Rough approximation of a preference relation by multi-decision dominance for a multi-agent conflict analysis problem

Abstract

Multi-attribute group decision-making (MAGDM) has evoked increasing attention in recent years. Meanwhile, many valuable approaches have been developed to solve various MAGDM problems. In this paper, we consider a MAGDM problem in the presence of multi-attribute and multi-decision decision making with preference, namely the MA&MD decision problem. It involves the assignment of objects (actions), evaluated based on a set of conditional attributes, to pre-defined and preference-ordered multi-decision making. The actions are described by a finite set of conditional attributes and decision attributes. Both types of attribute take the values from their domain with preference order. In order to construct a comprehensive preference evaluation model that could be used to support the optimal choice task, we define two dominance relations, one on the condition attribute set and the other on the decision attribute set. We then present the lower and upper approximations of a preference relation defined by the decision attribute set based on a multi- decision preference dominance relation. Meanwhile, we propose an approach to decision making based on the rough set model established in this paper. The approach to decision making is derived from the lower approximation of decision classes with a preference dominance relation. The idea and decision rule are applied to solving a multi-agent conflict analysis decision problem. This method addresses limitations of the Pawlak conflict analysis model and thus improves on that model. Furthermore, to give practical significance to this management decision making approach, we present two extended models of the multi-decision preference dominance-based rough set as well as the corresponding decision making method. Moreover, we compare the proposed approach to previous studies of dominance-based rough set approaches to multiple attribute (criteria) decision making. The main contribution of this paper is twofold. One is to establish a generalization of the classical dominance-based rough set approach, i.e., the model of multi-decision preference dominance-based rough set. Another is to present a new approach to deal with the multi-agent conflict analysis decision making problem based on the proposed multi-decision rough set approach.