Correlation coefficients of dual hesitant fuzzy sets and their application in engineering management

Engineering management plays an important role in the socio-economic field, where complex and uncertain factors usually exist. Dual hesitant fuzzy sets (DHFSs) are powerful tools to denote the decision makers’ uncertain and hesitant preferences. Correlation measures and correlation coefficients are two important types of indices in decision making. This paper focuses on correlation measures and correlation coefficients for DHFSs and their application in engineering management. To do this, two dual hesitant fuzzy correlation coefficients are defined, and their properties are studied. Considering the situation where interactive characteristics among elements exist, two Shapley correlation coefficients are defined. When the weighting information is incompletely known, models for the optimal two-additive measures are built. Then, an algorithm to clustering analysis and decision making with incomplete weighting information and interactive characteristics are presented, respectively. Two corresponding examples about real estate investment and engineering cost management are offered to demonstrate the application of the approaches.