{"title":"On Stonean triangle algebras","authors":"Saeide Zahiri , Arsham Borumand Saeid","doi":"10.1016/j.fss.2024.108989","DOIUrl":null,"url":null,"abstract":"<div><p>We introduce the notion of Stonean triangle algebra and consider it in details and give the relationships between Stonean triangle algebra and some of algebraic structures such as Gödel-triangle algebras. The notion of <em>L</em>-IVRL(Interval Valued Residuated Lattice)-filters has been defined and some classes of IVRL-filters have been studied. Then, we consider the relationship between these filters and Gödel-triangle algebras. In addition, Stonean IVRL-filters of triangle algebras studied in two view. In addition, IVRL-extended Stonean filter and Stonean IVRL-filters have been defined, by introducing these IVRL-filters on Stonean triangle algebras, we characterize classes of Stonean triangle algebras. Finally, the relationships among these types of IVRL-filters have been investigated.</p></div>","PeriodicalId":55130,"journal":{"name":"Fuzzy Sets and Systems","volume":null,"pages":null},"PeriodicalIF":3.2000,"publicationDate":"2024-04-25","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/S0165011424001350","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 notion of Stonean triangle algebra and consider it in details and give the relationships between Stonean triangle algebra and some of algebraic structures such as Gödel-triangle algebras. The notion of L-IVRL(Interval Valued Residuated Lattice)-filters has been defined and some classes of IVRL-filters have been studied. Then, we consider the relationship between these filters and Gödel-triangle algebras. In addition, Stonean IVRL-filters of triangle algebras studied in two view. In addition, IVRL-extended Stonean filter and Stonean IVRL-filters have been defined, by introducing these IVRL-filters on Stonean triangle algebras, we characterize classes of Stonean triangle algebras. Finally, the relationships among these types of IVRL-filters have been investigated.
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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