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On Fuzziness pp 691–695Cite as

Aggregation Operators

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Part of the book series: Studies in Fuzziness and Soft Computing ((STUDFUZZ,volume 299))

Abstract

It was in 1990, when I was still studying my degree in Computer Science, when I met Prof. Lotfi Zadeh for the first time, if I do not remember wrongly. It was in a conference I was participating in Barcelona where he gave one of the plenary talks. I remember clearly that he mentioned fuzzy systems and the successful Japanese applications of the late 80es. I have always used the applications of fuzzy systems in class as an example of successful applications of artificial intelligence and related technologies.

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References

  1. Beliakov, G., Warren, J.: Appropriate Choice of Aggregation Operators in Fuzzy Decision Support Systems. IEEE Transactions on Fuzzy Systems 9(6), 773–784 (2001)

    Article  Google Scholar 

  2. Dujmovic, J.J., de Tré, F.: Multicriteria methods and logic aggregation in suitability maps. International Journal of Intelligent Systems 26(10), 971–1001 (2011)

    Article  Google Scholar 

  3. Dujmovic, J.J., Nagashima, H.: LSP Method and its Use for Evaluation of Java IDEs. International Journal of Approximate Reasoning 41(41), 3–22 (2006)

    Article  MATH  Google Scholar 

  4. Grabisch, M.: k-order Additive Discrete Fuzzy Measures and Their Representation. Fuzzy Sets and Systems 92(2), 167–189 (1997)

    Article  MathSciNet  MATH  Google Scholar 

  5. Kojadinovic, I.: Unsupervised Aggregation by the Choquet Integral Based on Entropy Functionals: Application to the Evaluation of Students. In: Torra, V., Narukawa, Y. (eds.) MDAI 2004. LNCS (LNAI), vol. 3131, pp. 163–175. Springer, Heidelberg (2004)

    Chapter  Google Scholar 

  6. Murofushi, T., Narukawa, Y.: A Characterization of Multi-level Discrete Choquet integral Over a Finite Set. In: Proceedings of the 7th Workshop on Evaluation of Heart and Mind, pp. 33–36 (2002) (in Japanese)

    Google Scholar 

  7. O’Hagan, M.: Aggregating Template or Rule Antecedents in Real-time Expert Systems With Fuzzy Set Logic. In: Proceedings of the 22nd Annual IEEE Asilomar Conference Signals, Systems, Computers, Pacific Grove, CA, pp. 681–689 (1988)

    Google Scholar 

  8. Saaty, T.L.: The Analytic Hierarchy Process. McGraw-Hill, New York (1980)

    MATH  Google Scholar 

  9. Soria-Frisch, A.: Unsupervised Construction of Fuzzy Measures Through Self-organizing Feature Maps and its Application in Color Image Segmentation. International Journal of Approximate Reasoning 41, 23–42

    Google Scholar 

  10. Sugeno, M.: Theory of Fuzzy Integrals and its Applications, Ph. D. Dissertation, Tokyo Institute of Technology, Tokyo, Japan (1974)

    Google Scholar 

  11. Torra, V.: Consenso de funciones de pertenencia triangulares. Actas del Tercer Congreso Español sobre Tecnologías y Lógica Fuzzy, Santiago de Compostela, pp. 161–168 (1993)

    Google Scholar 

  12. Torra, V.: Combining Fuzzy Sets: The Geometric Consensus Function Family. Fuzzy Sets and Systems 74, 335–342 (1995)

    Article  MathSciNet  MATH  Google Scholar 

  13. Torra, V.: On Some Relationships Between Hierarchies of Quasi-arithmetic Means and Neural Networks. International Journal of Intelligent Systems 14(11), 1089–1098 (1999)

    Article  MATH  Google Scholar 

  14. Torra, V.: Aggregation Operators and Models. Fuzzy Sets and Systems 156(3), 407–410 (2005)

    Article  MathSciNet  Google Scholar 

  15. Torra, V., Narukawa, Y.: On the Meta-knowledge Choquet integral and Related Models. International Journal of Intelligent Systems 20(10), 1017–1036

    Google Scholar 

  16. Torra, V., Narukawa, Y.: Fuzzy Measure and Probability Distributions: Distorted Probabilities. IEEE Transactions on Fuzzy Systems 13(5), 617–629 (2005)

    Article  MathSciNet  Google Scholar 

  17. Torra, V., Narukawa, Y.: Modeling Decisions: Information Fusion and Aggregation operators. Springer, New York (2007)

    Google Scholar 

  18. Torra, V., Narukawa, Y.: A View of Averaging Aggregation Operators. IEEE Transactions on Fuzzy Systems 15(6), 1063–1067 (2007)

    Article  Google Scholar 

  19. Tunstel, E., de Oliveira, M.A.A., Berman, S.: Fuzzy Behavior Hierarchies for Multi-Robot Control. International Journal of Intelligent Systems 17, 449–470 (2002)

    Article  MATH  Google Scholar 

  20. Yager, R.R.: On Ordered Weighted Averaging Aggregation Operators in Multi-criteria Decision Making. IEEE Transactions on Systems, Man and Cybernetics 18, 183–190 (1988)

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  22. Zadeh, L.A.: From Computing With Numbers to Computing With Words – From Manipulation of Measurements to Manipulations of Perceptions. International Journal of Applied Mathematics and Computer Science 12(3), 307–324 (2002)

    MathSciNet  MATH  Google Scholar 

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Torra, V. (2013). Aggregation Operators. In: Seising, R., Trillas, E., Moraga, C., Termini, S. (eds) On Fuzziness. Studies in Fuzziness and Soft Computing, vol 299. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-35644-5_38

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  • DOI: https://doi.org/10.1007/978-3-642-35644-5_38

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-35643-8

  • Online ISBN: 978-3-642-35644-5

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