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In the process of evaluating the green levels of cold-chain logistics providers, experts may hesitate between several linguistic terms rather than give precise values over the alternatives. Due to the potential profit and risk of business decisions, decision-making information is often based on experts' expectations of programs and is expressed as hesitant fuzzy linguistic terms. The consistency of evaluation information of an alternative can reflect the clarity of the alternative in the mind of experts and its own controversy. This paper proposes a method to use the value transfer function in the cumulative prospect theory to convert the original hesitant fuzzy linguistic terms into evaluation information based on reference points. We also introduce the parameters related to the disorder of the system in the hesitant fuzzy thermodynamic method to describe the quantity and quality characteristics of the alternatives. In these kinds of multi-criteria decision-making problems, the weights of criteria are of great importance for decision-making results. Considering the conflicting cases among criteria, the weights were obtained by utilizing the PROMETHEE method. An illustrative example concerning green logistics provider selection was operated to show the practicability of the proposed method.

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In multi-criteria decision making (MCDM) problems, ratings are assigned to the alternatives on different criteria by the expert group. In this paper, we propose a thermodynamically consistent model for MCDM using the analogies for thermodynamical indicators -energy, exergy and entropy. The most commonly used method for analysing MCDM problem is Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS). The conventional TOPSIS method uses a measure similar to that of energy for the ranking of alternatives. We demonstrate that the ranking of the alternatives is more meaningful if we use exergy in place of energy. The use of exergy is superior due to the inclusion of a factor accounting for the quality of the ratings by the expert group. The unevenness in the ratings by the experts is measured by entropy. The procedure for the calculation of the thermodynamical indicators is explained in both crisp and fuzzy environment. Finally, two case studies are carried out to demonstrate effectiveness of the proposed model.