A fuzzy topological model of hemimetric-based fuzzy rough set and some applications to digital image processing

IF 0.6 4区数学 Q3 MATHEMATICS

Topology and its Applications Pub Date : 2025-03-06 DOI:10.1016/j.topol.2025.109327

Xinyue Han , Wei Yao , Chang-Jie Zhou

引用次数: 0

Abstract

This paper aims to present a fuzzy topological model of hemimetric-based fuzzy rough set by introducing the neighborhood-controlled fuzzy rough approximation operators as the fuzzy topological operators. Although the related fuzzy upper/lower rough approximation operators are no longer idempotent, they form a Galois adjoint pair, which makes their compositions idempotent. The composition of upper-lower operators is called the closing operator, which is a closure operator on the fuzzy power set; and that of lower-upper one is called the opening operator, which is an interior operator on the fuzzy power set. Results show that these two operators can be applied to hole filling, fingerprint cleaning and noise reduction in digital image processing.

查看原文本刊更多论文

求助全文

约1分钟内获得全文求助全文

来源期刊

Topology and its Applications 数学-数学

CiteScore

1.20

自引率

33.30%

发文量

251

审稿时长

6 months

期刊介绍： Topology and its Applications is primarily concerned with publishing original research papers of moderate length. However, a limited number of carefully selected survey or expository papers are also included. The mathematical focus of the journal is that suggested by the title: Research in Topology. It is felt that it is inadvisable to attempt a definitive description of topology as understood for this journal. Certainly the subject includes the algebraic, general, geometric, and set-theoretic facets of topology as well as areas of interactions between topology and other mathematical disciplines, e.g. topological algebra, topological dynamics, functional analysis, category theory. Since the roles of various aspects of topology continue to change, the non-specific delineation of topics serves to reflect the current state of research in topology. At regular intervals, the journal publishes a section entitled Open Problems in Topology, edited by J. van Mill and G.M. Reed. This is a status report on the 1100 problems listed in the book of the same name published by North-Holland in 1990, edited by van Mill and Reed.