Generalized extended Bonferroni means for isomorphic membership grades

IF 3.2 1区数学 Q2 COMPUTER SCIENCE, THEORY & METHODS

Fuzzy Sets and Systems Pub Date : 2024-05-10 DOI:10.1016/j.fss.2024.109009

Zhen-Song Chen , Yi Yang , LeSheng Jin , Bapi Dutta , Luis Martínez , Witold Pedrycz , Radko Mesiar , Humberto Bustince

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引用次数: 0

Abstract

The generalized extended Bonferroni mean (GEBM) is a powerful tool for modeling the complex process of aggregating information, whether it is homogeneously or heterogeneously connected, within a composite aggregation structure. It maintains several favorable characteristics and effectively captures the diverse and interconnected nature of expert opinions or criteria, which is commonly observed in various decision-making contexts. This research expands upon the existing GEBM framework by applying it to the specific domains of q-rung orthopair fuzzy sets (q-ROFSs) and extended q-rung orthopair fuzzy sets (Eq-ROFSs). Furthermore, it examines the transformation processes among different variants of GEBMs. To facilitate the development of generalized aggregation functions, the de Morgan triplets for q-ROFSs and Eq-ROFSs are established. By introducing an isomorphism, the transformation relationship between the aggregation functions for q-ROFSs and Eq-ROFSs is analyzed. Based on this foundation, the Bonferroni mean de Morgan triplet-based GEBMs for q-ROFSs and Eq-ROFSs are proposed, and the keeping-order relations for these proposed GEBMs are discussed. Finally, several special cases of the GEBMs for q-ROFSs and Eq-ROFSs are obtained, and several relevant theorems are verified.

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同构成员等级的广义扩展 Bonferroni 平均值

广义扩展邦费罗尼均值（GEBM）是一种强大的工具，可用于模拟在复合聚合结构中聚合信息的复杂过程，无论信息是同质还是异质关联。它保持了几个有利的特点，有效地捕捉了专家意见或标准的多样性和相互关联性，这在各种决策环境中都很常见。本研究在现有 GEBM 框架的基础上进行了扩展，将其应用于 q-rung 正对模糊集（q-ROFSs）和扩展 q-rung 正对模糊集（Eq-ROFSs）的特定领域。此外，它还研究了不同变体 GEBM 之间的转换过程。为便于开发通用聚合函数，本文建立了 q-ROFSs 和 Eq-ROFSs 的 de Morgan 三元组。通过引入同构，分析了 q-ROFSs 和 Eq-ROFSs 的聚合函数之间的转换关系。在此基础上，针对 q-ROFSs 和 Eq-ROFSs 提出了基于 Bonferroni 平均值 de Morgan 三元组的 GEBM，并讨论了这些提出的 GEBM 的保持阶次关系。最后，得到了 q-ROFS 和 Eq-ROFS 的 GEBM 的几个特例，并验证了几个相关定理。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Fuzzy Sets and Systems 数学-计算机：理论方法

CiteScore

6.50

自引率

17.90%

发文量

321

审稿时长

6.1 months

期刊介绍： Since its launching in 1978, the journal Fuzzy Sets and Systems has been devoted to the international advancement of the theory and application of fuzzy sets and systems. The theory of fuzzy sets now encompasses a well organized corpus of basic notions including (and not restricted to) aggregation operations, a generalized theory of relations, specific measures of information content, a calculus of fuzzy numbers. Fuzzy sets are also the cornerstone of a non-additive uncertainty theory, namely possibility theory, and of a versatile tool for both linguistic and numerical modeling: fuzzy rule-based systems. Numerous works now combine fuzzy concepts with other scientific disciplines as well as modern technologies. In mathematics fuzzy sets have triggered new research topics in connection with category theory, topology, algebra, analysis. Fuzzy sets are also part of a recent trend in the study of generalized measures and integrals, and are combined with statistical methods. Furthermore, fuzzy sets have strong logical underpinnings in the tradition of many-valued logics.