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The aim of this paper is to introduce the notions of lower and upper approximation of a subset of a hyper BCK-algebra with respect to a hyper BCK-ideal. We give the notion of rough hyper subalgebra and rough hyper BCK-ideal, too, and we investigate their properties.

The purpose of this paper is the study of multivalued linear transformations of hypervector spaces (or hyperspaces) in the sense of Tallini. In this regards first we introduce and study various multivalued linear transformations of hyperspaces and then constitute the categories of hyperspaces with respect the different linear transformations of hyperspaces as the morphisms in these categories. Also, we construct some algebraic hyperoperations on Hom K (V,W), the set of all multivalued linear transformations from a hyperspace V into hyperspaces W, and obtaine their basic properties. Finally, we construct the fundamental functor F from HV K , category of hyperspaces over field K into V K , the category of clasical vector space over K.

In this paper by considering the notion of hyper pseudo BCK-algebra, we classify the set of all non-isomorphic hyper pseudo BCK-algebras of order 3. For this, we define the notion of simple and normalcondition and we characterize the all of hyper pseudo BCK-algebras of order 3 that satisfies these conditions.