Multi fuzzifying topology

In this paper, characterization of stratified and transitive L-topologies and multi-fuzzifying topologies are introduced. First we introduce 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 -algebra. Second, we introduce the concepts of multi-fuzzifying topology, -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 a completely 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.