Multi-valued Choquet integral based on a couple of set functions with an application in multi-attribute decision-making

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

Fuzzy Sets and Systems Pub Date : 2024-12-18 DOI:10.1016/j.fss.2024.109249

Deli Zhang , Radko Mesiar , Endre Pap

引用次数: 0

Abstract

As a generalization of Choquet integrals, the generalized Choquet type set-valued integral of functions w.r.t. set multifunctions and σ-additive measures has been performed in our previous paper [66]. The present paper is its continuation and it brings a novel set-valued type Choquet integral, named double set function multi-valued Choquet integral (DSMVCI), where the σ-additive measure is replaced by a fuzzy measure. Various kinds of its properties and convergence theorems are obtained, and set-valued type Jensen's and Markov's type inequalities are proved. Its application in multi-attribute decision-making with hesitant fuzzy information is given.

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作为 Choquet 积分的广义化，我们在之前的论文[66]中进行了关于集合多元函数和 σ-additive 度量的广义 Choquet 型函数集值积分。本文是它的继续，它带来了一种新的集值型 Choquet 积分，命名为双集函数多值 Choquet 积分（DSMVCI），其中 σ-additive 度量由模糊度量代替。研究获得了它的各种性质和收敛定理，并证明了集值型詹森不等式和马尔可夫不等式。给出了它在具有犹豫模糊信息的多属性决策中的应用。

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.