Application of fundamental relations on n-ary polygroups

n-ary polygroups

polygroups are multivalued systems that satisfy group like axioms. in this paper the class of n-arypolygroups is introduced. the concepts of n-ary normal subpolygroups and strong homomorphisms of n-arypolygroups are adopted. with respect to these concepts the isomorphism theorems for n-ary polygroups arestated and proved. finally, we will consider the fundamental relation  * defined on an n-ar...

Algebraic Hyperstructures of Soft Sets Associated to N-ary Polygroups

This paper concerns a relationship between soft sets and n-ary polygroups. We consider the notion of an n-ary polygroup as a generalization of a polygroup and apply the notion of soft sets to n-ary polygroups. Some related notions are defined and several basic properties are discussed by using the soft set theory. Furthermore, we propose the homomorphism of n-ary polygroups and investigate the ...

Neutral Elements, Fundamental Relations and n-Ary hypersemigroups

The main tools in the theory of n-ary hyperstructures are the fundamental relations. The fundamental relation on an n-ary hypersemigroup is defined as the smallest equivalence relation so that the quotient would be the n-ary semigroup. In this paper we study neutral elements in n-ary hypersemigroups and introduce a new strongly compatible equivalence relation on an n-ary hypersemigroup so that ...

On $n$-ary Hypergroups and Fuzzy $n$-ary Homomorphism

Closed Pattern Mining from n-ary Relations

In this paper, we address the problem of closed pattern mining from n-ary relations. We propose CnS-Miner algorithm which enumerates all the closed patterns of the given n-dimensional dataset in depth first manner satisfying the user specified minimum size constraints. From the given input, the CnS-Miner algorithm generates an n-ary tree and visits the tree in depth first manner. We have propos...

Embracing n-ary Relations in Network Science

Most network scientists restrict their attention to relations between pairs of things, even though most complex systems have structures and dynamics determined by n-ary relation where n is greater than two. Various examples are given to illustrate this. The basic mathematical structures allowing more than two vertices have existed for more than half a century, including hypergraphs and simplici...