“…Several examples are provided from different biology points of view, and it is shown that the theory of hyperstructures exactly fits the inheritance issue. In [8], Al Tahan and Davvaz presented examples of five different types of Non-Mendelian inheritance and studied their relation with hyperstucture theory. They made some hypothetical crosses for the n-hybrid case for both simple and incomplete inheritances and studied their relations with hyperstructures.…”
Section: Applications Of Hyperstructures In Biology Physics and Chemmentioning
I am working on algebraic hyperstructures from 1995. During the last twenty years, I together with my students and co-authors studied and developed the theory of algebraic hyperstructures in many directions. In particular, we tried to find real examples of hyperstructures in nature. In this paper we review some parts of these works such as (1) Fundamental relations on hyperstructures; (2) Fuzzy sets and hyperstructures; (3) Rough sets and hyperstructures; (4) Topology and hyperstructures; (5) Number theory and hyperstructures; (6) n-ary hypergroups and there extension to hyperrings and hypermodules; (7) Applications of hyperstructures in biology, physics and chemistry.
“…Several examples are provided from different biology points of view, and it is shown that the theory of hyperstructures exactly fits the inheritance issue. In [8], Al Tahan and Davvaz presented examples of five different types of Non-Mendelian inheritance and studied their relation with hyperstucture theory. They made some hypothetical crosses for the n-hybrid case for both simple and incomplete inheritances and studied their relations with hyperstructures.…”
Section: Applications Of Hyperstructures In Biology Physics and Chemmentioning
I am working on algebraic hyperstructures from 1995. During the last twenty years, I together with my students and co-authors studied and developed the theory of algebraic hyperstructures in many directions. In particular, we tried to find real examples of hyperstructures in nature. In this paper we review some parts of these works such as (1) Fundamental relations on hyperstructures; (2) Fuzzy sets and hyperstructures; (3) Rough sets and hyperstructures; (4) Topology and hyperstructures; (5) Number theory and hyperstructures; (6) n-ary hypergroups and there extension to hyperrings and hypermodules; (7) Applications of hyperstructures in biology, physics and chemistry.
“…. ) were widely studied from the theoretical point of view and for their applications to many subjects of pure and applied mathematics (see [1,2,3,4,6,7,8,10,12,20,26,27]). There exists different kinds of hyperrings.…”
The class of constacyclic codes plays an important role in the theory or error-correcting codes. They are considered as a remarkable generalization of cyclic codes. In this paper, we study constacyclic codes over finite Krasner hyperfields in which we characterize them by their generating polynomial. Moreover, we study the dual of these codes by finding their parity check polynomial.
“…The class of algebraic hyperstructures is larger than that of algebraic structures where the operation on two elements in the latter is again an element, whereas the hyperoperation of two elements in the first class is a non-void set. For details about hyperstructure theory and its applications, we refer to the articles [12][13][14][15] and the books [16][17][18]. A generalization of algebraic hyperstructures, known as weak hyperstructures (H v -structures), was introduced in 1994 by Vougiouklis [19].…”
Neutrosophy, the study of neutralities, is a new branch of Philosophy that has applications in many different fields of science. Inspired by the idea of Neutrosophy, Smarandache introduced NeutroAlgebraicStructures (or NeutroAlgebras) by allowing the partiality and indeterminacy to be included in the structures’ operations and/or axioms. The aim of this paper is to combine the concept of Neutrosophy with hyperstructures theory. In this regard, we introduce NeutroSemihypergroups as well as NeutroHv-Semigroups and study their properties by providing several illustrative examples.
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