Generalized lower and upper approximations in a ring

YAMAK S., KAZANCI O., Davvaz B.

INFORMATION SCIENCES, vol.180, no.9, pp.1759-1768, 2010 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 180 Issue: 9
  • Publication Date: 2010
  • Doi Number: 10.1016/j.ins.2009.12.026
  • Journal Name: INFORMATION SCIENCES
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.1759-1768
  • Keywords: Lower approximations, Upper approximations, Set-valued mapping, Set-valued homomorphism, Rough sets, Rough subrings, Rough ideals, ROUGH SET-THEORY, ALGEBRAIC STRUCTURES, IDEALS, REDUCTION, SYSTEMS
  • Karadeniz Technical University Affiliated: Yes

Abstract

In this paper, the concepts of set-valued homomorphism and strong set-valued homomorphism of a ring are introduced, and related properties are investigated. The notions of generalized lower and upper approximation operators, constructed by means of a set-valued mapping, which is a generalization of the notion of lower and upper approximation of a ring, are provided. We also propose the notion of generalized lower and upper approximations with respect to an ideal of a ring which is an extended notation of rough ideal introduced lately by Davvaz [B. Davvaz, Roughness in rings, Information Science 164 (2004) 147-163] in a ring and discuss some significant properties of them. (C) 2009 Elsevier Inc. All rights reserved.