A decision-making methodology based on the weighted correlation coefficient in weighted extended hesitant fuzzy environments

摘要

Correlation is an important index in decision-making. In weighted extended hesitant fuzzy sets (WEHFSs) environment, researchers have only defined a class of correlation coefficients between WEHFSs with values in the unit interval [0,1]. This is not ideal because it does not extend the classical correlation coefficient in the case of classical sets. In fact, the negative values of the interval [-1,1] are ignored, and such neglectful-ness leads to unreasonable results in decision-making. In other words, the existing definitions are unconvincing and lack consistency, which hinder their application potentials. This article addresses this issue by introducing a new class of weighted correlation coefficients of WEHFSs with values in the interval [-1,1]. Three decision-making methodologies based on the weighted correlation coefficients of WEHFSs are compared with the existing methodologies based on their respective correlation coefficients in the unit interval [0,1]. The comparative analysis shows both the efficiency and effectiveness of the new correlation index.