Modeling Personalized Individual Semantics in Multicriteria Decision Making With Incomplete Linguistic Preference Relations: A Preference Disaggregation Perspective

In the field of linguistic decision making, it is widely acknowledged that different individuals may have different understandings of the same linguistic information. Consequently, the modeling of personalized individual semantics (PISs) has emerged as a prominent research avenue within the domain of linguistic decision making. In this article, we study multicriteria decision making problems with incomplete linguistic preference relations (ILPRs), particularly in scenarios where the marginal utility function of each criterion remain elusive. We develop a new approach for modeling PISs of decision makers from the preference disaggregation perspective. The proposed method initiates by representing the marginal utility of each alternative regarding to every criterion, employing piecewise linear functions. It then customizes linguistic preference values within an ILPR by translating them into numerical preference intensities. Subsequently, this article formulates optimization models to check and rectify the inconsistencies between the multicriteria assessment information and the known elements in the ILPR. Furthermore, an optimization model is devised with the objective of minimizing the inconsistency index of the complete linguistic preference relation, thereby enabling the estimation of missing elements of the ILPR and the ranking of alternatives. Consequently, this method also facilitates the derivation of marginal utility functions and PISs for the decision maker. The proposed method is illustrated using a practical scenario involving a car purchase problem, substantiated by a series of simulation experiments and comparative analysis, ultimately providing validation for the proposed approach.