Conflict Analysis Based on Three-Way Decision Theoretic Fuzzy Rough Set over Two Universes

Received: 10 August 2019 Accepted: 19 November 2019 Conflict is an inevitable feature of human endeavor. The conflict analysis has great theoretical and practical significance. Some scholars have discussed three-way decision in conflict analysis with probabilistic rough set (RS) over two universes, but have not probed deep into the fuzzy rough set (FRS) for conflict analysis. To make up for the gap, this paper firstly introduces the concepts and properties of conflict information system (CIS) and probabilistic CIS over two universes. Next, a brand-new system called FRS-CIS was established, followed by the construction of probability measure function and two novel mappings in the probabilistic FRS-CIS over two universes. Furthermore, the authors discussed the properties of probability measure and the lower and upper approximations of Y with parameters α and β corresponding to each mapping. Finally, (0,1)-probabilistic FRS and 0.5-probabilistic FRS were presented for the FRS-CIS and explained with examples, according to the three-way decision theoretic RS under the CIS over two universes. The research results shed new light to solving the FRS under FRS-CIS over two universes.