Multi-attribute decision-making based on comprehensive hesitant fuzzy entropy

Abstract

It is unquestionable that hesitant fuzzy set has developed into an important tool for handling uncertain data. As a measure between data, hesitant fuzzy entropy is significant in the decision-making process. However, existing entropy measures have a series of problems such as anti intuition. In the decision-making problem under hesitant fuzzy frameworks, traditional decision-making methods such as TOPSIS method assume that the decision-maker is absolutely rational, which also makes the calculation results unreasonable. Therefore, the present study provides a comprehensive hesitant fuzzy entropy. Additionally, the traditional TOPSIS method is enhanced based on the cumulative prospect theory and the entropy method, thereby generating a multi-attribute decision-making model with unknown attribute weights. First, a new axiomatic definition of hesitant fuzzy entropy is given, then the comprehensive hesitant fuzzy entropy is defined based on the two features of fuzziness and unclarity. Besides, we prove that our method meets the new axiomatic definition. Finally, the improved TOPSIS method is applied to evaluate the comprehensive entropy measure, while simulations verify the effectiveness of the proposed method. The results showed that compared to existing entropy measures, the comprehensive hesitant fuzzy entropy more accurately reflects the uncertainty of hesitant fuzzy elements, and also has the advantages of simple calculation and easy understanding. Meanwhile, the improved TOPSIS method takes into account the psychological preferences of decision-makers, which is more reasonable than traditional methods.