On Consensus of Group Decision Making with Interval Utility Values and Interval Preference Orderings

Uncertainty is a common phenomenon in our real world. Interval utility values and interval preference orderings are two of the simplest and most convenient tools to describe uncertain preferences in decision making. In this paper, we investigate consensus problems in group decision making with interval utility values and interval preference orderings. We first establish their transformation relations, and give a formula for calculating the association coefficients of individual uncertain preferences and group ones. We then develop a consensus procedure for group decision making with interval utility values and interval preference orderings, which takes interval utility values as the uniform preference representation. This procedure can be reduced to a series of processes for dealing with some special group decision making situations, such as: group decision making with utility values and preference orderings, group decision making with interval utility values, group decision making with interval preference orderings, etc. Finally, we illustrate the applications of the developed procedures with two practical examples.

[1]  S. Bodily.  Note—A Delegation Process for Combining Individual Utility Functions , 1979 .

[2]  Horace W. Brock,et al.  The Problem of "Utility Weights" in Group Preference Aggregation , 1980, Oper. Res..

[3]  T. Tanino.  Fuzzy preference orderings in group decision making , 1984 .

[4]  Masatoshi Sakawa,et al.  Fuzzy multiattribute utility analysis for collective choice , 1985, IEEE Transactions on Systems, Man, and Cybernetics.

[5]  Luis G. Vargas,et al.  Uncertainty and rank order in the analytic hierarchy process , 1987 .

[6]  Thomas M. Strat,et al.  Decision analysis using belief functions , 1990, Int. J. Approx. Reason..

[7]  Xu Ruoning,et al.  Extensions of the analytic hierarchy process in fuzzy environment , 1992 .

[8]  Ching-Lai Hwang,et al.  Fuzzy Multiple Attribute Decision Making - Methods and Applications , 1992, Lecture Notes in Economics and Mathematical Systems.

[9]  R. Ramanathan,et al.  Group preference aggregation methods employed in AHP: An evaluation and an intrinsic process for deriving members' weightages , 1994 .

[10]  Johan Schubert,et al.  On varrho in a decision-theoretic apparatus of Dempster-Shafer theory , 1995, Int. J. Approx. Reason..

[11]  G. Facchinetti,et al.  Note on ranking fuzzy triangular numbers , 1998 .

[12]  Linda M. Haines,et al.  A statistical approach to the analytic hierarchy process with interval judgements. (I). Distributions on feasible regions , 1998, Eur. J. Oper. Res..

[13]  Jacinto González-Pachón,et al.  Aggregation of partial ordinal rankings: an interval goal programming approach , 2001, Comput. Oper. Res..

[14]  Francisco Herrera,et al.  Multiperson decision-making based on multiplicative preference relations , 2001, Eur. J. Oper. Res..

[15]  Francisco Herrera,et al.  Integrating multiplicative preference relations in a multipurpose decision-making model based on fuzzy preference relations , 2001, Fuzzy Sets Syst..

[16]  Z. S. Xu,et al.  The uncertain OWA operator , 2002, Int. J. Intell. Syst..

[17]  Francisco Herrera,et al.  A consensus model for multiperson decision making with different preference structures , 2002, IEEE Trans. Syst. Man Cybern. Part A.

[18]  María Isabel Rodríguez-Galiano,et al.  Transitive approximation to pairwise comparison matrices by using interval goal programming , 2003, J. Oper. Res. Soc..

[19]  Zeshui Xu,et al.  On Compatibility of Interval Fuzzy Preference Relations , 2004, Fuzzy Optim. Decis. Mak..

[20]  Jian-Bo Yang,et al.  A two-stage logarithmic goal programming method for generating weights from interval comparison matrices , 2005, Fuzzy Sets Syst..

[21]  Jian-Bo Yang,et al.  A preference aggregation method through the estimation of utility intervals , 2005, Comput. Oper. Res..

[22]  Xiang-mei Li,et al.  The functional assessment of agricultural ecosystems in Hubei Province, China , 2005 .

[23]  Zeshui Xu,et al.  A C‐OWA operator‐based approach to decision making with interval fuzzy preference relation , 2006, Int. J. Intell. Syst..

[24]  Jian Ma,et al.  An optimization approach to multiperson decision making based on different formats of preference information , 2006, IEEE Transactions on Systems, Man, and Cybernetics - Part A: Systems and Humans.

[25]  Zeshui Xu,et al.  The continuous ordered weighted geometric operator and its application to decision making , 2006, Fuzzy Sets Syst..

[26]  Yunliang Jiang.  An approach to group decision making based on interval fuzzy preference relations , 2007 .

[27]  Zeshui Xu,et al.  Multiple-Attribute Group Decision Making With Different Formats of Preference Information on Attributes , 2007, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[28]  Stephen Lin,et al.  Rank-One Projections With Adaptive Margins for Face Recognition , 2007, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[29]  Jian Chen,et al.  MAGDM Linear-Programming Models With Distinct Uncertain Preference Structures , 2008, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[30]  Zeshui Xu,et al.  Note on “Some models for deriving the priority weights from interval fuzzy preference relations” , 2008 .

[31]  Luis Martínez-López,et al.  An Adaptive Consensus Support Model for Group Decision-Making Problems in a Multigranular Fuzzy Linguistic Context , 2009, IEEE Transactions on Fuzzy Systems.

[32]  Hui Li,et al.  The induced continuous ordered weighted geometric operators and their application in group decision making , 2009, Comput. Ind. Eng..

[33]  Zeshui Xu,et al.  An automatic approach to reaching consensus in multiple attribute group decision making , 2009, Comput. Ind. Eng..

[34]  Zeshui Xu,et al.  Interval multiplicative transitivity for consistency, missing values and priority weights of interval fuzzy preference relations , 2010, Inf. Sci..

[35]  Enrique Herrera-Viedma,et al.  Analyzing consensus approaches in fuzzy group decision making: advantages and drawbacks , 2010, Soft Comput..

[36]  Yang Liu,et al.  An Approach to Solve Group-Decision-Making Problems With Ordinal Interval Numbers , 2010, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[37]  Zeshui Xu,et al.  Nonlinear Programming Model Integrating Different Preference Structures , 2011, IEEE Transactions on Systems, Man, and Cybernetics - Part A: Systems and Humans.

[38]  Enrique Herrera-Viedma,et al.  Consensual Processes , 2011, Studies in Fuzziness and Soft Computing.

[39]  Zeshui Xu,et al.  Some Issues on Multiplicative Consistency of Interval Reciprocal Relations , 2011, Int. J. Inf. Technol. Decis. Mak..

[40]  Zeshui Xu,et al.  Consistency of interval fuzzy preference relations in group decision making , 2011, Appl. Soft Comput..

[41]  Zeshui Xu,et al.  Minimizing Group Discordance Optimization Model for Deriving Expert Weights , 2012 .

[42]  J. Kacprzyk,et al.  Consensus Under Fuzziness , 2012 .

[43]  Zeshui Xu,et al.  Uncertain Power Average Operators for Aggregating Interval Fuzzy Preference Relations , 2012 .