Unbalanced double hierarchy linguistic term set: The TOPSIS method for multi-expert qualitative decision making involving green mine selection

The double hierarchy linguistic term set is a linguistic technique to elaborately and accurately represent complex linguistic information for qualitative decision-making problems. Considering that unbalanced semantics may appear in the first and second hierarchy linguistic term sets, the unbalanced double hierarchy linguistic term set (UDHLTS) is proposed in this paper. To characterize the unbalanced distribution of semantics of the second hierarchy linguistic terms, we propose three linguistic scale functions with cognitive bias parameters. Then, a non-linear fitting method is presented to determine these parameters. Combining the first and second hierarchy linguistic term set, we construct eight semantic models with distinct risk appetite parameters and linguistic cognitive bias parameters to capture the semantics of linguistic terms in the UDHLTS. In this way, we can use specific semantic model to represent experts' opinions associated with the UDHLTS. In addition, by using the semantic model of the UDHLTS, linguistic information from different experts can be compared and aggregated quantitatively. To illustrate the applicability of the UDHLTS, we develop a UDHL-TOPSIS method for multi-expert qualitative decision making problems. An engineering example concerning green mine selection is given to illustrate the proposed method.