An improved TOPSIS method for multi-criteria decision making based on hesitant fuzzy β neighborhood

Multi-criteria Decision Making (MCDM) plays a very vital role in many application fields. There are many classical methods to solve the MCDM problems if the available information is crisp. However, the uncertainty and ambiguity inherent in the MCDM often makes these methods unsuitable for solving this kind of problem. Aims at the failures of TOPSIS method that can not rank the alternatives completely in a Hesitant Fuzzy β -Covering Approximation Space (HFβCAS), we develop an improved TOPSIS method. First, we define two pairs of hesitant fuzzy relationship based on hesitant fuzzy β -neighborhood, and construct the corresponding hesitant fuzzy covering rough set models; further we discuss the properties and relationships between the models. Second, we introduce a new comprehensive weight determination method by using the precision degree of hesitant fuzzy covering rough set and the maximizing deviation method. Third, we construct a γ-βCHF-TOPSIS method to MCDM which generalizes the TOPSIS method in an HFβCAS. Finally, two real decision-making problems are used to illustrate the concrete implementation process of γ-βCHF-TOPSIS method, and demonstrate its effectiveness and reasonability.