Abstract
The Sugeno integral has numerous successful applications, including but not limited to the areas of decision making, preference modeling, and bibliometrics. Despite this, the current state of the development of usable algorithms for numerically fitting the underlying discrete fuzzy measure based on a sample of prototypical values – even in the simplest possible case, i.e., assuming the symmetry of the capacity – is yet to reach a satisfactory level. Thus, the aim of this paper is to present some results and observations concerning this class of data approximation problems.
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References
Anderson, D., Keller, J., Havens, T.: Learning fuzzy-valued fuzzy measures for the fuzzy-valued Sugeno fuzzy integral. Lecture Notes in Artificial Intelligence, vol. 6178, pp. 502–511 (2010)
Beliakov, G.: How to build aggregation operators from data. Int. J. Intell. Syst. 18, 903–923 (2003)
Beliakov, G., Bustince, H., Calvo, T.: A Practical Guide to Averaging Functions. Springer (2016)
Beliakov, G., James, S.: Using linear programming for weights identification of generalized Bonferroni means in R. Lecture Notes in Computer Science, vol. 7647, pp. 35–44 (2012)
Bullen, P.: Handbook of Means and Their Inequalities. Springer Science+Business Media, Dordrecht (2003)
Dukhovny, A.: Lattice polynomials of random variables. Stat. Probab. Lett. 77, 989–994 (2007)
Gagolewski, M., Grzegorzewski, P.: S-statistics and their basic properties. In: Borgelt, C., et al. (eds.) Combining Soft Computing and Statistical Methods in Data Analysis. Advances in Intelligent and Soft Computing, vol. 77, pp. 281–288. Springer (2010)
Gagolewski, M., Mesiar, R.: Monotone measures and universal integrals in a uniform framework for the scientific impact assessment problem. Inf. Sci. 263, 166–174 (2014)
Grabisch, M., Marichal, J.L., Mesiar, R., Pap, E.: Aggregation Functions. Cambridge University Press, Cambridge (2009)
Hirsch, J.E.: An index to quantify individual’s scientific research output. Proc. Natl. Acad. Sci. 102(46), 16569–16572 (2005)
Johnson, S.G.: The NLopt nonlinear-optimization package (2017), http://ab-initio.mit.edu/nlopt
Klir, G.J., Yuan, B.: Fuzzy Sets and Fuzzy Logic. Theory and Applications. Prentice Hall PTR, New Jersey (1995)
Marichal, J.L.: Weighted lattice polynomials of independent random variables. Disc. Appl. Math. 156, 685–694 (2008)
Mesiar, R., Gagolewski, M.: H-index and other Sugeno integrals: some defects and their compensation. IEEE Trans. Fuzzy Syst. 24(6), 1668–1672 (2016)
Nocedal, J., Wright, S.: Numerical Optimization. Springer, New York (2006)
Prade, H., Rico, A., Serrurier, M.: Elicitation of Sugeno integrals: a version space learning perspective. Lecture Notes in Computer Science, vol. 5722, pp. 392–401 (2009)
R Development Core Team: R: A language and environment for statistical computing. R Foundation for Statistical Computing, Vienna, Austria (2017), http://www.R-project.org
Rios, L.M., Sahinidis, N.V.: Derivative-free optimization: a review of algorithms and comparison of software implementations. J. Global Optim. 56, 1247–1293 (2013)
Sugeno, M.: Theory of fuzzy integrals and its applications. Ph.D. thesis, Tokyo Institute of Technology (1974)
Torra, V.: Learning weights for the quasi-weighted means. IEEE Trans. Fuzzy Syst. 10(5), 653–666 (2002)
Torra, V., Narukawa, Y.: The \(h\)-index and the number of citations: two fuzzy integrals. IEEE Trans. Fuzzy Syst. 16(3), 795–797 (2008)
Yager, R.R.: On ordered weighted averaging aggregation operators in multicriteria decision making. IEEE Trans. Syst. Man Cybern. 18(1), 183–190 (1988)
Yager, R.R., Kacprzyk, J. (eds.): The Ordered Weighted Averaging Operators. Theory and Applications. Kluwer Academic Publishers, Norwell (1997)
Yuan, B., Klir, G.J.: Constructing fuzzy measures: a new method and its application to cluster analysis. In: Proceedings of NAFIPS 1996, pp. 567–571 (1996)
Acknowledgments
This study was supported by the National Science Center, Poland, research project 2014/13/D/HS4/01700. Data provided by Scopus.com.
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Gągolewski, M., James, S. (2018). Fitting Symmetric Fuzzy Measures for Discrete Sugeno Integration. In: Kacprzyk, J., Szmidt, E., Zadrożny, S., Atanassov, K., Krawczak, M. (eds) Advances in Fuzzy Logic and Technology 2017. EUSFLAT IWIFSGN 2017 2017. Advances in Intelligent Systems and Computing, vol 642. Springer, Cham. https://doi.org/10.1007/978-3-319-66824-6_10
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DOI: https://doi.org/10.1007/978-3-319-66824-6_10
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