New Applications and Theoretical Foundations of the Dominance-based Rough Set Approach

Abstract

Dominance-based Rough Set Approach (DRSA) has been proposed as an extension of the Pawlak's concept of Rough Sets in order to deal with ordinal data [see [2,3]]. Ordinal data are typically encountered in multi-attribute decision problems where a set of objects (also called actions, acts, solutions, etc.) evaluated by a set of attributes (also called criteria, variables, features, etc.) raises one of the following questions: (i) how to assign the objects to some ordered classes (ordinal classification), (ii) how to choose the best subset of objects (optimization), or (iii) how to rank the objects from the best to the worst (ranking). The answer to everyone of these questions involves an aggregation of the multi-attribute evaluation of objects, which takes into account a law relating the evaluation and the classification, or optimization, or ranking decision. This law has to be discovered from the data by inductive learning. In case of decision problems corresponding to some physical phenomena, this law is a model of cause-effect relationships, and in case of a human decision making, this law is a decision maker's preference model. In DRSA, these models have the form of a set of if..., then... decision rules. In case of multi-attribute classification the syntax of rules is: if evaluation of object a is better (or worse) than given values of some attributes, then a belongs to at least (at most) given class, and in case of multiattribute optimization or ranking: if object a is preferred to object b in at least (at most) given degrees with respect to some attributes, then a is preferred to b in at least (at most) given degree. Since its conception, DRSA has been adapted to a large variety of decision problems [10]. Moreover, it has been adapted to handle granular (fuzzy) information [5], and incomplete information [1]. Stochastic version of DRSA has also been characterized in [9]. In this presentation, we will concentrate on two recent applications of DRSA: decision under uncertainty and time preference [6], and interactive robust multi-objective optimization [4,7]. Moreover, we will give account of topological properties of DRSA [8], using the concept of a bitopological space.