A simple method is described, to prove some theorems for simple hyper K-algebras and to study positive implicative hyper K-ideals, weak (implicative ) hyper K-ideals in simple hyper K-algebras . Beside, some results on positive implicative and (weak) implicative simple hyper K-algebras are presented. Finally classification of simple hyper Kalgebras of order 4, which are satisfied in conditions ...

in this paper we characterize hyper mv -algebras in which 0 or1 are scalar elements . we prove that any nite hyper mv -algebra that 0is a scaler element in it, is an mv -algebra. finally we characterize hypermv -algebras of order 2 and order 3.

In this paper we characterize hyper MV -algebras in which 0 or1 are scalar elements . We prove that any nite hyper MV -algebra that 0is a scaler element in it, is an MV -algebra. Finally we characterize hyperMV -algebras of order 2 and order 3.

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.

We consider the notion of an isomorphism between two hyper BCI-algebras and obtain all of the hyper BCI-algebras of order 3. It is shown that there exist 14 proper hyper BCI-algebras and 5 proper weak hyper BCI-algebras of order 3 up to isomorphism. Finally, further study on the theory of hyper BCI-algebra and its related hyper structure and applications of our results in information sciences a...