Average-case consistency measurement and analysis of interval-valued reciprocal preference relations

The file attached to this record is the author's final peer reviewed version. The Publisher's final version can be found by following the DOI link.Measuring consistency of preferences is very important in decision-making. This paper addresses this key issue for interval-valued reciprocal preference relations. Existing studies implement one of two di erent measures: the "classical" consistency measure, and the "boundary" consistency measure. The classical consistency degree of an interval-valued reciprocal preference relation is determined by its associated reciprocal preference relation with highest consistency degree, while the boundary consistency degree is determined by its two associated boundary reciprocal preference relations. However, the consistency index of an interval-valued reciprocal preference relation should be determined by taking into account all its associated reciprocal preference relations. Motivated by this, a new consistency measure for interval-valued reciprocal preference relations, the average-case consistency measure, is suggested and introduced. The new average-case consistency measure of an interval-valued reciprocal preference relation is determined as the average consistency degree of all reciprocal preference relations associated to the interval-valued reciprocal preference relation. Furthermore, the analysis and comparison of the di erent consistency measure internal mechanisms is used to justify the validity of the average-case consistency measure. Finally, an average-case consistency improving method which aims to obtain a modi ed interval-valued reciprocal preference relation with a required average consistency degree is developed

Strategic Weight Manipulation in Multiple Attribute Decision Making in an Incomplete Information Context

The file attached to this record is the author's final peer reviewed version. The Publisher's final version can be found by following the DOI link.In some real-world multiple attribute decision making (MADM) problems, a decision maker can strategically set attribute weights to obtain her/his desired ranking of alternatives, which is called the strategic weight manipulation of the MADM. Sometimes, the attribute weights are given with imprecise or partial information, which is called incomplete information of attribute weights. In this study, we propose the strategic weight manipulation under incomplete information on attributes weights. Then, a series of mixed 0-1 linear programming models (MLPMs) are proposed to derive a strategic weight vector for a desired ranking of an alternative. Finally, a numerical example is used to demonstrate the validity of our models

A Local Adjustment Method to Improve Multiplicative Consistency of Fuzzy Reciprocal Preference Relations

The file attached to this record is the author's final peer reviewed version. The Publisher's final version can be found by following the DOI link.Preferences that verify the transitivity property are usually referred to as rational or consistent preferences. Existent methods to improve the consistency of inconsistent fuzzy reciprocal preference relations (FPRs) fail to retain the original preference values because they always derive a new FPR. This article presents a new inconsistency identification and modification (IIM) method to detect and rectify only the most inconsistent elements of an inconsistent FPR. As such, the proposed IIM can be considered a local adjustment method to improve multiplicative consistency (MC) of FPRs. The case of inconsistent FPRs with missing values, i.e., incomplete FPRs, is addressed with the estimation of the missing preferences with a constrained nonlinear optimization model by the application of the IIM method. The implementation process of the proposed algorithms is illustrated with numerical examples. Simulation experiments and comparisons with existent methods are also included to show that the new method requires fewer iterations than existent methods to improve the MC of FPRs and achieves better MC level, while preserving the original preference information as much as possible than the existent methods. Thus, the results presented in this article demonstrate the correctness, effectiveness, and robustness of the proposed method

An overview on managing additive consistency of reciprocal preference relations for consistency-driven decision making and Fusion: Taxonomy and future directions

The file attached to this record is the author's final peer reviewed version. The Publisher's final version can be found by following the DOI link.The reciprocal preference relation (RPR) is a powerful tool to represent decision makers’ preferences in decision making problems. In recent years, various types of RPRs have been reported and investigated, some of them being the ‘classical’ RPRs, interval-valued RPRs and hesitant RPRs. Additive consistency is one of the most commonly used property to measure the consistency of RPRs, with many methods developed to manage additive consistency of RPRs. To provide a clear perspective on additive consistency issues of RPRs, this paper reviews the consistency measurements of the different types of RPRs. Then, consistency-driven decision making and information fusion methods are also reviewed and classified into four main types: consistency improving methods; consistency-based methods to manage incomplete RPRs; consistency control in consensus decision making methods; and consistency-driven linguistic decision making methods. Finally, with respect to insights gained from prior researches, further directions for the research are proposed

Two-stage prioritization procedure for multiplicative AHP-group decision making

In this paper, we propose two-stage prioritization procedure (TSPP) for multiplicative Analytic Hierarchy Process-group decision making (AHP-GDM), which involves determining the group priority vector based on the individual pair-wise comparison matrices (PCMs), simultaneously considering the consensus and consistency of the individual PCMs. The first stage of the TSPP involves checking and revising the individual PCMs for reaching the acceptable consensus and consistency. The second stage of the TSPP involves estimating the group priority vector using Bayesian approach. The main characteristics of the proposed TSPP are as follows: 1) It makes full use of the prior information as well as the sample information during the Bayesian revision of the individual PCMs and the Bayesian estimation of the group priority vector; 2) It ensures that the revised individual PCMs reach the acceptable consensus and consistency; 3) It enriches the aggregation methods for the collective preference in multiplicative AHP-GDM. Finally, two numerical examples are used to evaluate the applicability and effectiveness of the proposed TSPP by the comparisons with several other methods