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

Abstract

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 neglectfulness 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.