Fuzzy rough sets based on Morsi fuzzy hemimetrics

Authors : Guangxv Zhang, Wei Yao

Pages : 107-120

Doi:10.15672/hujms.1192092

View : 249 | Download : 418

Publication Date : 2024-02-29

Article Type : Research Paper

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