Generalized Fuzzy Filters in Quantales and Their Approximations

摘要

The present paper represents the behaviour of fuzzy filters and (alpha, beta)-fuzzy filters in Quantale. The detailed study of relationship among crisp filter, fuzzy filters and (alpha, beta)-fuzzy filters in quantale are discussed. An important part is played by quantale homomorphism which shows inverse image of (is an element of, is an element of Vq)-fuzzy filter is again (is an element of, is an element of Vq)-fuzzy filter. Under (alpha, beta)-fuzzy map, it is seen that inverse image of (alpha, beta)-fuzzy filter is again a fuzzy filter under quantale homomorphism. The relationship between fuzzy filter and (is an element of(gamma) is an element of(gamma) Vq(delta))-fuzzy filters are also discussed. Further, generalized approximation of fuzzy filter, (is an element of, is an element of Vq)-fuzzy filter and (is an element of(gamma), is an element of(gamma) Vq(delta))-fuzzy filter are discussed.