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.

Modeling Uncertainty in Ontologies using Rough Set

“…We use the rough membership to approximate them. As shown in [18], a concept can be represented as attributed valued. We therefore construct a decision table based on concepts' attributes to approximate their rough membership.…”

“…are labelled with concepts, table rows labelled with instances of interest and entries of the table are concepts values. The function : × → is such that ( , ) ∈ , for every ( , ) ∈ × represents the information knowledge of i with respect to c. Where represents the set of values an instance i may have with respect to c.Furthermore, since it was proved in[18] that a concept can be defined by using attributes and relations with no regards to previously defined concepts, we can therefore define an attributed table for a specific vague concept say c, based on the set of attribute used in it definition as shown in table 2. Let B be a subset of the set of attributes A such that, the elements of B are the attributes used in…”