Fuzzy Optimization and Decision Making

, Volume 5, Issue 1, pp 21–32 | Cite as

A Direct Approach to Group Decision Making with Uncertain Additive Linguistic Preference Relations

  • Zeshui XuEmail author


In this paper, we study the group decision-making problem in which the preference information given by experts takes the form of uncertain additive linguistic preference relations. We define the concept of uncertain additive linguistic preference relation, and introduce a formula based on possibility measure for comparing two uncertain linguistic preference values. We introduce some aggregation operators such as the uncertain linguistic averaging (ULA) operator and uncertain linguistic weighted averaging (ULWA) operator, etc. Based on the ULA and ULWA operators, we develop a direct approach to group decision making with uncertain additive linguistic preference relations without loss of information. Finally, an illustrative numerical example is given to verify the developed approach.


group decision making uncertain additive linguistic preference relations uncertain linguistic averaging (ULA) operator uncertain linguistic weighted averaging (ULWA) operator 


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  1. Bordogna, G., Fedrizzi, M., Passi, G. 1997“A Linguistic Modeling of Consensus in Group Decision Making Based on OWA Operator”IEEE Transactions on Systems, Man, and Cybernetics27126132Google Scholar
  2. Bortolan, G., Degani, R. 1985“A Review of Some Methods for Ranking Fuzzy Numbers”Fuzzy Sets and Systems15119CrossRefMathSciNetGoogle Scholar
  3. Carlsson, C., Fuller, R. 2000“Benchmaking and Linguistic Importance Weighted Aggregations”Fuzzy Sets and Systems1143542CrossRefGoogle Scholar
  4. Chiclana, F., Herrera, F., Herrera-Viedma, E. 1998“Integrating Three Representation Models in Fuzzy Multipurpose Decision Making Based on Fuzzy Preference Relations”Fuzzy Set and Systems973348MathSciNetGoogle Scholar
  5. Chiclana, F., Herrera, F., Herrera-Viedma, E. 2001“Integrating Multiplicative Preference Relations in a Multipurpose Decision Making Model Based on Fuzzy Preference Relations”Fuzzy Sets and Systems122277291CrossRefMathSciNetGoogle Scholar
  6. Cordón, O., Herrera, F., Zwir, I. 2002“Linguistic Modeling by Hierarchical Systems of Linguistic Rules”IEEE Transactions on fuzzy systems10220Google Scholar
  7. Degani, R., Bortolan, G. 1988“The Problem of Linguistic Approximation in Clinical Decision Making”International Journal of Approximate Reasoning2143162Google Scholar
  8. Delgado, M., Verdegay, J.L., Vila, M.A. 1993“On Aggregation Operations of Linguistic Labels”International Journal of Intelligent Systems8351370Google Scholar
  9. Dubois, D., Prade, H. 1983“Ranking Fuzzy Numbers in the Setting of Possibility”Information Sciences30183224CrossRefMathSciNetGoogle Scholar
  10. Facchinetti, G., Ricci, R.G., Muzzioli, S. 1998“Note on Ranking Fuzzy Triangular Numbers”International Journal of Intelligent Systems13613622CrossRefGoogle Scholar
  11. Herrera, F. 1995“A Sequential Selection Process in Group Decision Making with Linguistic Assessment”Information Sciences85223239CrossRefzbMATHGoogle Scholar
  12. Herrera, F., Herrera-Viedma, E. 2000“Choice Functions and Mechanisms for Linguistic Preference Relations”European Journal of Operational Research120144161CrossRefMathSciNetGoogle Scholar
  13. Herrera, F., Herrera-Viedma, E., Chiclana, F. 2001“Multiperson Decision-Making Based on Multiplicative Preference Relations”European Journal of Operational Research129372385CrossRefMathSciNetGoogle Scholar
  14. Herrera, F., Martínez, L. 2000a“A 2-Tuple Fuzzy Linguistic Representation Model for Computing with Words”IEEE Transactions on Fuzzy Systems8746752Google Scholar
  15. Herrera, F., Martínez, L. 2000b“An Approach for Combining Linguistic and Numerical Information Based on 2-Tuple Fuzzy Linguistic Representation Model in Decision-Making”International Journal of Uncertainty, Fuzziness, Knowledge-based Systems8539562Google Scholar
  16. Herrera, F., Martínez, L. 2001“A Model Based on Linguistic 2-Tuples for Dealing with Multigranular Hierarchical Linguistic Contexts in Multi-Expert Decision-Making”IEEE Transactions on Systems, Man, and Cybernetics-Part B31227234Google Scholar
  17. Kacprzyk, J. 1986“Group Decision Making with a Fuzzy Linguistic Majority”Fuzzy Sets and Systems18105118zbMATHMathSciNetGoogle Scholar
  18. Liou, T.S., Wang, J.J.M. 1992“Ranking Fuzzy Numbers with Integral Value”Fuzzy Sets and Systems50247255CrossRefMathSciNetGoogle Scholar
  19. Lipovetsky, S., Michael Conklin, M. 2002“Robust Estimation of Priorities in the AHP”European Journal of Operational Research137110122CrossRefGoogle Scholar
  20. Nurmi, H. 1981“Approaches to Collective Decision Making with Fuzzy Preference Relations”Fuzzy Sets and Systems6249259CrossRefzbMATHMathSciNetGoogle Scholar
  21. Orlovsky, S.A. 1978“Decision-Making with a Fuzzy Preference Relation”Fuzzy Sets and Systems1155167CrossRefzbMATHMathSciNetGoogle Scholar
  22. Saaty, T.L. 1980The Analytic Hierarchy ProcessMcGraw-HillNew YorkGoogle Scholar
  23. Saaty, T.L. 1994Fundamentals of Decision Making and Priority Theory with the AHPRWS PublicationsPittsburghGoogle Scholar
  24. Sengupta, A., Pal, T.K. 2000“On Comparing Interval Numbers”European Journal of Operational Research1272843CrossRefMathSciNetGoogle Scholar
  25. Torra, V. 1996“Negation Functions Based Semantics for Ordered Linguistic Labels”International Journal of Intelligent Systems11975988CrossRefGoogle Scholar
  26. Xu, Z.S. 2000a“On Consistency of the Weighted Geometric Mean Complex Judgment Matrix in AHP”European Journal of Operational Research126683687CrossRefGoogle Scholar
  27. Xu, Z.S. 2000b“Generalized Chi Square Method for the Estimation of Weights”Journal of Optimization Theory and Applications107183192Google Scholar
  28. Xu, Z.S. 2004a“Goal Programming Models for Obtaining the Priority Vector of Incomplete Fuzzy Preference Relation”International Journal of Approximate Reasoning36261270CrossRefGoogle Scholar
  29. Xu, Z.S. 2004b“A Method Based on Linguistic Aggregation Operators for Group Decision Making with Linguistic Preference Relations”Information Sciences1661930CrossRefGoogle Scholar
  30. Xu, Z.S. 2004cUncertain Multiple Attribute Decision Making: Methods and ApplicationsTsinghua University PressBeijingGoogle Scholar
  31. Xu, Z.S., Wei, C.P. 1999“A Consistency Improving Method in the Analytic Hierarchy Process”European Journal of Operational Research116443449Google Scholar
  32. Xu, Z.S., Da, Q.L. 2002“The Uncertain OWA Operator”International Journal of Intelligent Systems17569575Google Scholar
  33. Xu, Z.S., Da, Q.L. 2003“An Approach to Improving Consistency of Fuzzy Preference Matrix”Fuzzy Optimization and Decision Making2312CrossRefMathSciNetGoogle Scholar
  34. Xu, Z.S., Da, Q.L. 2005“A Least Deviation Method to Obtain a Priority Vector of a Fuzzy Preference Relation”European Journal of Operational Research164206216CrossRefGoogle Scholar
  35. Zadeh, L.A., Kacprzyk, J. 1999Computing with Words in Information/Intelligent Systems-Part 1: Foundations: Part 2: ApplicationsPhysica-VerlagHeidelberg, GermanyGoogle Scholar

Copyright information

© Springer Science+Business Media, Inc. 2006

Authors and Affiliations

  1. 1.Department of Management Science and Engineering, School of Economics and ManagementTsinghua UniversityBeijingChina

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