Generalized Fuzzy Filters in Quantales and Their Approximations

Abstract

The present paper represents the behaviour of fuzzy filters and (α, β)-fuzzy filters in Quantale. The detailed study of relationship among crisp filter, fuzzy filters and (α, β)-fuzzy filters in quantale are discussed. An important part is played by quantale homomorphism which shows inverse image of (∈, ∈ ∨q)-fuzzy filter is again (∈, ∈ ∨q)-fuzzy filter. Under (α, β)-fuzzy map, it is seen that inverse image of (α, β)-fuzzy filter is again a fuzzy filter under quantale homomorphism. The relationship between fuzzy filter and (∈γ, ∈γ ∨qδ)-fuzzy filters are also discussed. Further, generalized approximation of fuzzy filter, (∈, ∈ ∨q)-fuzzy filter and (∈γ, ∈γ ∨qδ)-fuzzy filter are discussed.