Nature of decision valuations in elimination of redundant attributes

Abstract

Information systems are the basic building blocks of the theory of rough sets which, based on information signatures of objects, develops strategies for classifying concepts and/or deriving significant information about decision attributes. During such processes of aggregating decision information, one needs to focus on the aspects of designing its representation and considering various ways for reducing attributes. We introduce a general mathematical apparatus of decision valuations that are aimed at representing information derivable from data. We establish a strong connection between the notion of attribute reduction considered in the context of decision valuations and the analogous notions developed in relational databases, semigraphoid models of conditional independence statements, etc. Based on different decision making strategies, we discuss different properties of decision valuations and explore different examples in the light of those properties. We also investigate interrelationships among those properties. Going back to attribute reduction, i.e. elimination of redundant attributes, we consider the prevalent property of discernibility and compare it with the properties of semigraphoid models, such as weak union and decomposition.