Improving Reliability for Linguistic Preference Relations Considering New Ordinal and Cardinal Consistency Measures

Abstract

Abstract Linguistic preference relations (LPRs) and its variations served for different decision-making situations are significantly important instruments of qualitative decision-making. The consistency analysis of LPRs is a necessary prerequisite for further operations of these original preference relations so as to ensure that the final decision results are convincing. However, the existing consistency improvement methods for LPRs are difficult to guarantee the reliability of the revised LPRs. Because the suggested LPRs from these methods either not eliminate the ordinal inconsistency or not satisfy the expectation of minimum modification. In this paper, a new definition of ordinal consistency of LPRs is first proposed and then an optimization approach is constructed to eliminate ordinal inconsistency for LPRs. Secondly, a new cardinal consistency index for LPRs is proposed and a corresponding optimization model to increase the cardinal consistency level is presented. After that, an optimization model is proposed to simultaneously manage ordinal and cardinal inconsistency for LPRs. Last, the proposed models are applied to a real linguistic decision-making problem involving evaluation and selection of investment projects. The comparative analysis and discussion illustrate the applicability and effectiveness of the proposed models.

Keywords

• Linguistic preference relations
• Ordinal consistency
• Cardinal consistency
• Optimization approach
• Investment projects evaluation