N-ary Relations of Association in Class Diagrams: Design Patterns

Application of fundamental relations on n-ary polygroups

The class of  $n$-ary polygroups is a certain subclass of $n$-ary hypergroups, a generalization of D{"o}rnte $n$-arygroups and  a generalization of polygroups. The$beta^*$-relation and the $gamma^*$-relation are the smallestequivalence relations on an $n$-ary polygroup $P$ such that$P/beta^*$ and $P/gamma^*$ are an $n$-ary group and acommutative $n$-ary group, respectively. We use the $beta^*$-...

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...

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

Extending UML to Visualize Design Patterns In Class Diagrams

A design pattern describes a general solution to a design problem that recurs repeatedly in many projects. Software designers adapt the pattern solution to their specific project. Design patterns are usually modeled using UML. However, UML does not keep track of pattern-related information when a design pattern is applied or composed with other patterns. Thus, it is hard for a designer to ident...

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...