×

The support vector machine based on intuitionistic fuzzy number and kernel function. (English) Zbl 1264.68127

Summary: Fuzzy support vector machine applied a degree of membership to each training point and reformulated the traditional support vector machines, which reduced the effects of noises and outliers for classification. However, the degree of membership only considered the distance from samples to the class center in the sample space, while neglected the situation of samples in the feature space and easily mistook the edge support vectors as noises. To deal with the aforementioned problems, the support vector machine based on intuitionistic fuzzy number and kernel function is proposed. In the high-dimensional feature space, each training point is assigned with a corresponding intuitionistic fuzzy number by the use of kernel function. Then, a new score function of the intuitionistic fuzzy numbers is introduced to measure the contribution of each training point. In the end, the new support vector machine is constructed according to the score value of each training point. The simulation results demonstrate the effectiveness and superiority of the proposed method.

MSC:

68T05 Learning and adaptive systems in artificial intelligence

Software:

LIBSVM
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Atanssov K (1983) Intuitionistic fuzzy sets. VII ITKR’s Session, Sofia
[2] Atanssov K (1986) Intuitionistic fuzzy sets. Fuzzy Sets Syst 20:87-96 · Zbl 0631.03040 · doi:10.1016/S0165-0114(86)80034-3
[3] Bai P, Zhang XB, Zhang B et al (2008) Support vector machine and its application in mixed gas infrared spectrum analysis. Xidian University Press, Xi’an
[4] Bovolo F, Bruzzone L, Carlin L (2010) A novel technique for subpixel image classification based on support vector machine. IEEE Trans Image Process 19(11):2983-2999 · Zbl 1371.94058 · doi:10.1109/TIP.2010.2051632
[5] Burges CJC (1998) A tutorial on support vector machines for pattern recognition. Data Mining Knowl Discov 2(2):121-176 · doi:10.1023/A:1009715923555
[6] Chang CC, Lin CJ (2001) A library for support vector machines. http://www.csie.ntu.edu.tw/ cjlin/libsvm · Zbl 0139.24606
[7] Deng NY, Tian YJ (2009) Support vector machine theory, algorithms and generalization. Science Press, Beijing
[8] Gao J, Liu ZQ, Shen P (2009) On characterization of credibilistic equilibria of fuzzy-payoff two-player zero-sum game. Soft Comput 13(2):127-132 · Zbl 1156.91305 · doi:10.1007/s00500-008-0310-3
[9] Gao J, Zhang Q, Shen P (2011) Coalitional game with fuzzy payoffs and credibilistic Shapley value. Iran J Fuzzy Syst 8(4):107-117 · Zbl 1260.91017
[10] Ha MH, Huang S, Wang C et al (2011) Intuitionistic fuzzy support vector machine. J Hebei Univ (Nat Sci Edn) 3:225-229
[11] Lin CF, Wang SD (2002) Fuzzy support vector machines. IEEE Trans Neural Netw 13(2):464-471 · doi:10.1109/72.991432
[12] Li L, Zhou MM, Lu YL (2009) Fuzzy support vector machine based on density with dual membership. Comput Technol Dev 19(12):44-47
[13] Nello C, John S (2000) An introduction to support vector machines. Cambridge University Press, Cambridge · Zbl 0994.68074
[14] Ong CJ, Shao SY, Yang JB (2010) An improved algorithm for the solution of the regularization path of support vector machine. IEEE Trans Neural Netw 21(3):451-462 · doi:10.1109/TNN.2009.2039000
[15] Shen P, Gao J (2011) Coalitional game with fuzzy information and credibilistic core. Soft Comput 15(4):781-786 · Zbl 1243.91008 · doi:10.1007/s00500-010-0632-9
[16] Vapnik VN (1995) The nature of statistical learning theory. A Wiley-Interscience Publication, New York · Zbl 0833.62008
[17] Vapnik VN (1998) Statistical learning theory. A Wiley-Interscience Publication, New York · Zbl 0935.62007
[18] Vapnik VN (1999) An overview of statistical learning theory. IEEE Trans Neural Netw 10(5):988-999 · doi:10.1109/72.788640
[19] Zadeh LA (1965) Fuzzy sets. Inf Control 8:338-353 · Zbl 0139.24606 · doi:10.1016/S0019-9958(65)90241-X
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.