We consider the fuzzification of the notion of implicative hyper BCK-ideals, and then investigate several properties. Using the concept of level subsets, we give a characterization of a fuzzy implicative hyper BCK-ideal. We state a relation between a fuzzy hyper BCK-ideal and a fuzzy implicative hyper BCK-ideal. We establish a condition for a fuzzy hyper BCK-ideal to be a fuzzy implicative hype...

Bipolar-valued fuzzification of the notion of implicative hyper BCK-ideals is considered. Using the concepts of positive and negative lever sets, a characterization of a bipolar fuzzy implicative hyper BCK-ideal is provided. A relation between a bipolar fuzzy hyper BCK-ideal and a bipolar fuzzy implicative hyper BCK-ideal is established. A condition for a bipolar fuzzy hyper BCK-ideal to be a b...

In this paper we introduce the concepts of hyper P -semisimple Ialgebra and Abelian hyper I-algebra and we state and prove some related results. The hyper p-semi simple I-algebras is a generalization of p-semisimple BCI-algebras and a subclass of hyper I-algebras. Specially we show that every Abelian hyper I-algebra is a hyper psemisimple I-algebra and a commutative canonical hypergroup. In fol...

In this paper we study an outer measure on MV -algebras. In Section 1 the definition of MV -algebra and Mundici theorem are remind. In Section 2 there is defined an outer measure, measurable elements and there is proved Choquet lema for this structure. In conclusion some properties of measurable elements are resumed.

The purpose of this paper is to apply the theory of MV polytopes to the study of components of Lusztig’s nilpotent varieties. Along the way, we introduce reflection functors for modules over the non-deformed preprojective algebra of a quiver.

In this paper, we investigate related properties of some particular derivations and give some characterizations of additive derivations in MV-algebras. Then, we obtain that the fixed point set of additive derivations is still an MV-algebra. Also, we study Boolean additive derivations and their adjoint derivations. In particular, we get that the fixed point set of Boolean addition derivations an...

We present a preliminary study of applying the concepts of algebraic geometry over fields to the theory of MV-algebras. We proceed along lines similar to B. Plotkin and others where an algebraic geometry over groups is developed.

Micali and Valiant proposed a mechanism for combinatorial auctions that is dominant-strategy truthful, guarantees reasonably high revenue, and is very resilient against collusions. Their mechanism, however, uses as a subroutine the VCG mechanism, that is not polynomial time. We propose a modification of their mechanism that is efficient, while retaining their collusion resilience and a good fra...