{"title":"Updating information based on generalized credal sets. Part 2: General case","authors":"Andrey G. Bronevich , Igor N. Rozenberg","doi":"10.1016/j.fss.2024.108967","DOIUrl":null,"url":null,"abstract":"<div><p>In the first part of this paper, we have considered: a) generalized credal sets on the powerset of a finite set <em>X</em>; b) their general definition allowing a generalized credal set to be not convex; c) the justification of basic aggregation rules on generalized credal sets; d) ways of updating information. The second part is devoted to the solutions of the above problems for the general case, when generalized credal sets are defined on arbitrary measurable spaces. In addition, we prove that the conditionals after updating of a generalized credal set could be chosen ratio-equivalent. This result confirms the thesis by R.A. Fisher, which says that the likelihood function is defined uniquely up to a positive coefficient.</p></div>","PeriodicalId":55130,"journal":{"name":"Fuzzy Sets and Systems","volume":null,"pages":null},"PeriodicalIF":3.2000,"publicationDate":"2024-04-08","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/S0165011424001131","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
In the first part of this paper, we have considered: a) generalized credal sets on the powerset of a finite set X; b) their general definition allowing a generalized credal set to be not convex; c) the justification of basic aggregation rules on generalized credal sets; d) ways of updating information. The second part is devoted to the solutions of the above problems for the general case, when generalized credal sets are defined on arbitrary measurable spaces. In addition, we prove that the conditionals after updating of a generalized credal set could be chosen ratio-equivalent. This result confirms the thesis by R.A. Fisher, which says that the likelihood function is defined uniquely up to a positive coefficient.
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.