The axiomatic characterization on fuzzy variable precision rough sets based on residuated lattice

IF 2.4 4区计算机科学 Q2 COMPUTER SCIENCE, THEORY & METHODS

International Journal of General Systems Pub Date : 2023-05-28 DOI:10.1080/03081079.2023.2212849

Qiu Jin, Lingqiang Li

引用次数: 1

Abstract

Axiomatization is a lively research direction in fuzzy rough set theory. Fuzzy variable precision rough set (FVPRS) incorporates fault-tolerant factors to fuzzy rough set, so its axiomatic description becomes more complicated and difficult to realize. In this paper, we present an axiomatic approach to FVPRSs based on residuated lattice (L-fuzzy variable precision rough set (LFVPRS)). First, a pair of mappings with three axioms is utilized to characterize the upper (resp., lower) approximation operator of LFVPRS. This is distinct from the characterization on upper (resp., lower) approximation operator of fuzzy rough set, which consists of one mapping with two axioms. Second, utilizing the notion of correlation degree (resp., subset degree) of fuzzy sets, three characteristic axioms are grouped into a single axiom. At last, various special LFVPRS generated by reflexive, symmetric and transitive L-fuzzy relation and their composition are also characterized by axiomatic set and single axiom, respectively.

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基于残差格的模糊变精度粗糙集的公理化表征

公理化是模糊粗糙集理论中一个活跃的研究方向。模糊变精度粗糙集(FVPRS)在模糊粗糙集中加入了容错因素，使得其公理化描述变得更加复杂和难以实现。本文提出了一种基于剩余格的模糊变精度粗糙集(LFVPRS)的公理化方法。首先，利用具有三个公理的一对映射来表征上域。(下)LFVPRS近似算子。这与上面的描述不同。模糊粗糙集的下逼近算子，它由一个映射和两个公理组成。其次，利用关联度(resp)的概念。(子集度)，将三个特征公理归为一个公理。最后，给出了由自反、对称和传递l -模糊关系生成的各种特殊LFVPRS及其组成，并分别用公理集和单公理来表征。

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 General Systems 工程技术-计算机：理论方法

CiteScore

4.10

自引率

20.00%

发文量

审稿时长

6 months

期刊介绍： International Journal of General Systems is a periodical devoted primarily to the publication of original research contributions to system science, basic as well as applied. However, relevant survey articles, invited book reviews, bibliographies, and letters to the editor are also published. The principal aim of the journal is to promote original systems ideas (concepts, principles, methods, theoretical or experimental results, etc.) that are broadly applicable to various kinds of systems. The term “general system” in the name of the journal is intended to indicate this aim–the orientation to systems ideas that have a general applicability. Typical subject areas covered by the journal include: uncertainty and randomness; fuzziness and imprecision; information; complexity; inductive and deductive reasoning about systems; learning; systems analysis and design; and theoretical as well as experimental knowledge regarding various categories of systems. Submitted research must be well presented and must clearly state the contribution and novelty. Manuscripts dealing with particular kinds of systems which lack general applicability across a broad range of systems should be sent to journals specializing in the respective topics.