Abstract
The paper presents that with the application of \(Z^+\)-numbers arithmetic, the k nearest neighbors method can be adapted to various types of data. Both, the learning data and the input data may be in the form of the crisp number, interval, fuzzy or \(Z^+\)-number. The paper discusses the methods of performing arithmetic operations on uncertain data of various types and explains how to use them in the kNN method. Experiments show that the method works correctly and gives credible results.
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References
Zadeh, L.A.: A note on Z-numbers. Inf. Sci. 181, 2923â2932 (2011)
Atkeson, C.G., Moore, A.W., Schaal, S.A.: Locally weighted learning. Artif. Intell. Rev. 11, 11â73 (1997)
Cichosz, P.: Learning Systems. WNT Publishing House, Warsaw (2000). [in Polish]
Hand, D., Mannila, H., Smyth, P.: Principles of Data Mining. The MIT Press, Cambridge (2001)
Kordos, M., Blachnik, M., Strzempa, D.: Do we need whatever more than k-NN? In: Rutkowski, L., Scherer, R., Tadeusiewicz, R., Zadeh, L.A., Zurada, J.M. (eds.) ICAISC 2010. LNCS, vol. 6113, pp. 414â421. Springer, Heidelberg (2010)
KorzeĆ, M., KlÄsk, P.: Sets of approximating functions with finite Vapnik-Czervonenkis dimension for nearest-neighbours algorithm. Pattern Recogn. Lett. 32, 1882â1893 (2011)
PluciĆski, M.: Application of the information-gap theory for evaluation of nearest neighbours method robustness to data uncertainty. PrzeglÄ d Elektrotechniczny 88(10b), 272â275 (2012)
PluciĆski, M., Pietrzykowski, M.: Application of the \(k\) nearest neighbors method to fuzzy data processing. PrzeglÄ d Elektrotechniczny 93(1), 77â81 (2017)
Aliev, R.A., Huseynov, O.H., Aliyev, R.R., Alizadeh, A.A.: The Arithmetic of Z-Numbers: Theory and Applications. World Scientific, Singapore (2015)
Dubois, D., Prade, H.: Operations on fuzzy numbers. Int. J. Syst. Sci. 9(6), 613â626 (1978)
Grzegorzewski, P.: Metrics and orders in space of fuzzy numbers. Fuzzy Sets Syst. 97, 83â94 (1998)
Piegat, A.: Fuzzy Modeling and Control. Physica, Heidelberg (2001)
Moore, R.E., Kearfott, R.B., Cloud, M.J.: Introduction to Interval Analysis. Society for Industrial and Applied Mathematics, Philadelphia (2009)
Dutta, P., Boruah, H., Ali, T.: Fuzzy arithmetic with and without using \(\alpha \)-cut method: a comparative study. Int. J. Latest Trends Comput. 2(1), 99â107 (2011)
Hanss, M.: Applied Fuzzy Arithmetic. Springer, Heidelberg (2005)
Kaufmann, A., Gupta, M.M.: Introduction to Fuzzy Arithmetic. Van Nostrand Reinhold, New York (1991)
Springer, M.D.: The Algebra of Random Variables. John Wiley & Sons, New York (1979)
Jaroszewicz, S., KorzeĆ, M.: Arithmetic operations on independent random variables: a numerical approach. SIAM J. Sci. Comput. 34(3), 1251â1265 (2012)
Diamond, P., Rosenfeld, A.: Metric spaces of fuzzy sets. Fuzzy Sets Syst. 35, 241â249 (1990)
Tang, W., Li, X., Zhao, R.: Metric spaces of fuzzy variables. Comput. Ind. Eng. 57, 1268â1273 (2009)
Rachev S.T., Klebanov L., Stoyanov S.V., Fabozzi F.: The Methods of Distances in the Theory of Probability and Statistics. Springer Science and Business Media (2013)
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PluciĆski, M. (2019). Processing of \(Z^+\)-numbers Using the k Nearest Neighbors Method. In: PejaĆ, J., El Fray, I., Hyla, T., Kacprzyk, J. (eds) Advances in Soft and Hard Computing. ACS 2018. Advances in Intelligent Systems and Computing, vol 889. Springer, Cham. https://doi.org/10.1007/978-3-030-03314-9_7
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DOI: https://doi.org/10.1007/978-3-030-03314-9_7
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