in this paper, we define the notions of fuzzy congruence relations and fuzzy convex subalgebras on a commutative residuated lattice and we obtain some related results. in particular, we will show that there exists a one to one correspondence between the set of all fuzzy congruence relations and the set of all fuzzy convex subalgebras on a commutative residuated lattice. then we study fuzzy...

In this paper, the notions of fuzzy soft subalgebra and fuzzy soft convex subalgebra of a residuated lattice are introduced and some related properties are investigated. Then, we define fuzzy soft congruence on a residuated lattice and obtain the relation between fuzzy soft convex subalgebras and fuzzy soft congruence relations on residuated lattices. The concept of soft homomorphism is defined...

In this paper, we apply the concept of t-norm T to fuzzy structure of B-algebras. The notion of a fuzzy B-subalgebra of B-algebras with respect to t-norm is introduced and several related properties are investigated. The direct product and T -product of T -fuzzy subalgebra of B-algebra is investigated.

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 was introduced, and related properties were investigated in [3]. As a continuation of the paper [3], in this paper, the notion of a fuzzy subalgebra with thresholds is introduced, and its...

in this note the notion of interval-valued fuzzy b-algebras (briefly,i-v fuzzy b-algebras), the level and strong level b-subalgebra is introduced.then we state and prove some theorems which determine the relationshipbetween these notions and b-subalgebras. the images and inverse images ofi-v fuzzy b-subalgebras are defined, and how the homomorphic images andinverse images of i-v fuzzy b-subalge...

In this paper some properties of the uniformity topology on a BCI-algebras are discussed. Keywords—(Fuzzy) ideal, (Fuzzy) subalgebra, Uniformity, clopen sets.

Based on the theory of intuitionistic fuzzy sets, the concepts of intuitionistic fuzzy subalgebras with thresholds (λ, μ) and intuitionistic fuzzy ideals with thresholds (λ, μ) of BCI-algebras are introduced and some properties of them are discussed. Keywords—BCI-algebra, intuitionistic fuzzy set, intuitionistic fuzzy subalgebra with thresholds (λ, μ), intuitionistic fuzzy ideal with thresholds...

We introduce the notion of sensible fuzzy ideals of BCK-algebras with respect to a t-conorm and investigate some of their properties. We give the conditions for a sensible fuzzy subalgebra with respect to a t-conorm to be a sensible fuzzy ideal with respect to a t-conorm. Some properties of the direct product and S-product of fuzzy ideals of BCK-algebras with respect to a t-conorm are also disc...

The notion of bipolar fuzzy subalgebras and bipolar fuzzy ideals of a BCK/BCI-algebra is introduced, and several properties are investigated. Relations between a bipolar fuzzy subalgebra and a bipolar fuzzy ideal are given. A condition for bipolar fuzzy subalgebra to be a bipolar fuzzy ideal is provided, and the characterizations of a bipolar fuzzy ideal are stated. The concept of equivalence r...

In this paper, the notions of L-fuzzy subalgebra degree and L-subalgebras on an effect algebra are introduced some characterizations given. We use four kinds cut sets L-subsets to characterize degree. induce convexity by degree, we prove that a morphism between two algebras is preserving mapping monomorphism convex-to-convex mapping. Finally, it proved set all can form L-convexity, its L-convex...