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Fuzzification of the OWA Operators for Aggregating Uncertain Information with Uncertain Weights

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Recent Developments in the Ordered Weighted Averaging Operators: Theory and Practice

Part of the book series: Studies in Fuzziness and Soft Computing ((STUDFUZZ,volume 265))

Abstract

Yager’s ordered weighted averaging (OWA) operator has been widely applied in various domains. Yager’s traditional OWA operator focuses exclusively on the aggregation of crisp numbers with crisp weights. However, uncertainty prevails in almost every process of real world decision making, and so there is a need to find OWA mechanisms to aggregate uncertain information. In this chapter, we generalise Yager’s OWA operator and describe two novel uncertain operators, namely the type-1 OWA operator and type-2 OWA operator. The type-1 OWA operator is able to aggregate type-1 fuzzy sets, whilst the type-2 OWA operator is able to aggregate type-2 fuzzy sets. Therefore, the two new operators are capable of aggregating uncertain opinions or preferences with uncertain weights in soft decision making. This chapter also indicates that not only Yager’s OWA operator but also some existing operators of fuzzy sets, including the join and meet of type-1 fuzzy sets, are special cases of the type-1 OWA operators. We further suggest the concepts of joinness and meetness of type-1 OWA operators, which can be considered as the extensions of the concepts-orness and andness in Yager’s OWA operator, respectively. Given the high computing overhead involved in aggregating general type-2 fuzzy sets using the type-2 OWA operator, an interval type-2 fuzzy sets oriented OWA operator is also defined. Some examples are provided to illustrate the proposed concepts.

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References

  1. Yager, R.R.: On ordered weighted averaging aggregation operators in multi-criteria decision making. IEEE Trans. on Systems, Man and Cybernetics 18, 183–190 (1988)

    Article  MathSciNet  MATH  Google Scholar 

  2. Dubois, D., Prade, H.: A review of fuzzy set aggregation connectives. Information Sciences 36, 85–121 (1985)

    Article  MathSciNet  MATH  Google Scholar 

  3. Fodor, J., Roubens, M.: Fuzzy Preference Modelling and Multicriteria Decision Support. Kluwer, Dordrecht (1994)

    MATH  Google Scholar 

  4. McClean, S., Scotney, B., Shapcott, M.: Aggregation of imprecise and uncertain information in databases. IEEE Transactions on Knowledge and Data Engineering 13(6), 902–912 (2001)

    Article  Google Scholar 

  5. Chen, A.L.P., Chiu, J.-S., Tseng, F.S.C.: Evaluating aggregate operations over imprecise data. IEEE Transactions on Knowledge and Data Engineering 8(2), 273–284 (1996)

    Article  Google Scholar 

  6. Dubois, D., Prade, H.: On the use of aggregation operations in information fusion processes. Fuzzy Sets and Systems 142, 143–161 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  7. Xu, Z.S., Da, Q.L.: An overview of operators for aggregating information. International Journal of Intelligent Systems 18, 953–969 (2003)

    Article  MATH  Google Scholar 

  8. Chiclana, F., Herrera-Viedma, E., Herrera, F., Alonso, S.: Induced ordered weighted geometric operators and their use in the aggregation of multiplicative preference relations. International Journal of Intelligent Systems 19, 233–255 (2004)

    Article  MATH  Google Scholar 

  9. Chiclana, F., Herrera-Viedma, E., Herrera, F., Alonso, S.: Some induced ordered weighted averaging operators and their use for solving group decision-making problems based on fuzzy preference relations. European Journal of Operational Research 182, 383–399 (2007)

    Article  MATH  Google Scholar 

  10. Dong, W.M., Wong, F.S.: Fuzzy weighted averages and implementation of the extension principle. Fuzzy Sets and Systems 21, 183–199 (1987); weights, Fuzzy Sets and Systems 94, 157–169 (1998)

    Article  MathSciNet  MATH  Google Scholar 

  11. Guh, Y.-Y., Hon, C.-C., Lee, E.S.: Fuzzy weighted average: the linear programming approach via Charnes and Cooper’s rule. Fuzzy Sets and Systems 117, 157–160 (2001)

    Article  MATH  Google Scholar 

  12. Herrera, F., Herrera-Viedma, E.: Aggregation operators for linguistic weighted information. IEEE Trans. on Systems, Man and Cybernetics-part A 27, 646–656 (1997)

    Article  Google Scholar 

  13. Herrera, F., Herrera-Viedma, E., Chiclana, F.: A study of the origin and uses of the ordered weighted geometric operator in multicriteria decision making. International Journal of Intelligent Systems 18, 689–707 (2003)

    Article  MATH  Google Scholar 

  14. Zimmermann, H.-J.: Fuzzy Sets, Decision Making and Expert Systems. Kluwer Academic Publishers, Boston (1987)

    Google Scholar 

  15. Zimmermann, H.-J., Zysno, P.: Latent connectives in human decision making. Fuzzy Sets and Systems 4, 37–51 (1980)

    Article  MATH  Google Scholar 

  16. Ahn, B.S.: The OWA aggregation with uncertain descriptions on weights and input arguments. IEEE Trans. Fuzzy Systems 15(6), 1130–1134 (2007)

    Article  Google Scholar 

  17. Mitchell, H.B., Schaefer, P.A.: On ordering fuzzy numbers. Internaltional Journal of Intelligent Systems 15, 981–993 (2000)

    Article  MATH  Google Scholar 

  18. Meyer, P., Roubens, M.: On the use of the Choquet integral with fuzzy numbers in multiple criteria decision support. Fuzzy Sets and Systems 157(7), 927–938 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  19. Wang, Z., Yang, R., Heng, P.-A., Leung, K.-S.: Real-valued Choquet integrals with fuzzy-valued integrands. Fuzzy Sets and Systems 157(2), 256–269 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  20. John, R.I., Innocent, P.: Modelling uncertainty in clinical diagnosis using fuzzy logic. IEEE Trans. on Systems, Man and Cybernetics-part B 35, 1340–1350 (2005)

    Article  Google Scholar 

  21. Kao, C., Liu, S.-T.: Fractional programming approach to fuzzy weighted average. Fuzzy Sets and Systems 120, 435–444 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  22. Mendel, J.M.: Uncertain Rule-based Fuzzy Logic Systems: Introduction and New Direcctions. Prentice Hall PTR, Englewood Cliffs (2001)

    Google Scholar 

  23. Mizumoto, M., Tanaka, K.: Some Properties of fuzzy sets of type 2. Information and Control 31, 312–340 (1976)

    Article  MathSciNet  MATH  Google Scholar 

  24. Zadeh, L.A.: Fuzzy sets. Information and Control 8, 338–353 (1965)

    Article  MathSciNet  MATH  Google Scholar 

  25. Zadeh, L.A.: The concept of a linguistic variable and its application to approximate reasoning-1. Information Sciences 8, 199–249 (1975)

    Article  MathSciNet  Google Scholar 

  26. Zhou, S.-M., Chiclana, F., John, R.I., Garibaldi, J.M.: Type-1 OWA operators for aggregating uncertain information with uncertain weights induced by type-2 linguistic quantifiers. Fuzzy Sets and Systems 159, 3281–3296 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  27. Zhou, S.-M., Gan, J.Q.: Constructing accurate and parsimonious fuzzy models with distinguishable fuzzy sets based on an entropy measure. Fuzzy Sets and Systems 157, 1057–1074 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  28. Zhou, S.-M., Gan, J.Q.: Constructing parsimonious fuzzy classifiers based on L2-SVM in high-dimensional space with automatic model selection and fuzzy rule ranking. IEEE Trans. on Fuzzy Systems 15, 398–409 (2007)

    Article  Google Scholar 

  29. Zhou, S.-M., Gan, J.Q.: Extracting Takagi-Sugeno fuzzy rules with interpretable submodels via regularization of linguistic modifiers. IEEE Trans. on Knowledge and Data Engineering (2009) (in press)

    Google Scholar 

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Author information

Authors and Affiliations

  1. The Centre for Computational Intelligence, Department of Informatics, De Montfort University, Leicester, LE1 9BH, UK

    Shang-Ming Zhou, Francisco Chiclana & Robert I. John

  2. The Intelligent Modelling and Analysis Research Group, School of Computer Science, University of Nottingham, Nottingham, NG8 1BB, UK

    Jonathan M. Garibaldi

Authors
  1. Shang-Ming Zhou
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  2. Francisco Chiclana
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  3. Robert I. John
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  4. Jonathan M. Garibaldi
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Editor information

Editors and Affiliations

  1. Machine Intelligence Institute , Iona College, 10801, New Rochelle, NY, USA

    Ronald R. Yager

  2. Systems Research Institute , Polish Academy of Sciences, Ul. Newelska 6, 01-447, Warsaw, Poland

    Janusz Kacprzyk

  3. School of Information Technology , Deakin University, 221 Burwood Highway, 3125, Burwood, Victoria, Australia

    Gleb Beliakov

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Zhou, SM., Chiclana, F., John, R.I., Garibaldi, J.M. (2011). Fuzzification of the OWA Operators for Aggregating Uncertain Information with Uncertain Weights. In: Yager, R.R., Kacprzyk, J., Beliakov, G. (eds) Recent Developments in the Ordered Weighted Averaging Operators: Theory and Practice. Studies in Fuzziness and Soft Computing, vol 265. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-17910-5_5

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  • DOI: https://doi.org/10.1007/978-3-642-17910-5_5

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-17909-9

  • Online ISBN: 978-3-642-17910-5

  • eBook Packages: EngineeringEngineering (R0)

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