On Some Generalized Relations

Crisp set relations have been generalised to fuzzy relations, intuitionistic fuzzy relations, rough relations and also some hybrid relations related to these notions. Rough set is a fruitful model to capture imprecision in data. There are two approaches to the rough set notion. The approach by Pawlak is topological by nature and the approach of Iwinski is algebraic by nature. In this paper we define several generalised relations where the rough set definition considered is that of Iwinski and prove many properties of these relations. These relations can be used in different fields of computer science like, databases, artificial intelligence, granular computing and soft computing. We illustrate by example the structures of most of the concepts introduced in the paper.