In this paper by using the notiαon of anti fuzzy points and its besideness to andnon-quasi-coincidence with a fuzzy set the concepts of an anti fuzzy subalgebrasin BM-algebras are generalized and their inter-relations and related propertiesare investigated.

In this paper, by using the concept of belongingness (∈) and quasi-coincidence (q) between fuzzy points and fuzzy sets, we introduce (α, β)-fuzzy positive implicative ideals in BCK-algebras where α, β are any of {∈, q, ∈ ˅ q, ∈ ˄ q} with α ≠ ∈ ˄ q.

Using the belongs to relation (∈) and quasi-coincidence with relation (q) between fuzzy points and fuzzy sets, the concept of (α, β)-fuzzy subalgebras where α, β are any two of {∈, q, ∈∨ q, ∈ ∧ q} with α 6=∈ ∧ q is introduced, and related properties are

Topological structure of fuzzy soft sets has been recently introduced by Tanay and Kandemir in [23]. In this paper, we introduce the notion of soft quasi-coincidence for fuzzy soft sets and we use this notion to characterize fundamental concepts of fuzzy soft topological spaces such as fuzzy soft closures, fuzzy soft bases and fuzzy soft continuity. Some basic properties of this concept are als...

More general form of the notion of quasi-coincidence of a fuzzy point with a fuzzy subset is considered, and generalization of fuzzy fated of R0-algebras is discussed. The notion of an (∈,∈∨ qk)-fuzzy fated filter in a R0-algebra is introduced, and several properties are investigated. Characterizations of an (∈,∈∨ qk)-fuzzy fated filter in an R0-algebra are discussed. Using a collection of fate...

Using the notion of anti fuzzy points and its besideness to and non-quasi-coincidence with a fuzzy set, new concepts of an anti fuzzy subalgebras in BCK/BCI-algebras are introduced and their inter-relations and related properties are investigated in [3]. The notion of the new fuzzy subalgebra with thresholds are introduced and relationship between this notion and the new fuzzy subalgebra of a B...

small Polygroups are multi-valued systems that satisfy group-likeaxioms. Using the notion of “belonging ($epsilon$)” and “quasi-coincidence (q)” offuzzy points with fuzzy sets, the concept of ($epsilon$, $epsilon$ $vee$ q)-fuzzy subpolygroups isintroduced. The study of ($epsilon$, $epsilon$ $vee$ q)-fuzzy normal subpolygroups of a polygroupare dealt with. Characterization and some of the fundam...

In this paper we introduce various notions of continuous fuzzy proper functions by using the existing notions of fuzzy closure and fuzzy interior operators like Rτ -closure, Rτ -interior, etc., and present all possible relations among these types of continuities. Next, we introduce the concepts of α-quasi-coincidence, qα r -pre-neighborhood, qα r -pre-closure and qα r pre-continuous function in...

The concept of quasi-coincidence of an interval valued fuzzy set is considered. By using this idea, the notion of interval valued (α, β)−fuzzy sub-implicative ideals of BCIalgebras is introduced, which is a generalization of a fuzzy sub-implicative ideal. Also some related properties are studied and in particular, the interval valued (∈,∈ ∨q)−fuzzy subimplicative ideals in a BCI-algebra will be...