Score function based on concentration degree for probabilistic linguistic term sets: An application to TOPSIS and VIKOR.

• A novel definition of concentration degree for probabilistic linguistic term sets. • A novel score function for probabilistic linguistic term sets. • Two decision-making methods are proposed for probabilistic linguistic term sets. • The effectiveness and robustness of decision-making methods are tested. Probabilistic linguistic term sets (PLTSs) can express the qualitative information of decision makers more accurately in the complicated linguistic setting. However, the existing comparison methods for PLTSs cannot compare some special PLTSs. To tackle this problem, a novel score function based on the concentration degree of an PLTS, called ScoreC-PLTS, is proposed. Additionally, the existing distance measures may distort the original information and lead to unreasonable results. Therefore, a novel probability splitting algorithm is proposed to preprocess PLTSs, based on which, a novel generalized hybrid distance is proposed for PLTSs. Moreover, a novel multiplicative analytic hierarchy process (MAHP) based on ScoreC-PLTS is proposed to determine the weight vector of attributes. Based on the generalized hybrid distance and MAHP, two novel TOPSIS-ScoreC-PLTS and VIKOR-ScoreC-PLTS methods are put forward to handle multi-attribute decision-making problems with PLTSs. Afterwards, an illustrative example concerning the selection of children English educational organization is solved using the proposed TOPSIS-ScoreC-PLTS and VIKOR-ScoreC-PLTS methods. In this example, four indicators are developed and the superiority of our studies is verified by comparing with the previous TOPSIS and VIKOR methods. [ABSTRACT FROM AUTHOR]