格值直觉模糊子群型 3 的同态。

Homomorphisms of Lattice-Valued Intuitionistic Fuzzy Subgroup Type-3.

机构信息

Department of Mathematics and Statistics, International Islamic University Islamabad, Islamabad, Pakistan.

Department of Mathematics, Faculty of Arts and Sciences, Yildiz Technical University, Esenler 34210, Istanbul, Turkey.

出版信息

Comput Intell Neurosci. 2022 Apr 28;2022:6847138. doi: 10.1155/2022/6847138. eCollection 2022.

DOI:10.1155/2022/6847138

PMID:35915593

原文链接:https://pmc.ncbi.nlm.nih.gov/articles/PMC9338742/

Abstract

The lattice-valued intuitionistic fuzzy set was introduced by Gerstenkorn and Tepavcevi as a generalization of both the fuzzy set and the -fuzzy set by incorporating membership functions, nonmembership functions from a nonempty set to any lattice , and lattice homomorphism from to the interval [0,1]. In this article, lattice-valued intuitionistic fuzzy subgroup type-3 (LIFSG-3) is introduced. Lattice-valued intuitionistic fuzzy type-3 normal subgroups, cosets, and quotient groups are defined, and their group theocratic properties are compared with the concepts in classical group theory. LIFSG-3 homomorphism is established and examined in relation to group homomorphism. The research findings are supported by provided examples in each section.

摘要

格值直觉模糊集由 Gerstenkorn 和 Tepavcevi 引入，它通过将隶属函数、非隶属函数从非空集合到任意格，以及从到区间 [0,1]的格同态结合起来，将模糊集和 -模糊集推广。本文引入了格值直觉模糊子群 3 型（LIFSG-3）。定义了格值直觉模糊型 3 正规子群、陪集和商群，并将其群论性质与经典群论中的概念进行了比较。建立了 LIFSG-3 同态，并将其与群同态联系起来进行了研究。在每个部分都提供了示例来支持研究结果。