On fuzzy order in fuzzy sets based on t-norm fuzzy arithmetic

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

Fuzzy Sets and Systems Pub Date : 2024-04-26 DOI:10.1016/j.fss.2024.108992

Michał K. Urbański , Dominika Krawczyk , Kinga M. Wójcicka , Paweł M. Wójcicki

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Abstract

In this paper we study some fuzzy order in fuzzy sets based on t-norm fuzzy arithmetic. The definition of the order comes from the extension principle for interval order: $a > b$ iff $a - b > 0$ and from measurement sciences. In measurement sciences the order is given by a comparator whose operation is based on empirical determination of the difference of two input signals. Fuzzy comparison based on fuzzy sets subtraction is considered as an extension of substraction operation, namely a fuzzy set B is greater than a fuzzy set A if $B - A$ is greater than zero in fuzzy arithmetic. In the paper we show that this fuzzy order is irreflexive, transitive, asymmetric and compact, subhomothetic, Archimedean and semi-Ferrers. Our idea refers to the work of M. K. Urbański (Modeling the measurement in algebraic fuzzy structures, Warsaw 2003, in polish) and to the fundamental problems in the measurement theory.

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基于t-规范模糊运算的模糊集合中的模糊秩

本文研究了基于 t 规范模糊运算的模糊集合中的一些模糊阶。阶的定义来自区间阶的扩展原理：a>b iff a-b>0 和测量科学。在测量科学中，阶次是由比较器给出的，比较器的操作是基于对两个输入信号差值的经验判断。基于模糊集减法的模糊比较被视为减法运算的扩展，即在模糊运算中，如果 B-A 大于零，则模糊集 B 大于模糊集 A。在本文中，我们证明了这种模糊阶是不可反的、传递的、非对称的、紧凑的、亚同调的、阿基米德的和半费尔克斯的。我们的想法参考了 M. K. Urbański 的著作（《代数模糊结构中的测量建模》，华沙，2003 年，波兰文）和测量理论中的基本问题。

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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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.