A probabilistic hesitant fuzzy BWM-TODIM framework with coordinated consistency adjustment and a probability-sensitive dissimilarity measure for logistics provider selection

Abstract

Selecting a third-party logistics provider is a multicriteria decision problem involving delivery reliability, service quality, environmental performance, cost control, and transport risk. In such problems, expert assessments are often uncertain and hesitant, and different possible membership values may carry different confidence levels. To better represent this type of evaluation information, this study develops a probabilistic hesitant fuzzy BWM-TODIM framework for logistics provider selection. In the weighting stage, probabilistic hesitant fuzzy information is incorporated into the best–worst method (BWM) to derive criterion weights, and a coordinated inconsistency adjustment mechanism is introduced to reduce the loss of probability-weighted preference information and the resulting weight disturbance during consistency improvement. In the ranking stage, a probability-sensitive dissimilarity measure is constructed by adding a probability–membership interaction term, so that probabilistic hesitant fuzzy elements with similar membership structures but different probability distributions can be more clearly distinguished. The obtained dissimilarity information is then embedded into the TODIM procedure to support pairwise gain–loss dominance analysis under the decision maker’s risk preferences. A published logistics-provider selection case is used to illustrate the proposed framework. Since the source case does not provide direct BWM pairwise comparisons, the required comparison vectors are transparently reconstructed from the reported criterion-importance probabilistic hesitant fuzzy elements, and the decision matrix is normalized before calculation. The empirical analysis and supplementary tests show that the proposed methodological modifications can improve the interpretability of weighting and ranking under probabilistic hesitant fuzzy information. Sensitivity analyses, including dissimilarity-measure ablation, inconsistency stress testing, criterion-weight perturbation, probability perturbation, and comparison with alternative methods, further indicate that the framework is useful for identifying close competing alternatives and for examining the stability of the final ranking.