Unification of fuzzy Sheffer stroke and fuzzy Peirce arrow

IF 2.8 3区计算机科学 Q2 COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE

International Journal of Approximate Reasoning Pub Date : 2026-05-01 Epub Date: 2026-02-03 DOI:10.1016/j.ijar.2026.109640

Meiping Zhang, Feng-Xia Zhang, Xiaoheng Zhang, Maoen Qin

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引用次数: 0

Abstract

Recently, Michał Baczyński et al. presented the fuzzy Sheffer stroke within the framework of fuzzy logic, which generalizes the classical operation when truth values are restricted to the set {0, 1}². Inspired by this work, we investigate the fuzzy Peirce arrow as the dual of the fuzzy Sheffer stroke, and further introduce the UEL functions as a unification of the fuzzy Sheffer strokes and the fuzzy Peirce arrows in this paper. First, some basic properties of the fuzzy Peirce arrow are presented, and the construction methods of the most important fuzzy logical connectives using the fuzzy Peirce arrow in a dual manner are proposed. Second, the concept of UEL functions, which unifies the fuzzy Sheffer stroke and the fuzzy Peirce arrow, is introduced, and several properties of such functions are derived. Specifically, the relationship between the UEL functions and nullnorms is analyzed, and the N-dual and De Morgan’s laws for the UEL functions are studied. Third, several construction methods for the UEL functions are explored. Finally, a practical application example of the UEL functions in the design of automatic door and window opening-closing systems is presented.

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模糊谢弗泳姿与模糊皮尔斯箭的统一

最近，michaowBaczyński等人在模糊逻辑的框架内提出了模糊Sheffer笔画，它推广了真值限制在{0,1}2集合时的经典运算。受此启发，本文研究了模糊Peirce箭作为模糊Sheffer笔划的对偶，并进一步引入了作为模糊Sheffer笔划和模糊Peirce箭的统一的UEL函数。首先，给出了模糊皮尔斯箭头的一些基本性质，提出了利用模糊皮尔斯箭头以对偶方式构造最重要的模糊逻辑连接词的方法。其次，引入了模糊Sheffer冲程和模糊Peirce箭头相统一的UEL函数概念，并推导了该函数的若干性质；具体来说，分析了UEL函数与零范数的关系，研究了UEL函数的n对偶和De Morgan定律。第三，探讨了UEL函数的几种构造方法。最后，给出了UEL函数在自动门窗启闭系统设计中的实际应用实例。

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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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.