Fuzzy rough sets based on Morsi fuzzy hemimetrics

Year 2024, Volume: 53 Issue: 1, 107 - 120, 29.02.2024

Guangxv Zhang Wei Yao

https://doi.org/10.15672/hujms.1192092

Abstract

In this paper, we introduce a notion of Morsi fuzzy hemimetrics, a common generalization of hemimetrics and Morsi fuzzy metrics, as the basic structure to define and study fuzzy rough sets. We define a pair of fuzzy upper and lower approximation operators and investigate their properties. It is shown that upper definable sets, lower definable sets and definable sets are equivalent. Definable sets form an Alexandrov fuzzy topology such that the upper and lower approximation operators are the closure and the interior operators respectively.

Keywords

Morsi fuzzy hemimetric, fuzzy rough set, approximation operator, definable set, Alexandrov fuzzy topology

Supporting Institution

National Natural Science Foundation of China

Project Number

12231007, 12371462, JSSCRC2021521, YKJ202351

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