A parametric GP model dealing with incomplete information for group decision-making

Abstract We consider a group decision-making problem where preferences given by the experts are articulated into the form of pairwise comparison matrices. In many cases, experts are not able to efficiently provide their preferences on some aspects of the problem because of a large number of alternatives, limited expertise related to some problem domain, unavailable data, etc., resulting in incomplete pairwise comparison matrices. Our goal is to develop a computational method to retrieve a group priority vector of the considered alternatives dealing with incomplete information. For that purpose, we have established an optimization problem in which a similarity function and a parametric compromise function are defined. Associated to this problem, a logarithmic goal programming formulation is considered to provide an effective procedure to compute the solution. Moreover, the parameters involved in the method have a clear meaning in the context of group problems.

[1]  W. Cook,et al.  Deriving weights from pairwise comparison ratio matrices: An axiomatic approach , 1988 .

[2]  Jacinto González-Pachón,et al.  A Distance-Based Method for Preference Information Retrieval in Paired Comparisons , 2005, IDA.

[3]  Lajos Rónyai,et al.  On optimal completion of incomplete pairwise comparison matrices , 2010, Math. Comput. Model..

[4]  S. H. Zanakis,et al.  A Monte Carlo investigation of incomplete pairwise comparison matrices in AHP , 1997 .

[5]  H. Pastijn.  Handbook of critical issues in goal programming: Carlos Romero Pergamon Press, Oxford, 1990, xi + 124 pages, £25.00, ISBN 008 0406610 , 1992 .

[6]  Yi-Chung Hu,et al.  Backpropagation multi-layer perceptron for incomplete pairwise comparison matrices in analytic hierarchy process , 2006, Appl. Math. Comput..

[7]  F. Herrera,et al.  Group decision making with incomplete fuzzy linguistic preference relations , 2009 .

[8]  Mehrdad Tamiz,et al.  Goal programming for decision making: An overview of the current state-of-the-art , 1998, Eur. J. Oper. Res..

[9]  P. Harker.  Incomplete pairwise comparisons in the analytic hierarchy process , 1987 .

[10]  P. Lancaster,et al.  Approximation of positive matrices by transitive matrices , 2005 .

[11]  Francisco Herrera,et al.  A web based consensus support system for group decision making problems and incomplete preferences , 2010, Inf. Sci..

[12]  Eng Ung Choo,et al.  A common framework for deriving preference values from pairwise comparison matrices , 2004, Comput. Oper. Res..

[13]  T. Saaty,et al.  The Analytic Hierarchy Process , 1985 .

[14]  Z. S. Xu,et al.  Goal programming models for obtaining the priority vector of incomplete fuzzy preference relation , 2004, Int. J. Approx. Reason..

[15]  Enrique Herrera-Viedma,et al.  Managing the consensus in group decision making in an unbalanced fuzzy linguistic context with incomplete information , 2010, Knowl. Based Syst..

[16]  Zaiwu Gong,et al.  Least-square method to priority of the fuzzy preference relations with incomplete information , 2008, Int. J. Approx. Reason..

[17]  Francisco Herrera,et al.  Individual and Social Strategies to Deal with Ignorance Situations in Multi-Person Decision Making , 2009, Int. J. Inf. Technol. Decis. Mak..

[18]  Evangelos Triantaphyllou,et al.  Multi-criteria Decision Making Methods: A Comparative Study , 2000 .

[19]  F. Herrera,et al.  A consistency-based procedure to estimate missing pairwise preference values , 2008 .

[20]  Dylan F. Jones,et al.  A distance-metric methodology for the derivation of weights from a pairwise comparison matrix , 2004, J. Oper. Res. Soc..

[21]  Emilio Carrizosa,et al.  Combining Minsum And Minmax: A Goal Programming Approach , 2001, Oper. Res..

[22]  Jian Ma,et al.  An approach to multiple attribute decision making based on incomplete information on alternatives , 1999, Proceedings of the 32nd Annual Hawaii International Conference on Systems Sciences. 1999. HICSS-32. Abstracts and CD-ROM of Full Papers.

[23]  S. Shiraishi,et al.  PROPERTIES OF A POSITIVE RECIPROCAL MATRIX AND THEIR APPLICATION TO AHP , 1998 .

[24]  Francisco Herrera,et al.  Group Decision-Making Model With Incomplete Fuzzy Preference Relations Based on Additive Consistency , 2007, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[25]  Miroslaw Kwiesielewicz,et al.  Ranking Decision Variants by Subjective Paired Comparisons in Cases with Incomplete Data , 2003, ICCSA.

[26]  M. Kwiesielewicz.  The logarithmic least squares and the generalized pseudoinverse in estimating ratios , 1996 .

[27]  Francisco Herrera,et al.  A Consensus Model for Group Decision Making With Incomplete Fuzzy Preference Relations , 2007, IEEE Transactions on Fuzzy Systems.

[28]  Jacinto González-Pachón,et al.  Consistency-driven approximation of a pairwise comparison matrix , 2003, Kybernetika.

[29]  Esther Dopazo,et al.  Preference Learning from Interval Pairwise Data. A Distance-Based Approach , 2007, IDEAL.