The lower and upper approximations in a quotient hypermodule with respect to fuzzy sets

  • Authors:

  • Osman Kazancı;Sultan Yamak;B. Davvaz

  • Affiliations:

  • Department of Mathematics, Karadeniz Technical University, 61080 Trabzon, Turkey;Department of Mathematics, Karadeniz Technical University, 61080 Trabzon, Turkey;Department of Mathematics, Yazd University, Yazd, Iran

  • Venue:
  • Information Sciences: an International Journal
  • Year:
  • 2008

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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.