A shape similarity-based ranking method of hesitant fuzzy linguistic preference relations using discrete fuzzy number for group decision making

The aim of this paper is to develop a ranking method based on shape similarity applying to group decision-making problems. The proposed expressive method uses a symbolic representation to depict each membership function taking into account its shape characteristics and the relative length approximates on its X-axis segments. Considering the context of discrete fuzzy numbers, this paper employs the symbolic representation expressive method to represent the shape of membership function. The strategy of ranking is based on the similarity between unsorted evaluation and the “negative ideal” evaluation, and these evaluations have been depicted in symbolic representation basically. A signed similarity measure was carried at analyzing differences of the “negative ideal” one and unsorted one. The feasibility and applicability of the ranking method are illustrated with an example to give more details in this problem. Additionally, some comparative analyses are performed with other ranking methods combined with different fuzzy linguistic models (probabilistic linguistic term sets and hesitant fuzzy linguistic term sets) to validate the flexibility and robustness of the proposed methodology.