{"title":"Categories of fuzzy-type automata with Kleisli morphisms","authors":"Jiří Močkoř","doi":"10.1016/j.fss.2025.109366","DOIUrl":null,"url":null,"abstract":"<div><div>We introduce the categories of monadic automata, where morphisms between automata are relations defined by monads, that is, morphisms in the Kleisli categories. We show that many standard categories of automata including deterministic, non-deterministic, or fuzzy automata with relations as morphisms are special examples of this category. We also show that there is a strong relation among functors between the Kleisli categories, on the one hand, and functors between these categories of monadic automata, on the other. We extend the definition of a language accepted by a monadic automata with Kleisli morphisms and investigate relationships between categories of these languages and Kleisli categories.</div></div>","PeriodicalId":55130,"journal":{"name":"Fuzzy Sets and Systems","volume":"511 ","pages":"Article 109366"},"PeriodicalIF":2.7000,"publicationDate":"2025-03-13","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/S0165011425001058","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 introduce the categories of monadic automata, where morphisms between automata are relations defined by monads, that is, morphisms in the Kleisli categories. We show that many standard categories of automata including deterministic, non-deterministic, or fuzzy automata with relations as morphisms are special examples of this category. We also show that there is a strong relation among functors between the Kleisli categories, on the one hand, and functors between these categories of monadic automata, on the other. We extend the definition of a language accepted by a monadic automata with Kleisli morphisms and investigate relationships between categories of these languages and Kleisli categories.
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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