Scholarship at UWindsor

Title

A multi-step goal programming approach for group decision making with incomplete interval additive reciprocal comparison matrices

Authors

Zhou-Jing Wang, Zhejiang University of Finance & EconomicsFollow
Kevin Li, University of WindsorFollow

Document Type

Article

Publication Date

5-1-2015

Publication Title

European Journal of Operational Research

Volume

242

Issue

3

First Page

890

Keywords

Goal programming, Interval additive reciprocal comparison matrices, Multiplicative consistency, Uncertainty, Group decision making

Last Page

900

Abstract

This article presents a goal programming framework to solve group decision making problems where decision-makers’ judgments are provided as incomplete interval additive reciprocal comparison matrices (IARCMs). New properties of multiplicative consistent IARCMs are put forward and used to define consistent incomplete IARCMs. A two-step goal programming method is developed to estimate missing values for an incomplete IARCM. The first step minimizes the inconsistency of the completed IARCMs and controls uncertainty ratios of the estimated judgments within an acceptable threshold, and the second step finds the most appropriate estimated missing values among the optimal solutions obtained from the previous step. A weighted geometric mean approach is proposed to aggregate individual IARCMs into a group IARCM by employing the lower bounds of the interval additive reciprocal judgments. A two-step procedure consisting of two goal programming models is established to derive interval weights from the group IARCM. The first model is devised to minimize the absolute difference between the logarithm of the group preference and that of the constructed multiplicative consistent judgment. The second model is developed to generate an interval-valued priority vector by maximizing the uncertainty ratio of the constructed consistent IARCM and incorporating the optimal objective value of the first model as a constraint. Two numerical examples are furnished to demonstrate validity and applicability of the proposed approach.

DOI

10.1016/j.ejor.2014.10.025

Comments

This article was first published at doi:10.1016/j.ejor.2014.10.025. Copyright Elsevier 2015.

Available under a CC-BY-NC-ND license.

Creative Commons License

This work is licensed under a Creative Commons Attribution-NonCommercial-No Derivative Works 4.0 International License.

Recommended Citation

Wang, Zhou-Jing and Li, Kevin. (2015). A multi-step goal programming approach for group decision making with incomplete interval additive reciprocal comparison matrices. European Journal of Operational Research, 242 (3), 890-900.
https://scholar.uwindsor.ca/odettepub/90