System Portfolio Selection based on GRA Method Under Hesitant Fuzzy Environment

The hesitant fuzzy set (HFS) is an important tool to deal with uncertain and vague information. In equipment system portfolio selection, the index attribute of the equipment system may not be expressed by precise data; it is usually described by qualitative information and expressed as multiple possible values. We propose a method of equipment system portfolio selection under hesitant fuzzy environment. The hesitant fuzzy element (HFE) is used to describe the index and attribute values of the equipment system. The hesitation degree of HFEs measures the uncertainty of the criterion data of the equipment system. The hesitant fuzzy grey relational analysis (GRA) method is used to evaluate the score of the equipment system, and the improved HFE distance measure is used to fully consider the influence of hesitation degree on the grey correlation degree. Based on the score and hesitation degree of the equipment system, two portfolio selection models of the equipment system and an equipment system portfolio selection case is given to illustrate the application process and effectiveness of the method.