A Measure of Inconsistency for Simple Decision Systems over Ontological Graphs

摘要

Rough sets are an appropriate tool to deal with rough (ambiguous, imprecise) concepts in the universe of discourse. A general idea of rough sets is to approximate a given set of objects of interest by other sets of objects, called elementary sets, forming basic knowledge granules. Approximation can be either exact or rough. In the paper, we show that adding information on semantic relations between decision attribute values in a form of an ontological graph enables us to make a quantitative assessment of basic knowledge granules approximating a given set of objects. We focus on semantic relations fundamental in linguistics, called paradigmatic semantic relations. Based on approximation, the whole universe of objects can be divided into three disjoint regions, the positive region, the negative region, and the boundary region. The assessment measure has a fuzzy character, i.e., 0 for granules included in the negative region, 1 for granules included in the positive region, and between 0 and 1 for granules included in the boundary region. It is a measure of inconsistencies existing in simple decision systems over ontological graphs.