Extension of the GRA for group decision-making under fuzzy - Environment

The aim of this paper is to extend the grey relational analysis (GRA) to the fuzzy environment. Owing to vague concepts frequently represented in decision data, the crisp value are inadequate to model real-life situation. In this paper, the rating of each alternative and the weight of each criterion are described by linguistic terms which can be expressed in triangular fuzzy numbers. Then a vertex method is used to calculate the distance between two triangular fuzzy numbers. According to the concept of the GRA, a fuzzy relative relational degree is defined to determine the ranking order of all alternatives by calculating the degree of fuzzy grey relational coefficient to both the fuzzy positive-ideal solution (FPIS) and fuzzy negative-ideal solution (FNIS) simultaneously. Finally, an example is given to show the feasibility and effectiveness of the proposed method.