F1). In general, the government is the main initiator of humanitarian relief, and according to the statistics of 2015, the Chinese government has participated in humanitarian aid operations more than 200 times. Humanitarian relief has time-concentrated and labor-intensive demand characteristics, and the government has an absolute advantage in mobilizing human, material and financial resources. Therefore, the government plays a leading, organizing, and coordinating role in humanitarian relief, which can form the hierarchical structure and operating rules of the humanitarian supply chain [15]. Authoritative governance is at the core of the humanitarian supply chain and can ensure the effective coordination of the relationships among the participating organizational parties and thus promote the performance of the entire supply chain.

Active participation of NGOs (F2). Non-governmental organizations (NGOs) are organizations established by agreement, independent of government, to engage in international activities to meet needs that cannot be met by the market, state, or society [16]. In resource-limited situations, it is critical that NGOs use or manage resources effectively [35]. In recent years, NGOs have also become central members of the humanitarian supply chain. For example, in the case of the flash flooding events in the Henan Province, more than 430 civilian relief organizations went to Henan to respond to the disaster.

Coordination among participating organizations (F3). The individual members of the humanitarian relief supply chain are both independent and interconnected, and building a humanitarian supply chain with mutual trust and collaboration can effectively improve supply chain resilience [18]. Cao Ke-Yan et al. (2008) concluded that establishing partnerships among humanitarian relief providers can promote goal congruence among supply chain members, thus contributing to the synergistic development of humanitarian supply chains and improving their operational resilience [17]. Zhao Wenhong et al. (2010) argued that an effectively coordinated logistics operation mechanism is key to humanitarian supply chains in emergencies, and cooperation among relief organizations is particularly important [18]. Yang, K. (2010) suggested that the degree of coordination among relief organizations is closely related to the effectiveness of relief [19], and therefore, the establishment of an effectively coordinated organization is beneficial to enhance the resilience effect of humanitarian supply chains.

2.1.2. Reliability

The reliability of humanitarian supply chain organizations is a key factor in determining the resilience of this supply chain. Reliability refers to the ability of an organization to deliver the exact supplies to the disaster victims at the right time and at the fastest rate. Due to the urgent nature of humanitarian relief, there is no guarantee of orderliness in the delivery of supplies, which can lead to untimely or erroneous delivery of supplies [20]. Humanitarian supply chain reliability is about ensuring that supplies are delivered accurately to the people being rescued [21]. Uncertainty in the relief process has the potential to cause disruptions throughout the supply chain, and reliability is one way to ensure that the supply chain is functioning properly [22].

Logistics provider reliability (F4). Humanitarian logistics is an important way to ensure that supplies reach the rescued communities accurately and speedily [23]. Secondary disasters often occur in the humanitarian relief process, especially after natural disasters [24]. For example, aftershocks occur during earthquake relief, sudden secondary flooding during flood relief, and other situations. Once a humanitarian logistics network suffers a disruption in a rescue, the most important task is to quickly restore transport capacity [25]. Therefore, the reliability of the logistics provider is the basis for ensuring the reliability of the entire supply chain.

Material supplier reliability (F5). The provision of supplies in the humanitarian supply chain ensures the outcome and efficiency of the overall humanitarian response [28]. The types of supplies needed in the rescued areas vary widely and the quantity demanded is high, often requiring a large number of different necessities and medical relief supplies [29]. The suddenness of disasters in the rescued areas [30] leads to the inability of many material suppliers to supply sufficient quantities of materials in the short term [31], causing disruptions in the entire supply chain. Therefore, the reliability of the entire material suppliers is closely related to the resilience of the entire humanitarian supply chain.

2.1.3. Agility

Agility in the supply chain is necessary in disaster relief and rescue. In emergency relief, an agile and flexible supply chain ensures that the supply chain can react quickly and adjust to the appropriate state in the event of an emergency [32]. According to Dan'Asabe Godwin Geyi et al: agility has a positive impact on the operational performance of the supply chain [30]. Agility is now gaining attention as an important influencing factor in assessing supply chain resilience in a constantly fluctuating and unpredictable environment [35]. The availability of agility in humanitarian supply chains is a key indicator to evaluate their resilience [33].

Responsiveness (F6). In humanitarian supply chains, factors such as supply capacity, infrastructure, delivery time, material stockpiles, and demand variations may affect response capacity [36]. Responsiveness is more reflected in response time in humanitarian supply chains, including procurement time, order delivery time, lead time, and transportation time [37]. Also, inventory stocking and environmental adaptability are direct manifestations of responsiveness. Reducing response time is a key step to improving the overall performance of the supply chain [38]. Reducing the delivery time of suppliers, minimizing the waiting time for relief, and improving the efficiency of material transportation and unloading can most directly reduce response time. According to Sahebjamnia et al.( 2017), responsiveness is one of the most important performance indicators of humanitarian supply chain agility [35].

Resource Scheduling Capability (F7). Resource scheduling capability is an important factor in measuring supply chain agility and an efficiency capability that requires collaboration among all parties in the humanitarian supply chain. Since resources are scarce in humanitarian relief, efficient and quality-assured resource scheduling can reduce the waste of relief resources while improving relief efficiency. Harshala Shingne (2023) et al. argue that the use of cloud computing can effectively improve the accuracy and punctuality of resource scheduling [36]; while Samiksha Mathur et al. (2023) suggest that high-tech products such as artificial intelligence (AI), machine learning, and deep learning can significantly improve the efficiency of resource scheduling [37]. This also reveals that members of humanitarian supply chains should negotiate and use AI and big data to help improve the resource scheduling capabilities of the supply chain and make humanitarian supply chains more agile.

Timeliness of transportation (F8). Timely transportation of relief supplies to the affected party is a critical point in humanitarian relief. Humanitarian relief supplies are high-volume and multi-disciplinary in nature. The capacity of transport vehicles and the state of road infrastructure are key factors affecting the timeliness of transport, and Ghorbani and Ramezanian (2020) noted that the lack of suitable transport vehicles can severely affect humanitarian supply chain activities and thus their agility [38]. The type and number of transport vehicles should be adjusted in a timely manner according to the quantity and type of emergency supplies and equipment. The use of aircraft and drones can effectively improve the timeliness of transportation in the case of sudden disasters that disrupt roads. At the same time, natural disasters are destructive and may lead to obstruction of transportation routes and failure to deliver supplies as scheduled; therefore, the integrity of roads and other infrastructure will also directly affect the timeliness of transportation [43].

2.1.4. Cost Factor

The cost factor is the main indicator of financial performance in the supply chain. Costs in the supply chain are mainly derived from order delivery costs, warehousing and inventory costs, supply chain management costs, procurement costs, transportation costs, and marketing costs [40]. Compared to traditional commercial supply chains, humanitarian relief is a process of mobilizing human, material, and financial resources in a short period of time and dispatching and allocating resources, and the emergency management costs in humanitarian supply chain management costs can be significantly higher [23]. For humanitarian organizations, it is difficult to quantify the costs associated with serving the affected population [46]. The main criterion to be considered in disaster relief inventory management is the cost of deprivation, which is related to the value of the suffering of the affected population due to lack of access to relief supplies [48]. Low-cost supply chains are more resilient and sustainable; therefore, the cost factor is a key indicator to assess the resilience of humanitarian supply chains.

Transportation Costs (F9). Disasters can be highly disruptive to transportation networks, which severely affects the delivery of emergency supplies and equipment. Blocked transportation routes can significantly increase transportation costs [49], and reliable and low-cost transportation is particularly important for humanitarian supply chains. In addition, disaster sites are often in mountainous and riverine areas with remote locations, while unpredictable demand in local supply chains will increase transportation costs in humanitarian chains [50].

Inventory costs (F10). Inventory costs are a relatively large part of supply chain costs, which include inventory investment, fixed and variable costs, and holding costs [51]. Also, due to the uncertainty of demand, it is not possible to determine the lead time for supplying materials [45], so the humanitarian supply chain needs to maintain a portion of fixed inventory of materials, leading to an increase in inventory costs. Natural disasters have uncertainty in frequency and magnitude of occurrence and require high inventory costs, and these result in a significant financial burden [47].

Material Mobilization and Procurement Costs (F11). It is difficult to establish supply purchase orders and criteria before a disaster occurs. The unpredictability of the timing and quantity of material requirements adds to the complexity between suppliers and relief organizations [54]. Therefore it is difficult to control the cost of raising and procuring supplies. To change this situation, an increasing number of humanitarian organizations are entering into long-term contracts with suppliers [52 53]. Such contracts can control the cost of raising and procuring emergency supplies and ensure that a certain amount of supplies are available in the case of a disaster. Reducing the cost of material collection and procurement can effectively reduce the cost of humanitarian supply chains and increase their resilience.

2.1.5. Quality of service

Service quality in humanitarian supply chains is presented from the perspective of the rescued. Most of the previous studies on humanitarian supply chains have focused on the supplier and humanitarian relief party perspectives. While the rescued parties are also key nodal members of the overall supply chain, Ali Anjomshoae et al. (2022) suggested that the existing humanitarian supply chain literature has little consideration of the perceptions of the served parties and hoped that future research could include the perspective of the served parties to consider their performance levels [50]. Meanwhile, as the willingness of the demand side is increasingly valued, many studies on the evaluation of supply chain resilience have included the demand side perspective [55]. In this research, service quality in humanitarian supply chains is considered from two perspectives:

Supply of necessities for life (F12). In humanitarian relief, supplies are scarce and inaccessible [56] The affected people need a certain amount of necessities for post-disaster emergency survival. The lack of survival supplies can lead to injury or death of the affected people in non-disaster situations. Therefore, the availability of necessities is a key indicator for the quality of humanitarian supply chain services and can usefully be evaluated by the rescued people.

Timely arrival of rescue supplies (F13). Affected community members have an urgent need for medical and other relief supplies, for example, when Wuhan was hit by the new coronavirus in 2019, the local people had an urgent need for masks and disinfection tools [57]. The timely arrival of relief supplies can ensure the survival of people, and at the same time can effectively reduce fear levels and enhance the satisfaction levels of those rescued.

Table 1. summarises the findings of the literature review.

Table 1. summarises the findings of the literature review.

Standard	Indicator	Descriptions
Organizational involvement AReliability B	Active government involvement (F1)	Government plays a major role in the humanitarian supply chain
	Active participation of NGOs (F2)	NGOs are gaining ground in the humanitarian supply chain
	Coordination among participating organizations (F3)	Coordination among supply chain members is important for humanitarian supply chain resilience
	Logistics provider reliability (F4)	Logistics providers can accelerate the relief process and improve the resilience of the humanitarian supply chain
Agility C	Material supplier reliability (F5)	Timely supply of materials helps to speed up the rescue process and enhance rescue efficiency
	Responsiveness (F6)	Rapid supply chain response enhances supply chain agility
	Resource Scheduling Capability (F7)	Having the ability to quickly dispatch resources makes the humanitarian supply chain more resilient
Cost Factor D Quality of service E	Timeliness of transportation (F8)	Timely transportation allows for smooth relief efforts and further improves supply chain resilience performance
	Transportation Costs (F9)	Lower transportation costs can lead to increased supply chain revenue and increased supply chain operability
	Inventory costs (F10) Material Mobilization and Procurement Costs (F11)	Reducing inventory costs contributes to a sustainable supply chain, thereby increasing its resilience Lower material raising and procurement costs allow for more material to be raised on the same budget, and increased material availability helps improve supply chain performance
	Supply of necessities of life (F12)	The main function of the humanitarian supply chain is to provide the necessities of life to the relief workers
	Timely arrival of rescue supplies (F13)	The timely arrival of relief supplies can protect the lives and livelihoods of those waiting for help

2.2. Review of humanitarian supply chain assessment methods

In previous studies, many methods have been used to assess humanitarian supply chain resilience (refer to Table 2). Sharifyazdi, Mehdi et al. (2018) used a target planning approach and proposed that a combination of pre-positioning relief items in the interior and anticipating relief items on board ships and at the docks could help improve the efficiency of relief operations as well as improve supply chain resilience [54]. Altay, Nezih et al. (2018) used the dynamic capability view (DCV) to conceptualize a theoretical model of the humanitarian supply chain (HSC) in different phases before and after a disaster to investigate the impact of supply chain agility (SCAG) and supply chain resilience (SCRES) on performance, mediated by organizational culture [55]. Singh, Rajesh Kumar et al. (2018) identified and analyzed factors for developing resilience in humanitarian supply chains using the fuzzy MICMAC approach [56]. Wang Zhile et al. (2019) developed a model based on a spatially explicit proxy, which was used to assess deviations between the supply and demand of humanitarian relief goods in disaster-affected areas at pre-determined times [57]. Nezhadroshan Ali Mehdi et al. (2021) proposed a scenario-based stochastic likelihood objective planning method to solve the humanitarian logistics network design problem for the integration of warehouses and distribution centers to improve the efficiency of humanitarian logistics [58]. Nayak, Rakesh et al. (2022) conducted an empirical study of immature economies using an agile integrated approach framework for efficient management of humanitarian logistics and supply chain management (HLSCM). Through this agile framework, inefficiencies in humanitarian supply chains were identified and improvement methods were proposed [59]. Rahman Md Mostafizur et al. (2022) used Interpretive Structural Modeling (ISM) to assess the barriers in the humanitarian supply chain in coastal Bangladesh under the influence of cyclones [60]. Giedelmann-L Nicolas et al. (2022) used a dynamic systems model approach to compare centralized and decentralized supply chain configurations and applied it to humanitarian supply chains to provide applicable inventory management strategies for food relief in relief operations [61]. Bag assessed the weights of humanitarian supply chain barriers in a big data-driven context by means of a fuzzy full explanatory structural model (F-T-ISM) [62].

Based on the systematic literature review, we found that the current research in humanitarian supply chain resilience mainly focuses on the following three aspects: 1. studying the relationship between various elements in the humanitarian supply chain; 2. analyzing each element in the humanitarian supply chain and evaluating the most critical influencing factors through evaluation methods; 3. using fuzzy theory to make improvements to the evaluation methods to achieve evaluation results closer to the actual. We also found that the previous studies on the humanitarian supply chain have been very useful. In addition, we found that the previous studies on the resilience of humanitarian supply chains were mostly from the perspective of "providers" and rarely from the perspective of "recipients". This suggests that there is some room for improvement in the study of humanitarian supply chain resilience. Therefore, based on the above findings, this research considers the "recipient" perspective and the relationship between the factors to make a comprehensive assessment of humanitarian supply chain resilience using the ANP-PFs-VIKOR approach.

Table 2. Comparative analysis of previous studies and the present study.

Table 2. Comparative analysis of previous studies and the present study.

References	Description	Method
[54]	A combination of pre-positioning relief items in the mainland and anticipating them on board ships and at terminals is proposed to help improve the efficiency of disaster relief operations as well as the resilience of the supply chain.	Goal Planning
[55]	The impact of supply chain agility (SCAG) and supply chain resilience (SCRES) on performance, mediated by organizational culture, was investigated	DCV
[56]	Fuzzy MICMAC methodology was used to identify and analyze the factors that develop resilience in humanitarian supply chains	Fuzzy-MICMAC
[60]	Interpretive Structural Modeling (ISM) to assess the barriers in the humanitarian supply chain in coastal Bangladesh under the influence of cyclones	ISM
[61]	Use a dynamic systems model approach to compare centralized and decentralized supply chain configurations and apply them to humanitarian supply chains	Dynamic System Model
[62]	Weighting of humanitarian supply chain barriers in a big data-driven context assessed by fuzzy full explanatory structural model (F-T-ISM)	F-T-ISM
Proposed method	Thirteen representative indicators were selected to evaluate humanitarian supply chain resilience factors, and the VIKOR evaluation method was used to rank the resilience of humanitarian supply chains in five typical disaster areas	PFs-ANP-VIKOR

3. Methods

3.2. Pythagoras (PFs) fuzzy theory

Pythagorean Fuzzy Sets ("PFs"), are built on top of Intuitionistic Fuzzy Sets ("IFs"). Both PFs and IFs quantify the decision maker's linguistic description of the decision criterion using affiliation, non-affiliation, and hesitancy values. PFs describe fuzzy phenomena where the sum of affiliation and non-affiliation exceeds 1 and the sum of squares does not exceed 1, and can accommodate more uncertainty than IFs. It also describes the hesitation of the expressed decision maker in terms of affiliation and non-affiliation, which is much closer to the actual decision-making situation than Ifs, and thus it is a powerful tool for explaining the uncertainty phenomenon and better modeling the real decision-making situation.

3.2.1. Pythagorean fuzzy set definition

Assuming that $X$ is a nonempty set, there exists a fuzzy set $\mathsf{\Lambda }$ that

$$\Lambda =⟨x,{\mu }_P\left(x\right),{\upsilon }_P\left(x\right)\left|x\in X\right.⟩$$

(5)

${\mu }_p\left(x\right)、v_p\left(x\right)$ are the subordination and non-subordination values in the fuzzy set, respectively, and for any $x$ there is $x\in X$, ${\mu }_p\left(x\right)\mathrm{、}{v}_p\left(x\right)⟶\left[\mathrm{0,1}\right],0\le {\mu }_p{\left(x\right)}^2+v_p{\left(x\right)}^2\le 1$. For any $\mathsf{\Lambda }$ there is a hesitant function ${\pi }_p\left(x\right)$，${\pi }_p\left(x\right)=\sqrt{1-\left({\mu }_p{\left(x\right)}^2+v_p{\left(x\right)}^2\right)}$.

3.2.2. Pythagorean fuzzy set arithmetic rule

Assuming that$P_1$ and $P_2$ are two Pythagorean fuzzy numbers, denoted as, $P_1=P_1\left({\mu }_{p1},v_{p1}\right)$，${P_2=P}_2\left({\mu }_{p2},v_{p2}\right)$, respectively

Then there are，

$$P_1\oplus P_2=P(\sqrt{{\left({\mu }_{P1}\right)}^2+{\left({\upsilon }_{P2}\right)}^2-{\left({\mu }_{P1}\right)}^2{\left({\upsilon }_{P2}\right)}^2},{\upsilon }_{P1}{\upsilon }_{P2})$$

(6)

$$P_1\otimes P_2=P\left({\mu }_{P1}{\mu }_{P2}\sqrt{{\left({\mu }_{P1}\right)}^2+{\left({\upsilon }_{P2}\right)}^2-{\left({\mu }_{P1}\right)}^2{\left({\upsilon }_{P2}\right)}^2}\right)$$

(7)

$$P_1-P_2=P\left(\sqrt{\frac{{\left({\mu }_{P1}\right)}^2+{\left({\mu }_{P2}\right)}^2}{1-{\left({\mu }_{P2}\right)}^2}},\frac{{\upsilon }_{P1}}{{\upsilon }_{P2}}\right),\left({\mu }_{P1}\ge {\mu }_{P2},{\upsilon }_{P1}\le \mathit{min}\left\{{\upsilon }_{P2},\left.\frac{{\upsilon }_{P2}{\pi }_{P1}}{{\pi }_{P2}}\right\}\right.\right)$$

(8)

$$P_1÷P_2=P\left(\frac{{\mu }_{P1}}{{\mu }_{P2}},\sqrt{\frac{{\left({\upsilon }_{P1}\right)}^2+{\left({\upsilon }_{P2}\right)}^2}{1-{\left({\upsilon }_{P2}\right)}^2}}\right),\left({\mu }_{P1}\le \mathit{min}\left\{{\mu }_{P2},\left.\frac{{\mu }_{P2}{\pi }_{P1}}{{\pi }_{P2}}\right\},{\upsilon }_{P1}\ge {\upsilon }_{P2}\right.\right)$$

(9)

$$\lambda P_1=P\left(\sqrt{1-\left(1-{{\mu }_{p1}}^2\right)},{{\upsilon }_{p1}}^{\lambda }\right)$$

(10)

$${P_1}^{\lambda }=P\left({{\mu }_{p1}}^{\lambda },\sqrt{1-\left(1-{{\upsilon }_{p1}}^2\right)}\right),\lambda >0$$

(11)

3.2.3. Comparison of fuzzy numbers and the Hemming distance

Let P be a Pythagorean fuzzy number, then the score function of P is as follows:

$$S_P={\left({\mu }_P\right)}^2+{\left({\upsilon }_P\right)}^2$$

(12)

A larger value of $S\left(P\right)$ means a larger $P$. According to this rule one can have the following judgment:

If $S\left(P_1\right)<S\left(P_2\right)$，then $P_1{\prec P}_2$

If $S\left(P_1\right)>S\left(P_2\right)$，then $P_1{\succ P}_2$

If $S\left(P_1\right)=S\left(P_2\right)$，then $P_1{\sim P}_2$

To better illustrate the gap between two fuzzy numbers, the Hemming distance is measured here using the following formula:

$$D_h=\frac{1}{2}\times \left(\left|({{\mu }_{p1}}^2\right.-\left.{{\mu }_{p2}}^2)+({{\upsilon }_{p1}}^2-{{\upsilon }_{p2}}^2)+({{\pi }_{p1}}^2-{{\pi }_{p2}}^2)\right|\right)$$

(13)

3.2.4. Pythagorean fuzzy weighted averaging

In Pythagorean fuzzy theory, Yager proposed Pythagorean fuzzy weighted averaging (PWFA).

$$\Psi =PFWA\left(\sqrt{1-{\prod }_{k=1}^e{\left(1-({\mu }_{ij}^k{)}^2\right)}^{w_k}},{\prod }_{k=1}^e{\left(({\upsilon }_{ij}^k{)}^2\right)}^{w_k}\right)$$

(14)

${\mu }_{ij}^k$ and$v_{ij}^k$are the judgments given by the decision maker and$W_k$ is the fixed weight of the decision maker's decision, ${\sum }_{k=1}^e{W}_k=1$.

3.2.5. Fuzzy semantic transformation

In this research, based on the results of existing research literature, the fuzzy language was transformed into binary fuzzy numbers to facilitate the later numerical clarity process. Table 3 gives the reference scale for fuzzy semantic transformations, which is divided into a total of seven levels, very low (VL), low (L), low (ML), medium (M), high (MH), high (H), and very high (VH).

Table 3. Pythagorean Fuzzy Semantic Transformation Scale.

Table 3. Pythagorean Fuzzy Semantic Transformation Scale.

Fuzzy Natural Semantics	$\mathbf{The} \mathbf{Pythagorean} \mathbf{Fuzzy} \mathbf{Set}\text{（}{\mathit{\mu }}_{\mathit{P}}{，\mathit{\upsilon }}_{\mathit{P}}$）
Very low (VL)	(0.15,0.85)
Low (L)	(0.25,0.75)
Moderately low (ML)	(0.35,0.65)
Medium (M)	(0.55,0.45)
Moderately high (MH)	(0.65,0.35)
High (H)	(0.75,0.25)
Very high (VH)	(0.85,0.15)

3.3. PFs- VIKOR steps

Before we introduce the specific steps of the VIKOR method, let's define the meaning of the specific symbols in the formula as follows:

${\rho }_j$—— Attribute weights for the jth evaluation indicator；

$J^{+}$—— The total set of attribute values for the benefit type；

$J^{-}$—— Aggregate set with attribute values of cost type；

$P_j^{+}$—— Positive ideal solutions for each alternative under criterion j；

$P_j^{-}$——Negative ideal solutions for each alternative under criterion j；

${Ed}_i$—— Group benefit value for the ith alternative；

${EH}_i$—— Individual regret value for the ith alternative；

$Q_i$—— VIKOR value for the ith alternative.

Step 1: Obtain the initial fuzzy evaluation matrix

Suppose the problem has n decision criteria, $j=\mathrm{1,2},3\dots ,n$ $m$ evaluation schemes $(i=\mathrm{1,2},3\dots ,m)$, and the fuzzy semantic evaluation result of each scheme is given by e experts, $k=\mathrm{1,2},3\dots ,e$. The final fuzzy evaluation results constitute the initial fuzzy evaluation matrix R (all elements in R are PFs).

$$R=R\left(r_{ij}^k\right)=PFWA\left(\sqrt{1-{\prod }_{k=1}^e{\left(1-({\mu }_{ij}^k{)}^2\right)}^{w_k}},{\prod }_{k=1}^e{\left(({\upsilon }_{ij}^k{)}^2\right)}^{w_k}\right)$$

(15)

$$R=R\left(r_{ij}^k\right)=p_{ij}=\left(\begin{array}{cccc}{r}_{11}^k& r_{12}^k& \cdots & r_{1n}^k\\ r_{21}^k& r_{22}^k& \cdots & r_{21}^k\\ ⋮& ⋮& \ddots & ⋮\\ r_{m1}^k& r_{m2}^k& \cdots & r_{mn}^k\end{array}\right)$$

(16)

$w_k$ is the expert weight, and in this paper, we use the length of work experience to determine the expert weights.

$$W_k=\frac{T^k}{{\sum }_{k=1}^e{T}^k}$$

(17)

$T^k$ is the working time of the expert.

Step 2: Calculate the Pythagorean fuzzy number positive ideal solution PFPIS$\left(P_j^{+}\right)$ and the Pythagorean fuzzy number negative ideal solution PFNIS$\left(P_j^{-}\right)$.

where,$r_{ij}^k=p_{ij}$ is a Pythagorean fuzzy number that can be expressed as $r_{ij}^k=\left({\mu }_{ij},{\nu }_{ij}\right)$.

$$p_j^{+}=R\left(r_{ij}^k\right)=R({\mu }_j^{+},{\upsilon }_j^{+})=\left\{\begin{array}{c}R\left(\mathit{max}{\mu }_{ij},\mathit{min}{\upsilon }_{ij}\right),j\in J^{+}\\ R\left(\mathit{min}{\mu }_{ij},\mathit{max}{\upsilon }_{ij}\right),j\in J^{-}\end{array}\right.$$

(18)

$$p_j^{-}=R\left(r_{ij}^k\right)=R({\mu }_j^{-},{\upsilon }_j^{-})=\left\{\begin{array}{c}R\left(\mathit{min}{\mu }_{ij},\mathit{max}{\upsilon }_{ij}\right),j\in J^{+}\\ R\left(\mathit{max}{\mu }_{ij},\mathit{min}{\upsilon }_{ij}\right),j\in J^{-}\end{array}\right.$$

(19)

Step 3: Calculate the group benefit value${ Ed}_i$ and individual regret value ${EH}_i$ of each program.

$${Ed}_i={\sum }_{j=1}^n{\rho }_j\frac{D_h(p_j^{+},p_{ij})}{D_h(p_j^{+},p_j^{-})},i=\mathrm{1,2},3,...,m$$

(20)

$${EH}_i=\mathit{max}\left({\rho }_j\frac{D_h(p_j^{+},p_{ij})}{D_h(p_j^{+},p_j^{-})}\right),i=\mathrm{1,2},3,...,m$$

(21)

where${ \rho }_j$ is the weight calculated by ANP, 0≤${\rho }_j$≤1，且$\sum _{j=1}^n{\rho }_j$=1.

Step 4: Calculate the final VIKOR value $Q_i$ for each scenario.

(22)

Where, ${Ed}^{+}=\underset{\mathrm{i}}{\mathrm{m}\mathrm{i}\mathrm{n}}\left\{{Ed}_i\right\}$,${Ed}^{-}=max\left\{{Ed}_i\right\}$,${EH}^{+}=\underset{\mathrm{i}}{\mathrm{m}\mathrm{i}\mathrm{n}}\left\{{EH}_i\right\}$, ${Ed}^{-}=\underset{\mathrm{i}}{\mathrm{m}\mathrm{a}\mathrm{x}}\left\{{EH}_i\right\}$.

$x_1, x_2$∈[0，1] denote the decision coefficients, When $x_1＞x_2$, it indicates that the decision maker prefers the group view; $x_1＜x_2$, indicating that the decision maker is more biased toward personal view; $x_1=x_2=0.5$, indicating that there is no clear preference of the decision maker. In this paper, we use $x_1=x_2=0.5$ parameter coefficient approach.

Step 5: Rank the alternatives according to the calculated ${Ed}_i$、${EH}_i$ and $Q_i$, ${Ed}_i$、${EH}_i$ and $Q_i$ are cost variables, the smaller the value, the better the alternative.

4. Methodological research

4.3. Modeling based on the ANP-PFs-VIKOR approach

Step 1: Calculate Indicator Weights

Based on the questionnaire, an initial judgment matrix was derived and the results are shown in the annex. The weights were solved according to the steps of the ANP method presented in 3.1 above. At the same time, we use Figure 4 to represent the weights of each indicator so that we can show the importance of each indicator more clearly.The weighting results are shown in the table 4 below，

Table 4. ANP weights and rankings.

Table 4. ANP weights and rankings.

Standard	Weight	Indicator	Weight	Rank
Organizational involvement A	0.2813	Active government involvement (F1)	0.0987	5
		Active participation of NGOs (F2) Coordination among participating organizations (F3)	0.05730.1474	8 1
Reliability B Agility C	0.1663 0.3777	Logistics provider reliability (F4)	0.0832	6
		Material supplier reliability (F5)	0.0831	7
		Responsiveness (F6)	0.1174	3
		Resource Scheduling Capability (F7) Timeliness of transportation (F8)	0.1253 0.1129	2 4
Cost Factor D Quality of service E	0.1223 0.0524	Transportation Costs (F9)	0.0559	9
		Inventory costs (F10) Material Mobilization and Procurement Costs (F11) Supply of necessities of life (F12) Timely arrival of rescue supplies (F13)	0.0238 0.0426 0.0337 0.0187	12 10 11 13

Step 2: Obtain the PFs-VIKOR initial evaluation matrix

The experts conducted semantic evaluations of each evaluation object, and the semantic evaluations were converted into the initial evaluation matrix (Table 5).

Table 5. Initial evaluation matrix.

Table 5. Initial evaluation matrix.

	Xingyang		Gongyi		Dengfeng		Xinmi
	${\mathit{\mu }}_{\mathit{j}}$	${\mathit{\nu }}_{\mathit{j}}$	${\mathit{\mu }}_{\mathit{j}}$ ${\mathit{\nu }}_{\mathit{j}}$		${\mu }_j$ ${\nu }_j$		${ \mu }_j$ ${\nu }_j$
F1	0.6113	0.1521	0.5500	0.2025	0.7500	0.0625	0.6113	0.1521
F2	0.5110	0.2406	0.5500	0.2025	0.6982	0.0917	0.5974	0.1631
F3	0.3973	0.3660	0.4971	0.2546	0.6500	0.1225	0.5500	0.2025
F4	0.4500	0.3025	0.5110	0.2406	0.7500	0.0625	0.6113	0.1521
F5	0.4500	0.3025	0.4971	0.2546	0.7500	0.0625	0.6113	0.1521
F6	0.3973	0.3660	0.4500	0.3025	0.6500	0.1225	0.5110	0.2406
F7	0.3973	0.3660	0.4111	0.3492	0.7500	0.0625	0.6113	0.1521
F8	0.5500	0.2025	0.6500	0.1225	0.5500	0.2025	0.6500	0.1225
F9	0.5974	0.1631	0.5500	0.2025	0.7500	0.0625	0.5500	0.2025
F10	0.4500	0.3025	0.5500	0.2025	0.6500	0.1225	0.5110	0.2406
F11	0.6500	0.1225	0.6500	0.1225	0.4500	0.3025	0.6500	0.1225
F12	0.4500	0.3025	0.4500	0.3025	0.6982	0.0917	0.5500	0.2025
F13	0.5500	0.2025	0.4500	0.3025	0.7500	0.0625	0.6113	0.1521

Step 3:Calculate positive and negative ideal solutions $p_j^{+}$ and $p_j^{-}$，The results of the calculations are shown in Table 1 in the AppendixIII

Step 4:Calculate the Heming distance${ D}_h$ between $P_{ij}$ and $P_j^{-}$, $P_j^{+}$ and $P_j^{-}$.

Based on Eq. 13, the sea-mining distances ${ D}_h$ between $P_{ij}$ and $P_j^{-}$, $P_j^{+}$ and $P_j^{-}$ were calculated (as shown in AppendixIII Table 2), and the ratio of the two sea-mining distances was calculated (as shown in AppendixIII Table 3).

Step 5: Calculate the group benefit value ${Ed}_i$and individual regret value ${EH}_i$ for each scenario.

According to Eqs. (20-21) and combined with the weight ${\rho }_j$ calculated by ANP method, the group benefit value ${Ed}_i$, individual regret value ${EH}_i$and VIKOR value $Q_i$ are calculated, and the results are shown in Table 6.

5. Discussion

6. Conclusions and Recommendations

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