{"title":"Characterizations for union and intersection on non-normal membership functions of type-2 fuzzy sets","authors":"Zhi-qiang Liu , Jingxin Liu","doi":"10.1016/j.ijar.2025.109414","DOIUrl":null,"url":null,"abstract":"<div><div>In this work, we mainly investigate set operations for type-2 fuzzy sets. To be more exact, we present several algorithms under the left continuous t-norms that compute the join and meet operations of the non-normal convex secondary membership functions of type-2 fuzzy sets, and give some properties of operations that would enhance the application of fuzzy logic connectives. We anticipate that these algorithms can be applied to type-2 fuzzy logic systems as well as several fields of soft computing that tackle logical operations in type-2 fuzzy sets.</div></div>","PeriodicalId":13842,"journal":{"name":"International Journal of Approximate Reasoning","volume":"181 ","pages":"Article 109414"},"PeriodicalIF":3.2000,"publicationDate":"2025-03-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"International Journal of Approximate Reasoning","FirstCategoryId":"94","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0888613X25000556","RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE","Score":null,"Total":0}
引用次数: 0
Abstract
In this work, we mainly investigate set operations for type-2 fuzzy sets. To be more exact, we present several algorithms under the left continuous t-norms that compute the join and meet operations of the non-normal convex secondary membership functions of type-2 fuzzy sets, and give some properties of operations that would enhance the application of fuzzy logic connectives. We anticipate that these algorithms can be applied to type-2 fuzzy logic systems as well as several fields of soft computing that tackle logical operations in type-2 fuzzy sets.
期刊介绍：
The International Journal of Approximate Reasoning is intended to serve as a forum for the treatment of imprecision and uncertainty in Artificial and Computational Intelligence, covering both the foundations of uncertainty theories, and the design of intelligent systems for scientific and engineering applications. It publishes high-quality research papers describing theoretical developments or innovative applications, as well as review articles on topics of general interest.
Relevant topics include, but are not limited to, probabilistic reasoning and Bayesian networks, imprecise probabilities, random sets, belief functions (Dempster-Shafer theory), possibility theory, fuzzy sets, rough sets, decision theory, non-additive measures and integrals, qualitative reasoning about uncertainty, comparative probability orderings, game-theoretic probability, default reasoning, nonstandard logics, argumentation systems, inconsistency tolerant reasoning, elicitation techniques, philosophical foundations and psychological models of uncertain reasoning.
Domains of application for uncertain reasoning systems include risk analysis and assessment, information retrieval and database design, information fusion, machine learning, data and web mining, computer vision, image and signal processing, intelligent data analysis, statistics, multi-agent systems, etc.
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