Preprint Article Version 1 This version is not peer-reviewed

Characterization of Lattices in Terms of (∈γ,∈γ∨qδ)-Fuzzy Ideals

Version 1 : Received: 26 October 2024 / Approved: 26 October 2024 / Online: 28 October 2024 (13:22:53 CET)

How to cite: Farajdadeh, A.; Kocinac, L. Characterization of Lattices in Terms of (∈γ,∈γ∨qδ)-Fuzzy Ideals. Preprints 2024, 2024102090. https://doi.org/10.20944/preprints202410.2090.v1 Farajdadeh, A.; Kocinac, L. Characterization of Lattices in Terms of (∈γ,∈γ∨qδ)-Fuzzy Ideals. Preprints 2024, 2024102090. https://doi.org/10.20944/preprints202410.2090.v1

Abstract

In this paper, $(\alpha,\beta)$-fuzzy sublattices and $(\alpha,\beta)$-fuzzy ideals of a lattice, where $\alpha\in\{ \in_{\gamma}, q_{\delta}, \in_{\gamma}\vee q_{\delta}\}$, $\beta\in\{ \in_{\gamma}, q_{\delta}, \in_{\gamma}\vee q_{\delta},\in_{\gamma}\wedge q_{\delta}\}$, are introduced and studied. In the special case, $(\in_{\gamma}, \in_{\gamma}\vee q_{\delta})$-fuzzy sublattices and $(\in_{\gamma}, \in_{\gamma}\vee q_{\delta})$-fuzzy ideals of a lattice are presented and their characterizations by three level sublattices and ideals are given.

Keywords

Lattice; fuzzy ideal; $(\alpha,\beta)$-fuzzy sublattice

Subject

Computer Science and Mathematics, Mathematics

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