A brief survey on algebraic hyperstructures: Theory and applications

I am working on algebraic hyperstructures from 1995. During the last twenty years, I together with my stu- dents and co-authors studied and developed the theory of algebraic hyperstructures in many directions. In par- ticular, we tried to nd real examples of hyperstructures in nature. In this paper we review some parts of these works such as (1) Fundamental relations on hyperstruc- tures; (2) Fuzzy sets and hyperstructures; (3) Rough sets and hyperstructures; (4) Topology and hyperstructures; (5) Number theory and hyperstructures; (6) n-ary hy- pergroups and there extension to hyperrings and hyper- modules; (7) Applications of hyperstructures in biology, physics and chemistry.