Score-HeDLiSF: A score function of hesitant fuzzy linguistic term set based on hesitant degrees and linguistic scale functions: An application to unbalanced hesitant fuzzy linguistic MULTIMOORA

The Hesitant Fuzzy Linguistic Term Set (HFLTS) is a powerful tool to depict experts' cognitive complex linguistic information. This paper aims to propose a new score function of HFLTS to eliminate the defects of the subscript-based operations on HFLTSs. Hesitant degree is an intrinsic feature of HFLTS, and the greater the hesitant degree is, the lower the quality of the HFLTS will be. The asymmetric and non-uniform distributed linguistic term set is commonly used when expressing cognitive complex linguistic information. Considering both the hesitant degrees and the unbalanced linguistic terms in evaluations, a new score function of HFLTS, named the Score-HeDLiSF, is proposed based on the psychology of experts. The Score-HeDLiSF shows many advantages over the existing score function of HFLTS in terms of representing both the balanced and unbalanced linguistic information with hesitant degree and linguistic scale functions. Afterward, a hesitant degree-based weighting method is proposed to determine the weights of experts and criteria. To derive robust decision results, the MULTIMOORA method is improved by integrating the ORESTE method, and then we extend it to the unbalanced hesitant fuzzy linguistic context based on the introduced score function of HFLTS. Finally, an investment problem regarding the shared bicycles is solved by the proposed unbalanced HFL-MULTIMOORA method. The advantages of the unbalanced HFL-MULTIMOORA are highlighted by comparative analyses with two well-known multi-criteria decision-making methods.