Semantic relationships and approximations of sets: An ontological graph based approach

Approximation of sets is a fundamental notion of rough set theory (RST) proposed by Z. Pawlak. In a classic approach, considered in RST, approximation of sets is defined on the basis of an indiscernibility relation between objects in some universe of discourse. However, approximations of sets become problematic in many cases, especially, if attribute values describing objects are symbolical (e.g., words, terms, linguistic concepts, etc.). In fact, such a situation is natural in human cognition and description of the real world. Different approaches perfecting rough set theory in this area have been proposed in the literature. One of them is based on incorporating ontologies enabling us to add some new, valuable knowledge which can be used in data analysis, rule generation, reasoning, etc. In the paper, we propose to use ontological graphs in determining approximations of sets and show how ontological graphs change a look at them. The presented approach refers to a general trend in computations proposed by L. Zadeh and called “computing with words”.