Decomposition and construction of uninorms on the unit interval

IF 3.2 1区数学 Q2 COMPUTER SCIENCE, THEORY & METHODS

Fuzzy Sets and Systems Pub Date : 2024-07-18 DOI:10.1016/j.fss.2024.109083

Yao Ouyang , Hua-Peng Zhang , Bernard De Baets

引用次数: 0

Abstract

By analyzing the behaviour of uninorms on the boundary of the unit square, we present decomposition theorems for uninorms, showing that a conjunctive (resp. disjunctive) uninorm can be decomposed into a disjunctive (resp. conjunctive) uninorm on an upper set (resp. a lower set) and a triangular subnorm (resp. superconorm) on a lower set (resp. an upper set). As an application of the decomposition theorems, we propose several construction methods for uninorms that are not internal on the boundary.

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单位区间上非矩形的分解与构造

通过分析非矩形在单位正方形边界上的行为，我们提出了非矩形的分解定理，证明了连接（或不连接）非矩形可以分解为上集（或下集）上的不连接（或连接）非矩形和下集（或上集）上的三角形子矩形（或超矩形）。作为分解定理的应用，我们提出了几种边界上非内部非矩形的构造方法。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Fuzzy Sets and Systems 数学-计算机：理论方法

CiteScore

6.50

自引率

17.90%

发文量

321

审稿时长

6.1 months

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.