In this paper, we introduce the notion of hyper pseudo B C K - algebras, which is a generalization of pseudo BCK -algebras and hyper BCK -algebras and we investigates some related properties. In follow, we de ne some kinds of hyper pseudo BCK -ideals of a hyper pseudo BCK - algebra and we find the relations among them. Finally, we characterize the hyper pseudo BCK -ideals of type 4 generated by...

Fuzzy (weak) implicative hyper K-ideals are introduced, and relations among fuzzy weak implicative hyper K-ideals, fuzzy implicative hyper K-ideals and fuzzy hyper K-ideals are discussed.

A twistor construction of the hierarchy associated with the hyper-KK ahler equations on a metric (the anti-self-dual Einstein vacuum equations, ASDVE, in four dimensions) is given. The recursion operator R is constructed and used to build an innnite-dimensional symmetry algebra and in particular higher ows for the hyper-KK ahler equations. It is shown that R acts on the twistor data by multipli...

The study of BCK-algebras was initiated by K. Iséki in 1966 as a generalization of the concept of set-theoretic difference and propositional calculus. The hyperstructure theory (called also multialgebras) is introduced in 1934 by Marty [6] at the 8th congress of Scandinavian Mathematicians. Around the 40’s, several authors worked on hypergroups, especially in France and in the United States, bu...

Recall that a (hyper)graph is d-degenerate if every of its nonempty subgraphs has a vertex of degree at most d. Every d-degenerate (hyper)graph is (easily) (d + 1)colorable. A (hyper)graph is almost d-degenerate if it is not d-degenerate, but every its proper subgraph is d-degenerate. In particular, if G is almost (k − 1)-degenerate, then after deleting any edge it is k-colorable. For k ≥ 2, we...

Assume that n and k are positive integers with n ≥ 2k + 1. A non-hamiltonian graph G is hypo hamiltonian if G − v is hamiltonian for any v ∈ V (G). It is proved that the generalized Petersen graph P (n, k) is hypo hamiltonian if and only if k = 2 and n ≡ 5 (mod 6). Similarly, a hamiltonian graph G is hyper hamiltonian if G−v is hamiltonian for any v ∈ V (G). In this paper, we will give some nec...

In this note we consider the notion of intuitionistic fuzzy (weak) dual hyper K-ideals and obtain related results. Then we classify this notion according to level sets. After that we determine the relationships between intuitionistic fuzzy (weak) dual hyper K-ideals and intuitionistic fuzzy (weak) hyper K-ideals. Finally, we define the notion of the product of two intuitionistic fuzzy (weak) du...