Characterizations of fuzzy ideals of a pseudo-BCK algebra are established. Conditions for a fuzzy set to be a fuzzy ideal are given. Given a fuzzy set μ, the least fuzzy ideal containing μ is constructed. The homomorphic properties of fuzzy ideals of a pseudoBCK algebra are provided. Finally, characterizations of Noetherian pseudo-BCK algebras and Artinian pseudo-BCK algebras via fuzzy ideals a...

We study the properties and relations of fuzzy pseudo-filters of pseudo-BCK algebras. After we discuss the equivalent conditions of fuzzy normal pseudo-filter of pseudo-BCK algebra (pP), we propose fuzzy implicative pseudo-filter and its relation with fuzzy Boolean filter of (bounded) pseudo-BCK algebras (pP). Then two open problems: “In pseudo-BCK algebra or bounded pseudo-BCK algebra, Is the ...

Using the notion of bipolar-valued fuzzy sets, the concepts of bipolar fuzzy (weak, s-weak, strong) hyper BCK-ideals are introduced, and their relations are discussed in [3]. Further properties are investigated in this article. We show that if Φ = (H ;μΦ , μ N Φ ) is a bipolar fuzzy (weak, strong) hyper BCK-ideal of a hyper BCK-algebra H, then the set I := {x ∈ H | μΦ(x) = μΦ(0), μΦ (x) = μΦ (0...

The notion of intuitionistic fuzzy positive implicative hyper BCK-ideals of type-1, 2... 8 of hyper BCK-algebras was introduced in 2012 by Durga Prasad, Satyanarayana and Ramesh. In this paper, we investigate some related properties of intuitionistic fuzzy positive implicative hyper BCK-ideals of types-1. We characterize positive implicative Artinian (shortly, PI-Artinian) hyper BCK-algebras of...

The notions of $${{\mathcal {N}}}$$ -ideal types $$(\in , \in )$$ and \! \vee \, {q})$$ soft $${\mathcal N}_{\in }$$ -set, {N}}}_{q}$$ {N}}}_{\in {q}}$$ -subalgebra in BCK/BCI-algebra are introduced, several properties investigated. Characterizations N}$$ discussed.

The aim of this paper is to apply the concept of interval-valued intuitionistic fuzzy set to implicative ideals and commutative ideals in BCK-algebras and introduced the new notion of interval-valued intuitionistic fuzzy implicative ideals in BCK-algebras and interval-valued intuitionistic fuzzy commutative ideals in BCK-algebras and related properties are investigated.

we present some connections between the max-min general fuzzy automaton theory and the hyper structure theory. first, we introduce a hyper bck-algebra induced by a max-min general fuzzy automaton. then, we study the properties of this hyper bck-algebra. particularly, some theorems and results for hyper bck-algebra are proved. for example, it is shown that this structure consists of different ty...

Based on the theory of a falling shadow which was first formulated by Wang [15], a theoretical approach of the pseudo ideal structure in pseudo d-algebras is established. Several properties are investigated, and relations among a falling pseudo d-subalgebra, a falling pseudo BCK-ideal and a falling pseudo d-ideal are discussed. A characterization of a falling pseudo d-ideal is provided. Conditi...

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...