{"title":"Idempotent pseudo-n-uninorms","authors":"Juraj Kalafut , Andrea Mesiarová-Zemánková","doi":"10.1016/j.fss.2025.109387","DOIUrl":null,"url":null,"abstract":"<div><div>The structure of idempotent pseudo-<em>n</em>-uninorms, non-commutative generalizations of idempotent <em>n</em>-uninorms, is investigated. First, idempotent pseudo-2-uninorms are characterized by their decomposition into an idempotent pseudo-uninorm and a special idempotent pseudo-2-uninorm, for which the division point <em>z</em> is a (left/right) annihilator. These results are then used in characterization of all idempotent pseudo-<em>n</em>-uninorms by decomposition based on their set of left (right) annihilators and Clifford's ordinal sum. The achieved results reveal that the structure of pseudo-<em>n</em>-uninorms is significantly different from that of <em>n</em>-uninorms and general pseudo-<em>n</em>-uninorms cannot be decomposed via <em>z</em>-ordinal sum. These results provide new insights into the nature of non-commutative aggregation functions.</div></div>","PeriodicalId":55130,"journal":{"name":"Fuzzy Sets and Systems","volume":"513 ","pages":"Article 109387"},"PeriodicalIF":2.7000,"publicationDate":"2025-08-01","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/S0165011425001265","RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"2025/3/26 0:00:00","PubModel":"Epub","JCR":"Q2","JCRName":"COMPUTER SCIENCE, THEORY & METHODS","Score":null,"Total":0}
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Abstract
The structure of idempotent pseudo-n-uninorms, non-commutative generalizations of idempotent n-uninorms, is investigated. First, idempotent pseudo-2-uninorms are characterized by their decomposition into an idempotent pseudo-uninorm and a special idempotent pseudo-2-uninorm, for which the division point z is a (left/right) annihilator. These results are then used in characterization of all idempotent pseudo-n-uninorms by decomposition based on their set of left (right) annihilators and Clifford's ordinal sum. The achieved results reveal that the structure of pseudo-n-uninorms is significantly different from that of n-uninorms and general pseudo-n-uninorms cannot be decomposed via z-ordinal sum. These results provide new insights into the nature of non-commutative aggregation functions.
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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