Novel classes of coverings based multigranulation fuzzy rough sets and corresponding applications to multiple attribute group decision-making

The notion of covering based multigranulation fuzzy rough set (CMGFRS) models is a generalization of both granular computing and covering based fuzzy rough sets. Therefore it has become a powerful tool for coping with vague and multigranular information in cognition. In this paper we introduce three kinds of CMGFRS models by means of fuzzy β-neighborhoods and fuzzy complementary β-neighborhoods, and we investigate their axiomatic properties. We investigate three respective types of coverings based CMGFRS models, namely, optimistic, pessimistic and variable precision setups. In particular, by using multigranulation fuzzy measure degrees and multigranulation fuzzy complementary measure degrees, we derive three types of coverings based γ-optimistic (γ-pessimistic) CMGFRSs and E (F, G)-optimistic and E (F, G)-pessimistic CMGFRSs, respectively. We discuss the interrelationships among these three types of CMGFRS models and covering based Zhan-CMGFRS models. In view of the theoretical analysis for these three types of CMGFRS models, we put forward a novel methodology to multiple attribute group decision-making problem with evaluation of fuzzy information. An effective example is fully developed, hence concluding the applicability of the proposed methodology.