Novel operations of PLTSs based on the disparity degrees of linguistic terms and their use in designing the probabilistic linguistic ELECTRE III method

The probabilistic linguistic term set (PLTS), which allows people to give their qualitative preferences in linguistic terms with corresponding probabilities, is a powerful form to express people’s preferences. This paper proposes a new ELECTRE III method to address multiple criteria decision-making (MCDM) problems based on novel operations of PLTSs. The new operations, including the addition, subtraction, and division of PLTSs are developed by considering the disparity degrees of linguistic terms. Then, novel concepts named the standard vector and gap function of PLTSs are introduced to represent the errors caused by the cognition differences of assessors. After transforming cost and target-based criteria to beneficial criteria, we define the concordance index, discordance index and outstanding degrees in PLTSs. The distillation process and Borda rule are used to obtain the final ranking of alternatives. After giving the algorithm of the probabilistic linguistic ELECTRE III (PL-ELECTRE III) method, we implement it to solve a problem concerning the nurse–patient relationship with the modified Okatani Keyco nurse–patient relationship trust scale. Comparisons between our method and other two methods are provided to demonstrate the advantages of the PL-ELECTRE III method.