[PDF] Top 20 Fuzzy structures of PI(≪,⫅,⫅)BCK ideals in hyper BCK algebras

... a hyper BCK-algebra unless otherwise specified. We place a bar over a symbol to denote a fuzzy set, so ¯ A , ¯ B , ... all represent fuzzy sets in H . We write ¯ A(x) , a number in [ 0 , 1 ] , ... See full document

... intuitionistic fuzzy positive implicative hyper BCK-ideals of type-1, ...of hyper BCK-algebras was introduced in 2012 by Durga Prasad, Satyanarayana and ...intuitionistic ... See full document

... logical algebras introduced by Is´eki in 1966 see 1– ...of BCK-algebras see 4. The concept of fuzzy sets was introduced by Zadeh ...algebraic structures such as semigroups, groups, ... See full document

... of BCK-algebras was initiated by Imai and Iseki in 1966 as a generalization of both classical and non-classical positional ...implicative ideals in ...intuitionistic fuzzy positive implicative ... See full document

... of fuzzy sets was first initiated by Zadeh([36]) in ...algebraic structures such as group, semigroup, ring, vector spaces ...introduced BCK-algebras as a generalization of notion of the ... See full document

... a hyper-measurable structure on U if B is a σ-field in PU and ˙ U ⊆ ...a hyper-measurable structure PU, B on U, a random set on U is defined to be a mapping ξ : Ω → PU which is A-B measurable, that ... See full document

... of fuzzy congruence in some alge- braic structures, we specially study fuzzy congruence in ...of fuzzy ideals and the set of fuzzy congruences in ...each fuzzy ideal µ, ... See full document

... ν x ∗ y n ≥ min ν x ∗ y n + 1 ∗ z , ν(z) . (4.13) Thus ν is an n-fold fuzzy positive implicative ideal of X. Since the chain (4.9) is not ter- minating, ν has a strictly descending sequence of values. This ... See full document

... a fuzzy hyper BCK-ideal of H ...a hyper BCK-ideal of H for any t ∈ [ 0 , 1 ] ...implicative hyper BCK-ideal of H by Theorem ...a fuzzy multiply positive implicative ... See full document

... so that µ(x) = µ( 0 ) . Hence x ∈ I , which shows that I is a hyper BCK-ideal of H . Now let x,y ∈ H be such that x ◦(y ◦ x) I . Then for every b ∈ x ◦ (y ◦ x) there exists w ∈ I such that b w . Thus µ(b) ≥ ... See full document

... of BCK-algebras see [6-8]. If A is a BCK-algebra, then the relation ≤ defined by x  y iff is a partial order on A (which will be called the natural order on A; with respect to this order 1 is the ... See full document

... In this paper, we introduce the notion of a commutative pseudo valuation on a BCK-algebra, and investigate its characterizations. We discuss the relationship between a pseudo valuation and a commutative pseudo ... See full document

... of BCK/BCI- ...a BCK/BCI- algebra and provide several ...a BCK/BCI-algebra to be ...a BCK-algebra is a connected graph in which every nonzero vertex is adjacent to 0, but the associative graph ... See full document

... of fuzzy set to generalize the notion of a member belonging to a set ...of fuzzy set has been applied to various algebraic ...abstract algebras, BCK- algebra and BCI- ...of fuzzy set to ... See full document

... include Algebras re- lated to logic (BCK, BCI, BCC-algebras, Hilbert algebras, and implication algebras), soft algebraic structures, Algebraic Hyperstructures, Theory of ... See full document

... a hyper BCK-algebra and let I be a nonempty subset of H ...a hyper BCC-ideal of type 1 if and only if I is a hyper BCK-ideal of H, (ii) I is a hyper BCC-ideal of type 2 if and ... See full document

... Proof. Suppose that μ is a fuzzy ideal of X with respect to S. Since L(μ, α) is nonempty, there exists x ∈ L(μ,α). Now, from (SF1), μ(0) ≤ μ(x) ≤ α, we have 0 ∈ L(μ,α). Let x, y ∈ X be such that x ∗ y ∈ L(μ, α) ... See full document

... of hyper K-algebras that are necessary for this paper, and for more details we refer to [2, ...a hyper operation “ ◦ ,” that is, ◦ is a function from H × H to ᏼ ∗ (H ) = ᏼ(H ) \ {∅} ... See full document

... a BCK-algebra X, we let x ∧ y = y ∗ (y ∗ x) and in a bounded BCK-algebra X , we let x ∨ y = N (N x ∧ N y), for all x, y ∈ X ...commutative BCK-algebra X , ∨ is the least upper bound and ∧ is the ... See full document

... abstract algebras including the well-known BCK- algebras and several larger classes including the class of d-algebras which is a generalization of BCK-algebras, then it is ... See full document