An objective formulation of membership function based on fuzzy entropy and pairwise comparison

A Three-Dimensional Fuzzy Linguistic Evaluation Model

A probabilistic linguistic-based model is an effective tool to express preferences with different weights for different linguistic terms. This paper aims at introducing a new model for determining criteria weights in group decision-making problems, which is based on the concept of probabilistic linguistic terms. Different linguistic weights of respondents are also incorporated into the proposed model. Fuzzy numbers are used to quantify the linguistic terms. Using this model, first, a new concept called three-dimensional fuzzy linguistic representation is proposed to serve as an extension of the existing models. Then, a normalization process, an aggregation process, and a defuzzifying process for three-dimensional fuzzy linguistic representation are investigated. Next, a model for determining criteria weights is formulated. A case study of a beverage product in Thailand is provided to demonstrate the applicability of the proposed model. Finally, the results are compared with the existing models.