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The purpose of this paper is to develop some weight determining methods for hesitant fuzzy multi-criterion decision making (MCDM) in which the preference information on attributes is collected over different periods.

Based on the proposed weight determining methods and dynamic hesitant fuzzy aggregation operators, an approach is developed to solve the hesitant fuzzy multi-stage multi-attribute decision-making problem where all the preference information of attributes over different periods is represented in hesitant fuzzy values.

In order to determine the weights associated with dynamic hesitant fuzzy operators, the authors propose the improved maximum entropy method and the minimum average deviation method.

This paper does not consider the multi-stage multi-criteria group decision-making problem.

An example concerning the evaluation of rangelands is given to illustrate the validation and efficiency of the proposed approach. It should be stated that the proposed approach can also be implemented into other multi-stage MCDM problems.

The concept of hesitant fuzzy variable (HFV) is defined. Some operational laws and properties of the HFVs are given. Moreover, to fuse the multi-stage hesitant fuzzy information, the aggregation operators of hesitant fuzzy sets are extended to that of the HFVs.

Due to the increasing awareness of environmental and social issues, many practitioners and researchers have paid attention to sustainable supply chain management. As the performance of suppliers determines the success of supply chains, sustainable supplier selection becomes more and more important. Existing sustainable supplier selection models evaluated the sustainability of suppliers in three aspects (economic, environmental and social) and assumed that values on different criteria can completely compensate for each other directly. However, in reality, criteria in economic, environmental and social aspects are heterogeneous, and the decision-maker’s preferences on criteria belonging to different aspects are different. In this case, values on criteria belonging to different aspects are not allowed to completely compensate for each other directly. To solve this problem, this paper aims to propose a hybrid sustainable supplier selection approach integrating compensatory and non-compensatory decision rules.

In the proposed approach, the compensatory decision method Technique for Order of Preference by Similarity to Ideal Solution is used to evaluate performances of suppliers with respect to economic, environmental and social aspects. The non-compensatory decision method Elimination and Choice Translating Reality is used to evaluate performances of suppliers on sustainable criteria comprehensively. Through the proposed approach, only criteria belonging to the same aspects are allowed to compensate for each other directly. Finally, experimental results show that the proposed integrated approach is effective and efficient to help the decision-maker select optimal sustainable suppliers.

This is an original approach that integrates compensatory and non-compensatory decision rules, which can benefit from the two kinds of decision rules simultaneously. The integrated approach can be used as an aid for companies to select the best sustainable suppliers.

This paper presents an original integrated sustainable supplier selection approach using both compensatory and non-compensatory methods. It can benefit from the advantages of both compensatory and non-compensatory methods. The proposed approach can express preferences of the decision-maker on sustainable criteria sufficiently and maximize economic benefits while meeting environmental needs.