Novel fuzzy rough set models and corresponding applications to multi-criteria decision-making

By means of a fuzzy coimplication operator J and a triangular conorm S, we set forth two pairs of (J, S)-fuzzy rough set models, which are generalizations of fuzzy rough sets. Then, according to the classifications of the coimplication operators (R-coimplicators and T-coimplicators), we investigate relationships among our proposed models and some existing rough set models. In this paper, by the idea of the PROMETHEE method, we apply (J, S)-fuzzy rough set models to make decisions with evaluation of fuzzy information. An example illustrates the feasibility and effectiveness of our proposed method to solve practical problems. By comparing the ranking results of the existing methods and our proposed method, we observe that the optimal selected alternative is the same, which means that there is a consistency among our proposed decision-making method and the existing methods. In addition, we find that the traditional methods may fail in some practical situations while our proposed method is still valid. (C) 2019 Elsevier B.V. All rights reserved.