The lower and upper approximations in a quotient hypermodule with respect to fuzzy sets ?
This paper provides a continuation of ideas presented by Davvaz and Mahdavipour [B. Davvaz, M. Mahdavipour, Roughness in modules, Inform. Sci. 176 (2006) 36583674]. The notion of hypermodule is a generalization of the notion of module. In this paper, we consider the quotient hypermodule M/A M / A and interpret the lower and upper approximations as subsets of the quotient hypermodule M/A 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.
upper approximation hypermodule fuzzy set rough set lower approximation