{"title":"Generalizing comonotonicity: New insights and dual perspectives","authors":"M. Boczek, A. Hovana, O. Hutník","doi":"10.1016/j.fss.2025.109364","DOIUrl":null,"url":null,"abstract":"<div><div>We review, exemplify, and compare recently introduced classes of functions that generalize comonotone functions from two perspectives: algebraically through <span><math><msub><mrow><mo>⋆</mo></mrow><mrow><mi>inf</mi></mrow></msub></math></span>-associated functions and measure-theoretically via <em>m</em>-positively dependent functions, along with their dual versions – <span><math><msub><mrow><mo>⋆</mo></mrow><mrow><mi>sup</mi></mrow></msub></math></span>-associated functions and <em>m</em>-subadditive functions, respectively. While the concept of <em>m</em>-subadditive functions is well-documented in the literature, the concept of <span><math><msub><mrow><mo>⋆</mo></mrow><mrow><mi>sup</mi></mrow></msub></math></span>-associatedness appears to be novel. Furthermore, we present several applications of these function classes, particularly concerning integral inequalities for the generalized Sugeno integral. Additionally, we mention other extensions of comonotonicity, including weak comonotonicity and multivariate comonotonicity.</div></div>","PeriodicalId":55130,"journal":{"name":"Fuzzy Sets and Systems","volume":"510 ","pages":"Article 109364"},"PeriodicalIF":3.2000,"publicationDate":"2025-03-10","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/S0165011425001034","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}
引用次数: 0
Abstract
We review, exemplify, and compare recently introduced classes of functions that generalize comonotone functions from two perspectives: algebraically through -associated functions and measure-theoretically via m-positively dependent functions, along with their dual versions – -associated functions and m-subadditive functions, respectively. While the concept of m-subadditive functions is well-documented in the literature, the concept of -associatedness appears to be novel. Furthermore, we present several applications of these function classes, particularly concerning integral inequalities for the generalized Sugeno integral. Additionally, we mention other extensions of comonotonicity, including weak comonotonicity and multivariate comonotonicity.
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.