Difference operators on fuzzy sets

IF 3.2 3区计算机科学 Q2 COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE

International Journal of Approximate Reasoning Pub Date : 2024-07-19 DOI:10.1016/j.ijar.2024.109254

Bo Wen Fang

引用次数: 0

Abstract

Based on the properties of the difference operator on crisp sets, a fuzzy difference operator in fuzzy logic is defined as a continuous binary operator on the closed unit interval with some boundary conditions. In this paper, the structures and properties of fuzzy difference operators are studied. The main results are: (1) Using the axiomatic approach, some generalizations of classical tautologies for fuzzy difference operators are obtained. (2) Based on the model theoretic approach, the fuzzy difference operator constructed by a nilpotent t-norm and a strong negation is characterized. (3) the paper discusses the relationship between the fuzzy difference operator and symmetric difference operator which was raised in [3].

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模糊集合上的差分算子

根据简明集上差分算子的性质，模糊逻辑中的模糊差分算子被定义为封闭单位区间上的连续二元算子，并带有一些边界条件。本文研究了模糊差分算子的结构和性质。主要结果如下(1) 利用公理化方法，得到了模糊差分算子的一些经典同义反复的概括。(2) 基于模型论方法，描述了由零点 t-norm 和强否定构造的模糊差分算子的特征。(3) 本文讨论了[3]中提出的模糊差分算子与对称差分算子之间的关系。

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

International Journal of Approximate Reasoning 工程技术-计算机：人工智能

CiteScore

6.90

自引率

12.80%

发文量

170

审稿时长

67 days

期刊介绍： The International Journal of Approximate Reasoning is intended to serve as a forum for the treatment of imprecision and uncertainty in Artificial and Computational Intelligence, covering both the foundations of uncertainty theories, and the design of intelligent systems for scientific and engineering applications. It publishes high-quality research papers describing theoretical developments or innovative applications, as well as review articles on topics of general interest. Relevant topics include, but are not limited to, probabilistic reasoning and Bayesian networks, imprecise probabilities, random sets, belief functions (Dempster-Shafer theory), possibility theory, fuzzy sets, rough sets, decision theory, non-additive measures and integrals, qualitative reasoning about uncertainty, comparative probability orderings, game-theoretic probability, default reasoning, nonstandard logics, argumentation systems, inconsistency tolerant reasoning, elicitation techniques, philosophical foundations and psychological models of uncertain reasoning. Domains of application for uncertain reasoning systems include risk analysis and assessment, information retrieval and database design, information fusion, machine learning, data and web mining, computer vision, image and signal processing, intelligent data analysis, statistics, multi-agent systems, etc.