LAUSR

A number of useful mathematical tools such as fuzzy sets, rough sets and soft sets have been developed to deal with problems involving various uncertainties. These theories have been found to be particularly useful in decision making under uncertainty. This study develops the theory of dominance-based soft rough sets, which is used to propose a new method for analyzing conflicts in decision-making problems. The approach establishes a preference relation among the given objects subject to the available information, and based on this relation it approximates a given concept. The lower approximation is utilized to design an algorithm to handle problems involving both multi-attribute and multi-decision and preference. The algorithm aims at electing objects or actions based on their conditional attributes. The domain of conditional and decision attributes contains preference-ordered values. To achieve an optimal solution, we first collect alternatives (actions) graded as best by all the decision makers. We then use DBSR lower approximations to develop an algorithm to reach the optimal solution. This approach addresses some limitations of models based on Pawlak conflict analysis theory. There are two main contributions of this paper. One is a hybrid model based on rough and soft set theories that can handle preference-based domains. The other is a new approach that can handle multi-agent conflict analysis decision-making problems.