To investigate implicative filters of hoops furthermore, we apply n-fold theory to (?, ?)-hesitant fuzzy and introduce the notion (?,?)-hesitant filters, obtain some conditions for a filter be filter. We also study preimage image filters.

In this paper, we interrelate the intuitionistic fuzzification of the concept of BCI-(positive implicative, implicative, commutative) ideals in BCI-algebras and investigate some of their properties.

In this paper, first we introduce the notions of k-nilpotent (solvable) ideals and BCK-algebras. Specially, show that every commutative ideal is 1-nilpotent (solvable). Second, state an equivalent condition to k-nilpotency (solvablity) BCK-algebra. Finally, study n-fold 2-nilpotent BCK-algebras as a generalization BCK-algebras, relation between these two concepts. Basically, compare solvable (B...

In this note first we define the notion of dual positive implicative hyper Kideal of type 4, where for simplicity is written by DPIHKI − T4. Then we give some related results. Finally we determine all of hyper K-algebras of order 3, which have D1 = {1}, D2 = {1, 2} or D3 = {0, 1} as a DPIHKI − T4.

This paper is devoted to the foldness theory of implicative ideals in BCK-algebras. We use the fuzzy point concept to give some characterizations of fuzzy n-fold implicative ideals and establish some relationships with various n-fold ideals. We also construct some algorithms for studying the foldness of implicative ideals in BCK-algebras. AMS Mathematics Subject Classification: 06F35, 13A15, 8A...

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...

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.

In this paper, we present the notions of cubic (weak) implicative hyper BCK-ideals of hyper BCKalgebras and then we present some results which characterize the above notions according to the level subsets. In addition, we obtain the relationship among these notions, cubic positive implicative hyper BCK-ideals of types-1, 2...8 and obtain some related results.AMS (2010): 06F35.

in this paper rst we dene the notions of positive implicativehyper mv -ideals of types 1,2,3 and 4 in hyper mv -algebras and we investigatethe relationship between of them . then by some examples we show that thesenotions are not equivalent. finally we give some relations between these notionsand the notions of (weak) hyper mv -ideals and (weak) hyper mv -deductivesystems of hyper mv -algebras.