{"title":"A note on t-norms having additive generators","authors":"Wenwen Zong , Yong Su , Radko Mesiar","doi":"10.1016/j.fss.2024.109172","DOIUrl":null,"url":null,"abstract":"<div><div>This paper focuses on t-norms which have some additive generators. We show that a t-norm <em>T</em> has some additive generators if and only if the fully ordered semigroup induced by <em>T</em> can be embedded into some fully ordered semigroup induced by either the product <span><math><msub><mrow><mi>T</mi></mrow><mrow><mi>P</mi></mrow></msub></math></span> or the Lukasiewicz t-norm <span><math><msub><mrow><mi>T</mi></mrow><mrow><mi>L</mi></mrow></msub></math></span>.</div></div>","PeriodicalId":55130,"journal":{"name":"Fuzzy Sets and Systems","volume":null,"pages":null},"PeriodicalIF":3.2000,"publicationDate":"2024-10-31","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/S016501142400318X","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
This paper focuses on t-norms which have some additive generators. We show that a t-norm T has some additive generators if and only if the fully ordered semigroup induced by T can be embedded into some fully ordered semigroup induced by either the product or the Lukasiewicz t-norm .
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.
京公网安备 11010802042870号
京ICP备2023020795号-1
分享
求助内容：
应助结果提醒方式：
扫码关注我们
