Three-way decision making approach to conflict analysis and resolution using probabilistic rough set over two universes

Conflict analysis aims to identify the intrinsic reasons and find a feasible consensus strategy for a conflict situation. Rough set theory was used to study conflict analysis decision-making in the late 90s. The basic way to express the attitudes of every agent are against, favorable and neutral for any issue in the original Pawlak conflict analysis model. The notion of three-way decision (3WD) was initially developed as a means to interpret decision rules induced in probabilistic rough sets. In this paper, we first present the framework of three-way decision (3WD) using probabilistic rough set over two universes. With respect to the probabilistic positive, negative and boundary regions over two universes, we build the rules for making a decision of acceptance, rejection and non-commitment, respectively. So, there is an one-to-one correspondence between the three attitudes of every agent for any issue in a conflict situation and the three decisions in the probabilistic rough set over two universes. Based on this, we present an improved Pawlak conflict analysis model by using the principle of three-way decision based on probabilistic rough set over two universes. We construct the conflict decision-making information system under the framework of two universes. Then we define the favorable issues set and against issues set of any agent between the agent set and the dispute set over conflict decision-making information system, respectively. Furthermore, according to the principle of Bayesian risk decision-making process over two universes, we calculate the threshold value parameters used in the lower and upper approximations of a feasible consensus strategy over conflict decision-making information system. Finally, we present the decision rules and the algorithm of finding a feasible consensus strategy for conflict situation based on three-way decision-making with the probabilistic approximations over two universes. Compared with the original Pawlak conflict analysis model, the proposed model not only provides a new perspective and methodology to handle the conflict analysis problems but also overcomes the limitations of the original model. Lastly, we illustrate the idea and basic principles established in this paper by analyzing a conflict decision-making scenario.