The notions of bipolar fuzzy hyper MV-subalgebras, (weak) bipolar fuzzy hyper MV-deductive system and precisely weak bipolar fuzzy hyper MV-deductive system are introduced, and their relations are investigated. Characterizations of bipolar fuzzy hyper MV-subalgebras and weak bipolar fuzzy hyper MV-deductive systems are provided.

The foldness of PI( , ⊆, ⊆)BCK -ideals and PI( , , )BCK -ideals is considered. The fuzzy version of such notions is also discussed.

The foldness of PI( , , ⊆)BCK -ideals and PI(⊆, ⊆, ⊆)BCK -ideals is considered, and their properties are investigated. Hyper homomorphic inverse image of PI( , , ⊆)BCK -ideals, PI( , ⊆, ⊆)BCK -ideals, PI(⊆, ⊆, ⊆)BCK -ideals, and PI( , , )BCK -ideals are discussed.

The aim of this paper is to lay a foundation for providing a soft algebraic tool in considering many problems that contain uncertainties. In order to provide these soft algebraic structures, the notion of int-soft positive implicative ideals is introduced, and related properties are investigated. Relations between an int-soft ideal and an int-soft positive implicative ideal are established. Cha...

The notion of n-fold positive implicative filter in a lattice implication algebra is introduced, and related properties are investigated. Relations among a filter, an n-fold implicative filter and an n-fold positive implicative filter are stated. Characterizations of n-fold positive implicative filter are given, and the extension property for n-fold positive implicative filter is established.

in this paper we define the notions of ultra and involution ideals in bck-algebras. then we get the relation among them and other ideals as (positive) implicative, associative, commutative and prime ideals. specially, we show that in a bounded implicative bck-algebra, any involution ideal is a positive implicative ideal and in a bounded positive implicative lower bck-semilattice, the notions of...

We consider the fuzzification of the notion of an n-fold positive implicative ideal. We give characterizations of an n-fold fuzzy positive implicative ideal. We establish the extension property for n-fold fuzzy positive implicative ideals, and state a characterization of PIn-Noetherian BCK-algebras. Finally we study the normalization of n-fold fuzzy positive implicative ideals. 2000 Mathematics...

In this paper, we define the notions of ultra and involution ideals in $BCK$-algebras. Then we get the relation among them and other ideals as (positive) implicative, associative, commutative and prime ideals. Specially, we show that in a bounded implicative $BCK$-algebra, any involution ideal is a positive implicative ideal and in a bounded positive implicative lower $BCK$-semilattice, the not...

The notion of a positive implicative pseudo-valuation on a BCKalgebra is introduced, and its characterizations are investigated. The relationship between a pseudo-valuation and a positive implicative pseudovaluation is examined. Reduction property for a positive implicative pseudo-valuation is established. Mathematics Subject Classification: 06F35, 03G25