Uncertainty of Multi-granulation Hesitant Fuzzy Rough Sets Based on Three-Way Decisions

摘要

Three-way decisions, whose extensive application finds relevance in risk decision making, have become an indispensable tool for handling uncertainty information. This paper investigates the decision-theoretic rough sets approach in the framework of multi-granulation hesitant fuzzy approximation space. Primarily, a basic theoretical framework has been developed by combining decision-theoretic with multi-granulation rough sets using three-way decisions. Thereafter, two types of double parameter rough membership degree of a hesitant fuzzy set have been constructed based on the multi-granulation decision-theoretic hesitant fuzzy rough sets, and their basic properties and relationship are discussed. Further, a modified entropy has been constructed.