Attribute reduction algorithms for hesitant fuzzy decision systems based on hypergraphs

Abstract

The rough set has been proven to be a powerful tool for dealing with uncertainty and vagueness in different fields. The hesitant fuzzy rough set is a generalization of rough sets to solve more complex problems. Since the existing hesitant fuzzy rough sets don’t satisfy the inclusive property, a novel hesitant fuzzy rough set based on the dual score functions is proposed. Then four generalized hesitant fuzzy rough set about the novel one are presented. Next, the lower approximation distribution reductions can be obtained by the discernibility matrix. Moreover, it is discovered that finding the lower approximation distribution reductions of a hesitant fuzzy decision system is equivalent to finding the minimal transversals of its hypergraph. An improved algorithm for hesitant fuzzy decision systems based on hypergraphs is presented to accelerate the reduction process. Finally, The hybrid data of Hepatitis C Virus from UCI is used as an instance background for data analyses to reflect the feasibility of the proposed algorithm.