An Algebra of Ontologies Approximation under Uncertainty

Abstract

Ontologies are widely used in modeling the real world for the purpose of information sharing and reasoning. Traditional ontologies contain only concepts and relations that describe asserted facts about the world. Modeling in a dynamic world requires taking into consideration the uncertainty that may arise in the domain. In this paper, the concept of soft sets initiated by Molodtsov and the concept of rough sets introduced by Pawlack are used to define a way of instantiating ontologies of vague domains. We define ontological algebraic operations and their properties while taking into consideration the uncertain nature of domains. We show that, by doing so, intra ontological operations and their properties are preserved and formalized as operations in a vague set of objects and can be proved algebraically.