聚集函数作为量子的松弛态射

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

Fuzzy Sets and Systems Pub Date : 2025-03-27 DOI:10.1016/j.fss.2025.109395

Alejandro Fructuoso-Bonet, Jesús Rodríguez-López

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引用次数: 0

摘要

我们将数学结构的聚集函数的概念推广为量子之间的某个函数。事实上，这些函数恰好是量子的松弛态射。这为研究聚合函数提供了一个全局框架。作为我们理论的结果，我们能够推断出关于度量和模糊度量集合的几个已知结果。

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Aggregation functions as lax morphisms of quantales

We will generalize the concept of aggregation function for mathematical structures as a certain function between quantales. In fact, these functions turn to be exactly the lax morphism of quantales. This provides a global framework for the study of aggregation functions. As a consequence of our theory, we are able to deduce several known results about the aggregation of metrics and fuzzy metrics.

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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.