Algebraic Hyperstructures and Applications

Abstract

Algebraic Hyperstructures and Applications Downloaded from www.worldscientific.com by UNIVERSITY OF BIRMINGHAM on 08/27/15. For personal use only. ALGEBRAIC HYPER�RU�URESAND APPLICATIONS Algebraic Hyperstructures and Applications Downloaded from www.worldscientific.com by UNIVERSITY OF BIRMINGHAM on 08/27/15. For personal use only. This page is intentionally left blank Algebraic Hyperstructures and Applications Downloaded from www.worldscientific.com by UNIVERSITY OF BIRMINGHAM on 08/27/15. For personal use only.

Interval Valued Intuitionistic (S, T)–fuzzy H v –submodules

“…As it is well known [12], a hyperstructure is a non-empty set H together with a map · : H × H → P * (H), called a hyperoperation, where P * (H) is the family of all non-empty subsets of H. The image of pair (x, y) is denoted by x · y. If x ∈ H and A, B ⊆ H, then by A · B, A · x and x · B we mean…”

“…Hypersructures have many applications to several branches of both pure and applied sciences (see for example [4] and [5]). Vougiouklis [12,10] introduced a new class of hyperstructures called now H v -structures, and Davvaz [7] surveyed the theory of H v -structures. After the introduction of fuzzy sets by Zadeh [14], there have been a number of generalizations of this fundamental concept.…”

A further study on ordered regular equivalence relations in ordered semihypergroups

“…Later on, people have observed that hyperstructures have many applications to several branches of both pure and applied sciences (see [2][3][4][5]). In particular, a semihypergroup is the simplest algebraic hyperstructure which possess the properties of closure and associativity.…”

Operations on hyperideals in ordered Krasner hyperrings

“…The hyperstructure theory and its applications have been investigated by the contribution of many mathematicians. The principal notions of hyperstructure theory can be found in [9,10,11,12,14,29].…”