Multi fuzzifying topology

In this paper, characterizations of stratified and transitive L -topologies and multi-fuzzifying topology are introduced. First weintroduce the concepts of stratified and transitive L -co-topology and stratified and transitive L -closure operator to characterize the concept of stratified and transitive L -topology, where L is a complete MV -algebra. Second, we introduce the concepts of multi-fuzzifying topology, L-fuzzifying co-neighborhood system, L-fuzzifying co-contiguity, L-fuzzifying interior operator and L -fuzzifying closure operator to characterize multi-fuzzifying topology, where L is acompletely distributive complete residuated lattice satisfying the double negation law, characterizations of stratified and transitive L -topology are introduced where L is a complete MV -algebra, characterizations of multi-fuzzifying topology are introduced where L is a completely distributive complete residuated lattice in which the double negation law is satisfied.