A Hesitant Fuzzy Multiplicative Base-criterion Multi-criteria Group Decision Making Method

Hesitant fuzzy sets have a unique characteristic that its basic element could manifest the assessment values of different decision makers on the same option under a certain criterion. Base-criterion method is a very significant tool for calculating the weights of the criteria in multiple criteria decision-making. In this paper, we developed a novel approach hesitant fuzzy BCM based on hesitant fuzzy multiplicative preference relation for multiple criteria group decision making. The base-comparison of the preferential criterion relative to other criteria is expressed as linguistic terms, which might be converted into hesitant multiplicative elements (HMEs). HMEs are extended along the same length according to the attitude of the decision makers. Then normalized optimal hesitant fuzzy weights are calculated. The normalized optimal hesitant fuzzy weights of criteria may be transferred to crisp values by employing score function. To illustrate the applicability and suitability of hesitant fuzzy BCM, we analyse the optimal transportation mode selection problem and car selection problem under hesitant fuzzy environment. The outcomes of the proposed model indicate that the hesitant fuzzy BCM is highly consistent and can yield appreciable preference ranking of criteria and alternatives.