[0,1]上三角模糊数的模糊不相似性和模糊乔奎特积分

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

Fuzzy Sets and Systems Pub Date : 2025-01-15 DOI:10.1016/j.fss.2025.109277

A.F. Roldán López de Hierro , A. Cruz , R.H.N. Santiago , C. Roldán , D. García-Zamora , F. Neres , H. Bustince

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引用次数: 0

摘要

考虑到世界上每天登记的数据量巨大，汇总数据集中的信息变得越来越重要。在统计学和计算机科学领域，这项任务是通过聚合函数成功完成的。应用最广泛的数据聚合方法之一就是 Choquet 积分。本文的主要目的是在模糊数的背景下引入适当的 Choquet 积分概念。为此，我们面临三个挑战：处理模糊数时的基本不确定性、通过适当的二进制关系对模糊数进行排序的方法以及计算模糊数之间的不相似性的方法。举例说明的例子涉及所有支持在 [0,1] 上的三角模糊数族的α阶。

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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Fuzzy dissimilarities and the fuzzy Choquet integral of triangular fuzzy numbers on [0,1]

Having in mind the huge amount of data daily registered in the world, it is becoming increasingly important to summarize the information included in a data set. In Statistics and Computer Science, this task is successfully carried out by aggregation functions. One of the most widely applied methodologies of aggregating data is the Choquet integral. The main aim of this paper is to introduce an appropriate notion of Choquet integral in the context of fuzzy numbers. To do this, we face three challenges: the underlying uncertainty when handling fuzzy numbers, the way to order fuzzy numbers by appropriate binary relations and the way to compute the dissimilarity among fuzzy numbers. Illustrative examples are given by involving the α-order on the family of all triangular fuzzy numbers with support on

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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.