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References [1] Bullen, Peter S. Handbook of means and their inequalities. Vol 560 of Mathematics and its Applications. Dordrecht: Kluwer Academic Publishers Group, 2003. Cited on 38. [2] Carleman, Torsten. “Sur les fonctions quasi-analitiques.” Conférences faites au cinquième congrès des mathematiciens Scandinaves: tenu a Helsingfors du 4 au 7 juillet 1922 , 181–196. Helsinki: Libr. Académique, 1932. Cited on 41. [3] Daróczy, Zoltán and László Losonczi. “Über den Vergleich von Mittelwerten.” Publ. Math. Debrecen 17 (1970): 289–297 (1971). Cited on 40. [4

References [1] Abdel-Kader, R.F. Genetically Improved PSO Algorithm for Efficient Data Clustering. in Machine Learning and Computing (ICMLC), 2010 Second International Conference on .2010, 71-75. [2] Abdeyazdan, M., Data clustering based on hybrid K-harmonic means and modifier imperialist competitive algorithm. Journal of Supercomputing , 68 , 2, 2014, 574-598. [3] Anaya, A.R. and J.G. Boticario, Application of machine learning techniques to analyse student interactions and improve the collaboration process. Expert Syst. Appl. , 38 , 2, 2011, 1171-1181. [4

convergence theorem for the fuzzy ISODATA clustering Algorithms. IEEE Trans. Pattern Anal. Machine Intell , 2, 1–8. Bezdek, J.C. (1981). Pattern recognition with fuzzy objective function algorithms. New York: Plenum Press. Bezdek, J.C., Ehrlich, R. & Full, W. (1984). FCM: the fuzzy c-means clustering algorithm. Computers and Geosciences , 10, 191–203. Błażewicz, J., Kubiak, W., Morzy, T. & Rusinkiewicz, M. (2003). Handbook on Data Management in Information Systems. Springer-Verlag. Bose, I. & Mahapatra, R.K. (2001). Business data mining – a machine learning

have the greatest similarity and data objects between different clusters have the smallest similarity. A variety of data clustering algorithms have been researched in past years, which include nonnegative matrix factorizsation [ 11 , 12 , 13 , 14 ], mean shift [ 15 , 16 , 17 ], spectral clustering [ 18 , 19 , 20 ], sparse subspace clustering [ 21 , 22 , 23 ], and K -means [ 24 , 25 , 26 , 27 ], etc. Undoubtedly, K -means is the most commonly used and important clustering algorithm. The purpose of K -means clustering purpose is to minimizse the sum of squared

-type and Bullen-type inequalities for Lipschitzian functions and their applications, Comput. Math. Appl., (2012), doi:10.1016/j.camwa.2011.12.076. [22] C. P. Niculescu, The Hermite-Hadamard inequality for log-convex functions, Nonlinear Anal.:TMA, 75(2012), 662-669. [23] U. S. Kirmaci, Inequalities for difierentiable mappings and applications to special means of real numbers and to midpoint formula, Appl. Math. Comput., 147(2004), 137-146. [24] U. S. Kirmaci, M. E. Özdemir, On some inequalities for difierentiable mappings and applications to special means of real numbers

Czech Republic, pp. 346-349, Svratka 2016. [8] Landowski, B., Perczyński, D., Kolber, P., Muślewski, Ł., Economic aspects of a city transport means purchase, Proceedings of 58th International Conference of Machine Design Departments – ICMD 2017, Publisher: Czech University of Life Sciences Prague, Czech Republic, pp. 194-199, Prague 2017. [9] Landowski, B., Woropay, M., Neubauer, A., Sterowanie niezawodnością w systemach transportowych , Biblioteka Problemów Eksploatacji, ITE, Bydgoszcz-Radom 2004. [10] Landowski, B., Muślewski, Ł., Decision model of an operation

clustering data mining techniques. In Grouping multidimensional data, pages 25–71. Springer, 2006. [5] Xiao Cai, Feiping Nie, and Heng Huang. Multi-view k-means clustering on big data. In Twenty-Third International Joint conference on artificial intelligence, 2013. [6] Xiaoli Cui, Pingfei Zhu, Xin Yang, Keqiu Li, and Changqing Ji. Optimized big data k-means clustering using mapreduce. The Journal of Supercomputing, 70(3):1249–1259, 2014. [7] Kenneth Cukier and Viktor Mayer-Schoenberger. The rise of big data: How it’s changing the way we think about the world. Foreign Aff

References 1. Fraley, C., A. E. Rafter y. Model-Based Clustering, Discriminant Analysis, and Density Estimation. - Journal of the American Statistical Association, Vol. 97, 2002, No 458, p. 611. 2. Adebis i, A. A., O. E. Olusay o, O. S. Olatunde. An Exploratory Study of K-Means and Expectation Maximization Algorithms. - British Journal of Mathematics & Computer Science, Vol. 2, 2012, No 2, pp. 62-71. 3. Wu, X., V. Kumar, J. R. Quinlan, J. Ghosh, Q. Yang, H. Motoda, G. J. Mc Lachlan, A. Ng, B. Liu, P. S. Yu, Z.-H. Zhou, M. Steinbach, D. J. Hand, D. Steinberg

References Components of Emotional Meaning. A Sourcebook (2013). Fontaine, Johnny, Scherer, Klaus R., Soriano, Cristina (eds.). Oxford, Oxford University Press, UK. Frijda, Nico H. (1986). The Emotions. Cambridge University Press, Cambridge, UK. Кyseliuk, N.P. (2007). "Syntactic means of expressing emotion "joy" (in modern English"). Language and culture, iss. 9, vol. VI (94), 146-150 [in Russian]. Likhareva, Irina (1982). Interrelations of prosodic, lexical and lexico-grammatical means of expressing modal meanings in English (based on phrases expressing

References P. CZINDER and Z. PALES, Local monotonicity properties of two-variable Gini means and the comparison theorem revisited, J. Math. Anal. Appl., 301 (2005), 427-438. CHAO-PING CHEN, Asymptotic Representations for Stolarsky, Gini and the Generalized Muirhead Means, RGMIA COLLECTION, 11 (4)(2008), 1-13. C. GINI, Di una formula compressiva delle medie, Metron, 13 (1938) 3-22. D. H. LEHMER, On the compounding of certain means, J. Math. Anal. Appl., 36 (1971), 183-200. J. SÁNDER, A Note on Gini Mean, General Mathematics, 12 (4)(2004), 17-21. H. N. SHI, J