Vague BCK/BCI-algebras

In this note, by using the concept of vague sets, the notion of vague $BCK/BCI$-algebra is introduced. And the notions of $\alpha$-cut and vague-cut are introduced and the relationships between these notions and crisp subalgebras are studied

An investigation on the nn-fold IVRL-filters in triangle algebras

summary:The present study aimed to introduce $n$-fold interval valued residuated lattice (IVRL for short) filters in triangle algebras. Initially, the notions of $n$-fold (positive) implicative IVRL-extended filters and $n$-fold (positive) implicative triangle algebras were defined. Afterwards, several characterizations of the algebras were presented, and the correlations between the $n$-fold IVRL-extended filters, $n$-fold (positive) implicative algebras, and the Gödel triangle algebra were discussed

Neutrosophic filters in BE-algebras

Inthispaper, weintroducethenotionof(implicative)neutrosophicfilters in BE-algebras. The relation between implicative neutrosophic filters and neutrosophic filters is investigated and we show that in self distributive BE-algebras these notions are equivalent

(α,β,T)-Convex vague sets

By using vague sets we generalize the notion of convex sets and introduce the notion of (α, β ,T )-convex vague sets and study their properties, where T is a triangular norm on [0, 1].

Some properties of residual mapping and convexity in ∧-hyperlattices

The aime of this paper is the study of residual mappings and convexity in hyperlattices. To get this point, we study principal down set in hyperlattices and we give some conditions for a mapping between two hyperlattices to be equivalent with a residual maping. Also, we investigate convex subsets in ∧-hyperlattices

Soft n-Ary Subgroups

AbstractSoft set theory plays a vital role in solving many complicated problems with inherited uncertainty. An n-ary algebraic systems is a generalization of algebraic structures and it is the most natural way for the further development, deeper understanding of their properties. In this paper, we apply soft set theory to an n-ary algebraic systems and introduce the notions of soft n-ary groups and soft n-ary subgroups. Further, some operations on soft sets are extended to the former. Finally, we provide the characterization of soft n-ary subgroups over an n-ary group (G,f) and study their related properties