Abstract
With the development of the social economy and an enlarged volume of information, the application of multiple-criteria decision making (MCDM) has become increasingly wide and deep. As a brilliant MCDM technique, the best–worst method (BWM) has attracted many scholars’ attention because it can determine the weights of criteria with less comparison time and higher consistency between judgments than analytic hierarchy process. However, the effectiveness of the BWM is based on complete comparison information among criteria. Considering the fact that the decision makers may have limited time and energy to study all criteria, they cannot construct a complete comparison system. In this paper, we propose a novel MCDM method named BW-MaxEnt that combines BWM and the maximum entropy method (MaxEnt) to identify the weights of unfamiliar criteria with incomplete decision information. The model can be translated into a convex optimization problem that can be solved effectively and has an overall optimal solution. Finally, a practical application concerning the procurement of GPU workstations illustrates the feasibility of the proposed BW-MaxEnt method.
Highlights
The questionnaire can be divided into two parts: One part is the comparison between criteria, where we provided a full description of the 1–9 scale for the comparison
The first column is the scores for the Leadtek W2030 (LT), and the second column is the scores for the Stend IW 4213 (SD)
The best–worst method (BWM) is a brilliant technique for solving this task because it requires fewer comparisons and obtains more consistent results than AHP
Summary
Many popular and topical MCDM (multiple-criteria decision making) methods have been proposed by researchers, such as AHP (Analytic Hierarchy Process) [1], TOPSIS (Technique for Order of Preference by Similarity to Ideal Solution) [2], ELECTRE (Elimination and Choice Expressing Reality) [3], VIKOR Limited knowledge and experience mean that DMs cannot give crisp pairwise comparison values for some criteria [18] To address this issue, researchers extended the BWM to the fuzzy environment by describing DMs’ preferences with various fuzzy information types, such as fuzzy sets [19], intuitionistic fuzzy sets [20], interval type-2 fuzzy sets [21], probabilistic hesitant fuzzy sets [22], Z-numbers [23], rough fuzzy sets [24], etc. Based on the above analysis, this paper introduces the maximum entropy principle into the BWM method to assign weights for the unfamiliar criteria. The BW-MaxEnt method can determine the weights of unfamiliar criteria with minimum risk to ensure the reliability of decision making.
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