ROUGHNESS IN (∊γ ∊γVqδ)-FUZZY SUBSTRUCTURES OF SEMIGROUPS BASED ON SET VALUED MAPPING.

Study of generalized roughness for fuzzy algebraic substrucures of semigroups has been initiated. Many different kinds of set valued maps are needed to preserve an algebraic substrucure while considering its lower and upper approximations. In the present paper generalized lower and upper approximations in (∊γ ∊γVqδ)-fuzzy ideals of semigroups have been investigated. An (∊γ ∊γVqδ)-fuzzy subset of a subsemigroup have two parts viz. lower and upper parts. Several properties of lower and upper approximations have been given for these. To conclud this paper, lower and upper approximations for (∊γ ∊γVqδ)-fuzzy interior ideals and (∊γ ∊γVqδ)-fuzzy bi-ideals have been discussed in semigroups. [ABSTRACT FROM AUTHOR]