Two types of coverings based multigranulation rough fuzzy sets and applications to decision making

Covering based multigranulation rough fuzzy set, as a generalization of granular computing and covering based rough fuzzy set theory, is a vital tool for dealing with the vagueness and multigranularity in artificial intelligence and management sciences. By means of neighborhoods, we introduce two types of coverings based (optimistic, pessimistic and variable precision) multigranulation rough fuzzy set models, respectively. Some axiomatic systems are also obtained. The relationships between two types of coverings based (optimistic, pessimistic and variable precision) multigranulation rough fuzzy set models are established. Based on the theoretical discussion for the covering based multigranulation rough fuzzy set models, we present an approach to multiple criteria group decision making problem. These two types of basic models and the procedure of decision making methods as well as the algorithm for the new approach are given in detail. By comparative analysis, the ranking results based on two different models have a highly consensus. Although there exist some different ranking results on these two methods, the optimal selected alternative is the same.