用渐进元素和渐进集合模糊化脆函数

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

Fuzzy Sets and Systems Pub Date : 2025-03-03 DOI:10.1016/j.fss.2025.109358

Hsien-Chung Wu

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引用次数: 0

摘要

将清晰函数模糊化为模糊函数有两种方法。一种是使用可拓原理。另一个是用分解定理中的表达式。本文提出了一种利用渐元和渐集的概念对非正态模糊集的清晰函数进行模糊化的新方法。本文的主要目的是建立在隶属函数为上半连续的条件下，利用可拓原理得到的模糊函数与渐近元之间的等价性。这种技术是基于这样的思想，即模糊集是由渐进的元素组成的，就像通常的元素组成的通常的集合一样。在这种情况下，可以借用集合间的运算来建立模糊集合间的运算。

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Fuzzification of crisp functions using gradual elements and gradual sets

There are two ways to fuzzify the crisp functions into fuzzy functions. One is using the extension principle. Another one is using the expression in decomposition theorem. In this paper, we present a new methodology to fuzzify the crisp functions for non-normal fuzzy sets using the concepts of gradual elements and gradual sets. The main purpose of this paper is to establish the equivalence between the fuzzy functions that are obtained using the extension principle and the gradual elements when the membership functions are assumed to be upper semi-continuous. This kind of technique is based on the idea in which the fuzzy set is formulated as consisting of gradual elements like the usual set consisting of usual elements. In this case, the operations among sets can be borrowed to set up the operations among fuzzy sets.

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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.