与可容许阶相关的 Choquet 类算子是汇总多值数据的工具

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

Fuzzy Sets and Systems Pub Date : 2024-11-15 DOI:10.1016/j.fss.2024.109197

Michał Boczek, Tomasz Józefiak, Marek Kaluszka, Andrzej Okolewski

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引用次数: 0

摘要

在本文中，我们提出了一种将经典离散 Choquet 积分推广到多值框架的新方法，即利用可容许阶来完善所考虑值集的自然偏阶。新的 Choquet 类算子将给定类型（尤其是实数、区间和向量）的有限数量的值作为输入，并返回与输入值类型相同的单个输出值。我们给出了该算子在可容许阶数方面单调的必要条件和充分条件。然后，我们将 Choquet 类算子完整地描述为一个与可容许阶相关的聚集函数，并研究其选定的特例。

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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The Choquet-like operator with respect to an admissible order as a tool for aggregating multivalued data

In this paper, we propose a new generalization of the classical discrete Choquet integral to the multivalued framework in terms of an admissible order that refines the natural partial order on the considered value set. The new Choquet-like operator takes as input a finite number of values of a given type, in particular real numbers, intervals, and vectors, and returns a single output value of the same type as the input values. We give necessary and sufficient conditions for the operator to be monotone with respect to the admissible order. We then provide a complete characterization of the Choquet-like operator as an aggregation function with respect to the admissible order and study its selected special cases.

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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.