Extremal values-based aggregation functions

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

Fuzzy Sets and Systems Pub Date : 2024-07-30 DOI:10.1016/j.fss.2024.109097

Radomír Halaš , Radko Mesiar , Anna Kolesárová , Reza Saadati , Francisco Herrera , Iosu Rodriguez-Martinez , Humberto Bustince

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引用次数: 0

Abstract

We introduce and study aggregation functions based on extremal values, namely extended $(l, u)$ -aggregation functions whose outputs only depend on a fixed number l of extremal lower input values and a fixed number u of extremal upper input values, independently of the arity of the input n-tuples ( $n \geq l + u$ ). We discuss several general properties of $(l, u)$ -aggregation functions and we study special $(l, u)$ -aggregation functions with neutral element, including t-conorms, t-norms and uninorms. We also study $(l, u)$ -aggregation functions defined by means of integrals with respect to discrete fuzzy measures, as well as $(l, u)$ -ordered weighted quasi-arithmetic means based on appropriate weighting vectors. We also stress some generalizations based on recently introduced new types of monotonicity. Some possible applications are sketched, too.

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基于极值的聚合函数

我们引入并研究了基于极值的聚合函数，即扩展聚合函数，其输出只取决于固定数量的极值下限值和固定数量的极值上限值，与输入元组（）的枚举无关。我们讨论了聚敛函数的几个一般性质，并研究了具有中性元素的特殊聚敛函数，包括 t-矩形、t-矩形和非矩形。我们还研究了通过与离散模糊度量有关的积分定义的聚集函数，以及基于适当加权向量的有序加权准算术平均数。我们还强调了基于最近引入的新型单调性的一些概括。我们还简要介绍了一些可能的应用。

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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.