Fuzzy β-covering based (I, T)-fuzzy rough set models and applications to multi-attribute decision-making

Multi-attribute decision-making (MADM) can be regarded as a process of selecting the optimal one from all alternatives. Traditional MADM problems with fuzzy information are mainly focused on a fundamental tool which is a fuzzy binary relation. However some complicated problems cannot be effectively solved by a fuzzy relation. For this reason, in order to solve these issues, we set forth two decision-making methods that are stated in terms of novel and flexible fuzzy rough set models. For the purpose of defining these models we employ a fuzzy implication operator I and a triangular norm T. With these adaptable tools we design four kinds of fuzzy beta-coverings based (I, T)-fuzzy rough set models. The elements that make these models different are the combination of fuzzy beta-neighborhoods that intervene in the definitions of the lower (upper) approximations. Then, we discuss the relationships among these given four types of models. Finally, we propose two novel methodologies to solve MADM problems with evaluation of fuzzy information, which rely on these models. Through the analysis of the ranking results of these two methods, we observe that the optimal selected alternative is the same, which means that these two decision-making methods are reasonable. In addition, by comparing the ranking results of these two methods and the existing traditional methods (WA operator and TOPSIS), we observe that our proposed methods can solve the ranking problems that traditional methods cannot solve, which means that our proposed methods are superior to traditional methods.