{"title":"Multi-valued Choquet integral based on a couple of set functions with an application in multi-attribute decision-making","authors":"Deli Zhang , Radko Mesiar , Endre Pap","doi":"10.1016/j.fss.2024.109249","DOIUrl":null,"url":null,"abstract":"<div><div>As a generalization of Choquet integrals, the generalized Choquet type set-valued integral of functions w.r.t. set multifunctions and <em>σ</em>-additive measures has been performed in our previous paper <span><span>[66]</span></span>. 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 <em>σ</em>-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.</div></div>","PeriodicalId":55130,"journal":{"name":"Fuzzy Sets and Systems","volume":"503 ","pages":"Article 109249"},"PeriodicalIF":3.2000,"publicationDate":"2024-12-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Fuzzy Sets and Systems","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0165011424003956","RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"COMPUTER SCIENCE, THEORY & METHODS","Score":null,"Total":0}
Multi-valued Choquet integral based on a couple of set functions with an application in multi-attribute decision-making
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.
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.
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