Vikor method based on the entropy measure for generalized trapezoidal hesitant fuzzy numbers and its application

There are many vague and uncertain issues in real-life. To address these problems, many models and theories have been developed. Entropy is used to express the mathematical values of the fuzziness of generalized hesitant trapezoidal fuzzy numbers (GHTF-numbers) and so it is a measure of the fuzziness of the GHTF-numbers. However, the entropy measures have not been applied to GHTF-numbers. Therefore, in the paper, we introduce the concept of entropy measures for GHTF-number and discuss its desirable properties. Then, we develop a VIKOR method based on the entropy measure for novel multi-criteria decision-making (MCDM) method. In the decision-making framework, the proposed method is not only a way to solve the problem of MCDM, but also contains an important mathematical idea as a different solution approach. We solve an illustrative example of the MCDM method and compare the obtained results with the results of other existing methods. The proposed VIKOR decision-making process is more suitable than the existing ones to deal with uncertain and imprecise information and offers numerous choices to the decision-maker for accessing the infinite alternatives. Furthermore, the result is more significant because the difference between any two values of alternatives is greater.

Automated summary

This paper introduces the application of entropy measures in generalized hesitant trapezoidal fuzzy numbers and develops a new multi-criteria decision-making method based on this. The proposed method is not only a way to solve multi-criteria decision-making problems, but also contains important mathematical ideas. By solving an illustrative example and comparing the results with other methods, it is shown that the proposed method is more suitable for dealing with uncertain and imprecise information.