Generalised roughness in (∈,∈Vq)-fuzzy substructures of LA-semigroups

LA-semigroups are non-associative sturctures of great importance. Study of generalised roughness for fuzzy algebraic substrucures of LA-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 generalised lower and upper approximations in (ϵ,ϵ Vԛ)- fuzzy ideals of LA-semigroups have been investigated. An (ϵ,ϵ Vԛ)- fuzzy subset of an LA-subsemigroup has two parts, viz. lower and upper parts. Many properties of lower and upper approximations have been given for these. In conclusion, lower and upper approximations for (ϵ,ϵ Vԛ)- fuzzy interior ideals and (ϵ,ϵ Vԛ)- fuzzy bi-ideals have been discussed in LA-semigroups.