Redefined fuzzy Hυ-submodules and many valued implications

This paper considers a relationship between fuzzy sets and algebraic hyperstructures. A generalization of ideas presented by Davvaz [B. Davvaz, Fuzzy H-upsilon-submodules, Fuzzy Sets Syst. 117 (2001) 477-484] and Bhakat and Das [S.K. Bhakat, P. Das, (epsilon, epsilon V q)-fuzzy subgroup, Fuzzy Sets Syst. 80 (1996) 359-368], is presented. In fact, the main purpose of this paper is to introduce and study a new sort of fuzzy H-upsilon-submodule of an H-upsilon-module called (epsilon, epsilon V q)-fuzzy H-upsilon-submodules. These fuzzy H-upsilon-submodules are characterized by their level H-upsilon-submodules. The concept of a fuzzy H-upsilon-submodule with thresholds is introduced, and some interesting properties are investigated. (C) 2006 Elsevier Inc. All rights reserved.