The lower and upper approximations in a quotient hypermodule with respect to fuzzy sets
INFORMATION SCIENCES, vol.178, no.10, pp.2349-2359, 2008 (SCI-Expanded, Scopus)
- Publication Type: Article / Article
- Volume: 178 Issue: 10
- Publication Date: 2008
- Doi Number: 10.1016/j.ins.2008.01.006
- Journal Name: INFORMATION SCIENCES
- Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
- Page Numbers: pp.2349-2359
- Keywords: hypermodule, lower approximation, upper approximation, rough set, fuzzy set, ROUGHNESS, IDEALS, OPERATORS, VIEW
- Karadeniz Technical University Affiliated: Yes
Abstract
This paper provides a continuation of ideas presented by Davvaz and Mahdavipour [B. Davvaz, M. Mahdavipour, Roughness in modules, Inform. Sci. 176 (2006) 3658-3674]. The notion of hypermodule is a generalization of the notion of module. In this paper, we consider the quotient hypermodule M/A and interpret the lower and upper approximations as subsets of the quotient hypermodule M/A. Then, we introduce the concept of quotient rough sub-hypermodule. Also, using the concept of fuzzy sets, we introduce and discuss the concept of fuzzy rough hypermodules and then we obtain the relation between fuzzy rough sub-hypermodules and level rough sets. This relation is characterized as a necessary and sufficient condition. (C) 2008 Elsevier Inc. All rights reserved.