Covering-based generalized IF rough sets with applications to multi-attribute decision-making

Multi-attribute decision-making (MADM) can be regarded as a process of selecting the optimal one from all objects. Traditional MADM problems with intuitionistic fuzzy (IF) information are mainly focused on an IF binary relation. However, some complicated problems can not be effectively solved by an IF relation. In order to solve these issues, we set forth two novel decision-making methods that are stated in terms of novel and flexible generalized IF rough set models. For defining these models, four types of IF neighborhoods based on an IF implicator J and an IF triangular norm T are firstly proposed. Secondly, by means of four types of IF neighborhoods, four types of coverings-based generalized IF rough set models are proposed. Furthermore, the relationships among the four types of coverings-based generalized IF rough set models and other types of IF rough set models are also discussed. By means of the principle of the IF-TOPSIS methods, MADM with IF information based on covering-based generalized IF rough sets or based on covering-based generalized fuzzy rough sets is put forward. Finally, we solve MADM problems with the evaluation of IF information based on covering-based generalized IF rough set models. By comparative analysis, we find that the results of this method based on covering-based generalized IF rough set models and based on covering-based generalized fuzzy rough set models are highly consistent. In particular, this method based on covering-based generalized IF rough set models is more effective to deal with MADM than that based on covering-based generalized fuzzy rough set models. (C) 2018 Elsevier Inc. All rights reserved.