We introduce a new n-ary λ similarity classifier that is based on a new n-ary λ-averaging operator in the aggregation of similarities. This work is a natural extension of earlier research on similarity based classification in which aggregation is commonly performed by using the OWA-operator. So far λ-averaging has been used only in binary aggregation. Here the λ-averaging operator is extended to the n-ary aggregation case by using t-norms and t-conorms. We examine four different n-ary norms and test the new similarity classifier with five medical data sets. The new method seems to perform well when compared with the similarity classifier.
@article{bwmeta1.element.bwnjournal-article-amcv26i2p407bwm,
author = {Onesfole Kurama and Pasi Luukka and Mikael Collan},
title = {An n-ary $\lambda$-averaging based similarity classifier},
journal = {International Journal of Applied Mathematics and Computer Science},
volume = {26},
year = {2016},
pages = {407-421},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-amcv26i2p407bwm}
}
Onesfole Kurama; Pasi Luukka; Mikael Collan. An n-ary λ-averaging based similarity classifier. International Journal of Applied Mathematics and Computer Science, Tome 26 (2016) pp. 407-421. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-amcv26i2p407bwm/
[000] Alsina, C., Trillas, E. and Valverde, L. (1983). On some logical connectives for fuzzy set theory, Mathematical Analysis and Applications 93(1): 15-26. | Zbl 0522.03012
[001] Calvo, T., Mayer, G. and Mesiar, R. (2002). Aggregation Operators: New Trends and Applications, Physica-Verlag, Heidelberg/New York, NY. | Zbl 0983.00020
[002] Detyniecki, M. (2000). Mathematical Aggregation Operators and Their Application to Video Querying, Ph.D. thesis, University of Paris, Paris.
[003] Dubois, D. and Prade, H. (1985). A review of fuzzy sets aggregation connectives, Information Sciences 36(1): 85-121. | Zbl 0582.03040
[004] Dubois, D. and Prade, H. (2004). On the use of aggregation operations in information fusion processes, Fuzzy Sets and Systems 142(1): 143-161. | Zbl 1091.68107
[005] Duda, R., Hart, P. and Stork, G.D. (1973). Pattern Classification and Scene Analysis, John Wiley and Sons, New York, NY. | Zbl 0277.68056
[006] Ezghari, S., Belghini, N., Zahi, A. and Zarghili, A. (2015). A gender classification approach based on 3D depth-radial curves and fuzzy similarity based classification, Intelligent Systems and Computer Vision Conference, Fez, Morocco, pp. 1-6.
[007] Fengqiu, L. and Xiaoping, X. (2012a). Constructing kernels by fuzzy rules for support vector regressions, International Journal of Innovative Computing, Information and Control 8(7): 4811-4822.
[008] Fengqiu, L. and Xiaoping, X. (2012b). Design of natural classification kernels using prior knowledge, IEEE Transactions on Fuzzy Systems 20(1): 135-152.
[009] Gabryel, M., Korytkowski, M., Pokropinska, A., Scherer, R. and Drozda, S. (2010). Evolutionary Learning for NeuroFuzzy Ensembles with Generalized Parametric Triangular Norms, Springer-Verlag, Berlin/Heidelberg.
[010] Gil, G., Girela, L.J., De Juan, J., Gomez-Torres, J.M. and Johnsson, M. (2012). Predicting seminal quality with artificial intelligence methods, Expert Systems with Applications 39(16): 12564-12573.
[011] Hohle, U. (1978). Probabilistic uniformization of fuzzy topologies, Fuzzy Sets and Systems 1(4): 311-332. | Zbl 0413.54002
[012] Klement, E.P., Mesiar, R. and Pap, E. (2000). Triangular Norms, Kluwer Academic Publishers, Dordrecht. | Zbl 0972.03002
[013] Klement, E.P., Mesiar, R. and Pap, E. (2003a). Triangular norms, Position paper I: Basic analytical and algebraic properties, Fuzzy Sets and Systems 143(1): 5-26. | Zbl 1038.03027
[014] Klement, E.P., Mesiar, R. and Pap, E. (2003b). Triangular norms, Position paper II: General constructions and parametrized families, Fuzzy Sets and Systems 145(3): 411-438. | Zbl 1059.03012
[015] Klir, G.J. and Folger, T.A. (1988). Fuzzy Sets, Uncertainty and Information, Prentice Hall, Englewood Cliffs, NJ. | Zbl 0675.94025
[016] Klir, G.J. and Yuan, B. (1995). Fuzzy Sets and Fuzzy Logic: Theory and Applications, Prentice Hall, Englewood Cliffs, NJ. | Zbl 0915.03001
[017] Korytkowski, M. and Scherer, R. (2010). Modular Neurofuzzy Systems Based on Generalized Parametric Triangular Norms, Springer-Verlag, Berlin/Heidelberg.
[018] Łukasiewicz, J. (1970). Selected Works, North Holland, Amsterdam/London. | Zbl 0212.00902
[019] Li, P. and Fang, S.C. (2008). On the resolution and optimization of a system of fuzzy relational equations with sup-t composition, Fuzzy Optimization Decision Making 7(2): 169-214. | Zbl 1169.90493
[020] Luukka, P. (2005). Similarity Measure Based Classification, Ph.D. thesis, Lappeenranta University of Technology, Lappeenranta.
[021] Luukka, P. (2007). Similarity classifier using similarity measure derived from Yu's norms in classification of medical data sets, Computers in Biology and Medicine 37(7): 1133-1140.
[022] Luukka, P. (2008). Similarity classifier using similarities based on modified probabilistic equivalence relations, Knowledge Based Systems 22(1): 57-62.
[023] Luukka, P. (2009). Classification based on fuzzy robust PCA algorithms and similarity classifier, Expert Systems with Applications 36(4): 7463-7468.
[024] Luukka, P. (2011). Feature selection using fuzzy entropy measures with similarity classifier, Expert Systems with Applications 38(4): 4600-4607.
[025] Luukka, P. and Kurama, O. (2013). Similarity classifier with ordered weighted averaging operators, Expert Systems with Applications 40(4): 995-1002.
[026] Luukka, P. and Leppalampi, T. (2006). Similarity classifier with generalized mean applied to medical data, Computers in Biology and Medicine 36(9): 1026-1040.
[027] Luukka, P., Saastamoinen, K. and Kononen, V. (2001). A classifier based on the maximal fuzzy similarity in the generalized Łukasiewicz structure, Proceedings of the FUZZ-IEEE 2001 Conference, Melbourne, Australia, pp. 195-198.
[028] Mattila, J.K. (2002). Fuzzy Logic Course Book, Art House, Helsinki, (in Finnish).
[029] Menger, K. (1942). Statistical metrics, Proceedings of the National Academy of Sciences of the United States of America 28(12): 535-537. | Zbl 0063.03886
[030] Newman, D.J., Hettich, S., Blake, C.L. and Merz, C.J. (2012). UCI Repository of Machine Learning Databases, www.ics.uci.edu/˜{}mlearn/ MLRepository.html.
[031] O'Hagan, M. (1988). Aggregating template or rule antecedents in real time expert systems with fuzzy set logic, Proceedings of the 22nd Annual IEEE Asilomar Conference on Signals, Systems, Computers, Pacific Grove, CA, USA, pp. 681-689.
[032] Saminger, P.S., Mesier, R. and Dubois, D. (2007). Aggregation operators and commuting, IEEE Transactions on Fuzzy Systems 15(6): 1032-1045.
[033] Schweizer, B. and Sklar, A. (1960). Statistical metric spaces, Pacific Journal of Mathematics 10(1): 313-334. | Zbl 0091.29801
[034] Schweizer, B. and Sklar, A. (1983). Probabilistic Metric Spaces, North-Holland, New York, NY. | Zbl 0546.60010
[035] Sivaramakrishnan, R. and Arun, C. (2014). Classification of Denver systems of chromosomes using similarity classifier guided by OWA operators, Current Bioinformatics 9(5): 449-508.
[036] Turunen, E. (2002). Mathematics Behind Fuzzy Logic, Physic-Verlag, Heidelberg. | Zbl 0940.03029
[037] Vlahogianni, E. and Karlaftis, M.G. (2013). Fuzzy-entropy neural network freeway incident duration modeling with single and competing uncertainties, Computer-aided Civil and Infrastructure Engineering 28(6): 420-433.
[038] Xu, Z.S. (2008). Linguistic aggregation operators: An overview, Fuzzy Sets and Their Extension, Representation, Aggregation and Models 220(1): 163-181. | Zbl 1147.68083
[039] Yager, R.R. (1988). On ordered weighted averaging aggregation operators in multi-criteria decision making, IEEE Transactions on Systems, Man and Cybernetics, 18(1): 183-190. | Zbl 0637.90057