Group Decision and Negotiation

, Volume 22, Issue 4, pp 715–738 | Cite as

The Continuous Quasi-OWA Operator and its Application to Group Decision Making

  • Jinpei LiuEmail author
  • Sheng Lin
  • Huayou Chen
  • Ligang Zhou


In this paper, we extend the Quasi-OWA operator to the case in which the input argument is a continuous valued interval and present the continuous Quasi-OWA (C-QOWA) operator, which generalizes a wide range of continuous operators such as the continuous ordered weighted averaging (C-OWA) operator, the continuous generalized OWA operator (C-GOWA) and the continuous generalized ordered weighted logarithm aggregation (C-GOWLA) operator. Then an orness measure to reflect the or-like degree of the C-QOWA operator is proposed. Moreover, some desirable properties of the C-QOWA operator associated with its orness measure are investigated. In addition, we apply the C-QOWA operator to the aggregation of multiple interval arguments and obtain the weighted C-QOWA operator, the ordered weighted C-QOWA (OWC-QOWA) operator, the combined C-QOWA (CC-QOWA) operator. Finally, a CC-QOWA operator-based approach for multi-attribute group decision making problem is presented, and a numerical example shows that the developed approach is feasible and the results are credible.


Group decision-making Aggregation operator Quasi-OWA C-QOWA operator CC-QOWA operator 


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  1. Beliakov G, Pradera A, Calvo T (2007) Aggregation functions: a guide for practitioners. Springer, BerlinGoogle Scholar
  2. Calvo T, Beliakov G (2010) Aggregation functions based on penalties. Fuzzy Sets Syst 161: 1420–1436CrossRefGoogle Scholar
  3. Chen HY, Liu JP, Wang H (2008) A class of continuous ordered weighted harmonic (C-OWH) averaging operators for interval argument and its applications. Syst Eng Theory Pract 28: 86–92Google Scholar
  4. Chiclana F, Herrera F, Herrera-Viedma E (2000) The ordered weighted geometric operator: properties and application. In: Proceedings of the eighth international conference on information processing and management of uncertainty in knowledge-based systems. Madrid, Spain, pp 985–991Google Scholar
  5. Dujmović J (1974) Weighted conjunctive and disjunctive means and their application in system evaluation. Univ Beograd Publ Elektrotechn Fak 483: 147–158Google Scholar
  6. Fodor J, Marichal JL, Roubens M (1995) Characterization of the ordered weighted averaging operators. IEEE Trans Fuzzy Syst 3: 236–240CrossRefGoogle Scholar
  7. Jiang H, Li SH, Li J, Yang FQ, Hu X (2010) Ant clustering algorithm with K-harmonic means clustering. Expert Syst Appl 37: 8679–8684CrossRefGoogle Scholar
  8. Kolesárová A, Mesiar R (2009) Parametric characterization of aggregation functions. Fuzzy Sets Syst 160: 816–831CrossRefGoogle Scholar
  9. Liu XW (2006) An orness measure for quasi-arithmetic means. IEEE Trans Fuzzy Syst 14: 837–848CrossRefGoogle Scholar
  10. Liu XW (2009) Parameterized defuzzification with continuous weighted quasi-arithmetic means-an extension. Inf Sci 179: 1193–1206CrossRefGoogle Scholar
  11. Marichal JL (1998) Aggregation operators for multicriteria decision aid. Ph.D. Thesis, Institute of Mathematics, University of Liège, LiègeGoogle Scholar
  12. Salido JMF, Murakami S (2003) Extending Yager’s orness concept for the OWA aggregators to other mean operators. Fuzzy Sets Syst 139: 515–542CrossRefGoogle Scholar
  13. Torra V, Narukawa Y (2007a) Modeling decision: information fusion and aggregation operators. Springer, BerlinGoogle Scholar
  14. Torra V, Narukawa Y (2007b) A view of averaging aggregation operators. IEEE Trans Fuzzy Syst 15: 1063–1067CrossRefGoogle Scholar
  15. Xu ZS, Da QL (2002) The ordered weighted geometric averaging operators. Int J Intell Syst 17: 709–716CrossRefGoogle Scholar
  16. Xu ZS (2009) Fuzzy harmonic mean operators. Int J Intell Syst 24: 152–172CrossRefGoogle Scholar
  17. Yager RR (1988) On ordered weighted averaging aggregation operators in multicriteria decision making. IEEE Trans Syst Man Cybern 18: 183–190CrossRefGoogle Scholar
  18. Yager RR, Filev DP (1999) Induced ordered weighted averaging operators. IEEE Trans Syst Man Cybern B Cybern 29: 141–150CrossRefGoogle Scholar
  19. Yager RR (2004a) Generalized OWA aggregation operators. Fuzzy Opt Decis Mak 2: 93–107CrossRefGoogle Scholar
  20. Yager RR (2004b) OWA aggregation over a continuous interval argument with applications to decision making. IEEE Trans Syst Man Cybern B Cybern 34: 1952–1963CrossRefGoogle Scholar
  21. Yager RR, Xu ZS (2006) The continuous ordered weighted geometric operator and its application to decision making. Fuzzy Sets Syst 157: 1393–1402CrossRefGoogle Scholar
  22. Yager RR (2009) On generalized Bonferroni mean operators for multi-criteria aggregation. Int J Approx Reason 50: 1279–1286CrossRefGoogle Scholar
  23. Yager RR, Beliakov G (2010) OWA operators in regression problems. IEEE Trans Fuzzy Syst 18: 106–113CrossRefGoogle Scholar
  24. Zhou LG, Chen HY (2010) Generalized ordered weighted logarithm aggregation operators and their application to group decision making. Int J Intell Syst 25: 683–707CrossRefGoogle Scholar
  25. Zhou LG, Chen HY (2011) Continuous generalized OWA operator and its application to decision making. Fuzzy Sets Syst 168: 18–34CrossRefGoogle Scholar
  26. Zhou SM, Chiclana F, John RI, Garibaldi JM (2008) Type-1 OWA operator for aggregating uncertain information with uncertain weights induced by type-2 linguistic quantifiers. Fuzzy Sets Syst 159: 3281–3296CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media B.V. 2012

Authors and Affiliations

  • Jinpei Liu
    • 1
    Email author
  • Sheng Lin
    • 1
  • Huayou Chen
    • 2
  • Ligang Zhou
    • 2
  1. 1.Department of ManagementTianjin UniversityTianjinChina
  2. 2.School of Mathematical SciencesAnhui UniversityHefeiChina

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