Generalized unified well-posedness of equilibrium solutions for fuzzy multi-leader-multi-follower games under bounded rationality

IF 2.7 1区数学 Q2 COMPUTER SCIENCE, THEORY & METHODS

Fuzzy Sets and Systems Pub Date : 2025-06-17 DOI:10.1016/j.fss.2025.109512

Li Zhou , Wensheng Jia

引用次数: 0

Abstract

In this paper, we concentrate on a new class of fuzzy multi-leader-multi-follower games with fuzzy set payoffs, abbreviated as FMLMFG, which is a fuzzy extension of the classical multi-leader-multi-follower games. First, we propose the concept of fuzzy weak Nash equilibrium (FWNE) for FMLMFG based on fuzzy sets and study the existence of FWNE. Subsequently, we formulate the bounded rationality model for FMLMFG by integrating a rationality function and study the generalized unified well-posedness (GU-wp) and unified well-posedness (U-wp). Moreover, we demonstrate the characteristics of GU-wp and U-wp for FMLMFG by utilizing the Kuratowski measure of non-compactness.

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有限理性下模糊多领导-多随从对策均衡解的广义统一适定性

本文主要研究一类具有模糊收益集的模糊多领导-多追随者对策，简称为FMLMFG，它是经典多领导-多追随者对策的模糊推广。首先，我们提出了基于模糊集的FMLMFG模糊弱纳什均衡的概念，并研究了模糊弱纳什均衡的存在性。随后，通过对理性函数的积分，建立了FMLMFG的有限理性模型，并研究了广义统一适定性（GU-wp）和统一适定性（U-wp）。此外，我们利用非紧性的Kuratowski度量证明了FMLMFG的GU-wp和U-wp的特性。

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.