Certain types of covering-based multigranulation (I, T)-fuzzy rough sets with application to decision-making

As a generalization of Zhan’s method (i.e., to increase the lower approximation and decrease the upper approximation), the present paper aims to define the family of complementary fuzzy β-neighborhoods and thus three kinds of covering-based multigranulation (I, T)-fuzzy rough sets models are established. Their axiomatic properties are investigated. Also, six kinds of covering-based variable precision multigranulation (I, T)-fuzzy rough sets are defined and some of their properties are studied. Furthermore, the relationships among our given types are discussed. Finally, a decision-making algorithm is presented based on the proposed operations and illustrates with a numerical example to describe its performance.