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...

first we show that the cosets of a fuzzy ideal μ in a bck-algebrax form another bck-algebra  x/μ (called the fuzzy quotient bck-algebra of x by μ). also we show thatx/μ is a fuzzy partition of x and we prove several some isomorphism theorems. moreover we prove that if the associated fuzzy similarity relation of a fuzzy partition p of a commutative bck-algebra iscompatible, then p is a fuzzy quo...

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...

In this paper, we have enhanced the notion of the direct product of two intuitionistic fuzzy sets to the notion of the generalised direct product oftwo doubt intuitionistic fuzzy subalgebras and two doubt intuitionistic fuzzy H-ideals of two BCK/BCI-algebras using max-min operations. Andwe study some interesting properties of such direct product of doubt intuitionistic fuzzy H-ideal...

In 1982, Pawlak introduced the concept of a rough set (see [6]). This concept is fundamental for the examination of granularity in knowledge. It is a concept which has many applications in data analysis (see [7]). Rough set theory is applied to semigroups and groups (see [4, 5]), and BCK-algebras (see [3]). In this paper, we apply the rough set theory to BCC-algebras, and we discuss the notion ...

The notion of (∈,∈ ∨q)-interval-valued fuzzy prime ideals in commutative BCK-algebras is introduced. Some characterization theorems in (∈,∈ ∨q)-interval-valued fuzzy prime ideals in commutative BCK-algebras are derived. Also we study relation between (∈,∈ ∨q)-interval-valued fuzzy prime ideal and (∈ ∨q)-interval-valued fuzzy level prime ideals. Characterization of interval-valued fuzzy set to b...

The notion of ∈-soft set and q-soft set based on a fuzzy set is introduced, and characterizations for an ∈-soft set and a q-soft set to be (idealistic) soft BCK/BCIalgebras are provided. Using the notion of (∈,∈∨ q)-fuzzy BCK/BCI subalgebras/ideals, characterizations for an ∈-soft set and a q-soft set to be (idealistic) soft BCK/BCI-algebras are established. AMS subject classifications: 06D72, ...

in this note first we define the notions of fuzzy positive implicativehyper bck-ideals of types 1,2,3 and 4. then we prove some theorems whichcharacterize the above notions according to the level subsets. also we obtainthe relationships among these notions, fuzzy (strong, weak, reflexive) hyperbck-ideals and fuzzy positive implicative hyper bck-ideals of types 5,6,7and 8. then, we define the no...

Abstract We explored new algebra structures such as ? —algebra, —subalgebra and —ideal in this work. In addition, we study their fundamental characteristics connections with other algebras, d/?/BCK - – subalgebras ideals. Also, some examples to illustrate our notions are given. MSC (2010): 20G05, 20D06, 20B30, 20B35