Rough sets based on fuzzy ideals in distributive lattices-Reference-Cited by-同舟云学术

Rough sets based on fuzzy ideals in distributive lattices

Published:2020-01-01 Issue:1 Volume:18 Page:122-137
ISSN:2391-5455
Container-title:Open Mathematics
language:en
Short-container-title:

Author:

Yang Yongwei¹,Zhu Kuanyun²,Xin Xiaolong³

Affiliation:

1. School of Mathematics and Statistics , Anyang Normal University , Anyang , 455000 , China

2. School of Information and Mathematics , Yangtze University , Jingzhou , 434023 , China

3. School of Mathematics , Northwest University , Xi’an , 710127 , China

Abstract

Abstract In this paper, we present a rough set model based on fuzzy ideals of distributive lattices. In fact, we consider a distributive lattice as a universal set and we apply the concept of a fuzzy ideal for definitions of the lower and upper approximations in a distributive lattice. A novel congruence relation induced by a fuzzy ideal of a distributive lattice is introduced. Moreover, we study the special properties of rough sets which can be constructed by means of the congruence relations determined by fuzzy ideals in distributive lattices. Finally, the properties of the generalized rough sets with respect to fuzzy ideals in distributive lattices are also investigated.

Publisher

Walter de Gruyter GmbH

Subject

General Mathematics

Link

https://www.degruyter.com/document/doi/10.1515/math-2020-0013/pdf

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