Skip to main content

Part of the book series: The Handbooks of Fuzzy Sets Series ((FSHS,volume 4))

  • 1304 Accesses

Abstract

In Section 1.1 we defined a classifier as any function D:ℜp ↦ Npc. The value y = D(z) is the label vector for z in ℜP. D is a crisp classifier if D [ℜp] = Nhc; otherwise, the classifier is fuzzy, possibilistic or probabilistic, which for convenience we lump together as soft classifiers. This chapter describes some of the most basic (and often most useful) classifier designs, along with some fuzzy generalizations and relatives.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 259.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 329.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 329.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Comments and bibliography

  • Hughes, G. F. (1968). On the mean accuracy of statistical pattern recognizers, IEEE Trans. Inf. Theory, 14, 55–63.

    Article  Google Scholar 

  • Haykin, S. (1994). Neural Networks: A Comprehensive Foundation, MacMillan, NY.

    MATH  Google Scholar 

  • Chiang, J. and Gader, P. (1997). Hybrid fuzzy-neural systems in handwritten word recognition. IEEE Trans. Fuzzy Syst., 5 (4), 497–510.

    Article  Google Scholar 

  • Gader, P., Keller, J. M., Krishnapuram, R., Chiang, J., and Mohamed, M. (1997b). Neural and fuzzy methods in handwriting recognition, IEEE Computer, 30 (2) 79–86.

    Article  Google Scholar 

  • Rosenfeld, A. (1979). Fuzzy digital topology, Inf. and Control, 40, 7687.

    Article  MathSciNet  Google Scholar 

  • Rosenfeld, A. (1984). The fuzzy geometry of image subsets, Patt. Recog. Lett., 2, 311–317.

    Article  Google Scholar 

  • Rosenfeld, A. (1992). Fuzzy geometry: An overview, Proc. IEEE Int. Conf on Fuzzy Syst., 113–118.

    Google Scholar 

  • Rosenfeld, A. and Haber, S. (1985). The perimeter of a fuzzy set, Patt. Recog., 18, 125–130.

    Article  MATH  MathSciNet  Google Scholar 

  • Pal, S. K. and Rosenfeld, A. (1988). Image enhancement and thresholding by optimization of fuzzy compactness, Patt. Recog. Lett., 7, 77–86.

    Article  MATH  Google Scholar 

  • Pal, S. K. and Ghosh, A. (1990). Index of area coverage of fuzzy subsets and object extraction, Patt. Recog. Lett., 11, 831–841.

    Article  MATH  Google Scholar 

  • Pal, S. K. (1992a). Fuzzy set theoretic measure for automatic feature evaluation–II, Inform. Sci., 64, 165–179.

    Article  MATH  Google Scholar 

  • Dubois, D. and Jaulent, M. C. (1987). A general approach to parameter evaluation in fuzzy digital pictures, Patt. Recog. Lett., 6, 251–259.

    Article  MATH  Google Scholar 

  • Krishnapuram, R. and Chen, L. (1993). Implementation of parallel thinning algorithms using recurrent neural networks, IEEE Trans. Neural Networks, 4, 142–147.

    Article  Google Scholar 

  • Krishnapuram, R. and Medasani, S. (1995). Recovery of geometric properties of binary objects from blurred images, Proc. IEEE Int. Conf. on Fuzzy Syst., IEEE Press Piscataway, NJ, 1793–1798.

    Google Scholar 

  • Medasani, S., Krishnapuram, R. and Keller, J. M. (1999). Are fuzzy definitions of image properties really useful?, IEEE Trans. Syst., Man and Cyberns., in press.

    Google Scholar 

  • Keller, J. M. and Chen, Z. (1992a). Learning in fuzzy neural networks utilizing additive hybrid operators, Proc. Int. Conf. on Fuzzy Logic and Neural Networks, Iizuka, Japan, 85–87.

    Google Scholar 

  • Keller, J. M. and Wang, X. (1996). Learning spatial relationships in computer vision, Proc. IEEE Int. Conf on Fuzzy Syst., IEEE Press, Piscataway, NJ, 118–124.

    Google Scholar 

  • Miyajima, K. and Ralescu, A. L. (1994). Spatial organization in 2D segmented images: representation and recognition of primitive spatial relations, Fuzzy Sets and Syst., 65, 225–236.

    Google Scholar 

  • Wang, X. and Keller, J. M. (1999a). Human-based spatial relationship generalization through neural/fuzzy approaches, Fuzzy Sets and Syst., 101 (1), 5–20.

    Article  Google Scholar 

  • Bezdek, J. C. and Castelaz, P. F. (1977). Prototype classification and feature selection with fuzzy sets, IEEE Trans. Syst., Man and Cyberns., 7, 87–92.

    MATH  Google Scholar 

  • Gesu, V. and Maccarone, M.C. (1986). Feature selection and possibility theory, Patt. Recog., 19, 63–72.

    Article  Google Scholar 

  • Davenport, J. W., Bezdek, J. C. and Hathaway, R. (1988). Parameter estimation for finite mixture distributions, Int. J. Comp. and Math. with Applications, 15 (10), 819–828.

    Article  MATH  MathSciNet  Google Scholar 

  • Petersen, J., Stockmanns, G., Kochs, H-D. and Kochs, E. (1997). Automatic feature extraction in clinical monitoring data, Proc. Fuzzy-Neuro Systems- Computational Intelligence, eds. A. Grauel, W. Becker and F. Belli, Infix Press, St. Augustine, Germany, 411–418.

    Google Scholar 

  • Cios, K. and Sztandera, L. M. (1992). Continuous ID3 algorithm with fuzzy entropy measures, Proc. IEEE Int. Conf. on Fuzzy Syst., IEEE Press, Piscataway, NJ 469–476.

    Chapter  Google Scholar 

  • Pal, S. K. and Chakraborty, B. (1986). Fuzzy set theoretic measure for automatic feature evaluation, IEEE Trans. Syst. Man and Cyberns., 16 (5), 754–760.

    Article  Google Scholar 

  • Pal, S. K. (1991). Fuzzy tools for the management of uncertainty in pattern recognition, image analysis, vision and expert system, Int. J. Syst. Sci., 22 (3), 511–549.

    Article  MATH  Google Scholar 

  • Pal, S. K. (1992a). Fuzzy set theoretic measure for automatic feature evaluation–II, Inform. Sci., 64, 165–179.

    Article  MATH  Google Scholar 

  • Thawonmas R. and Abe S. (1997). A novel approach to feature selection based on analysis of class regions, IEEE Trans. Syst., Man and Cyberns., B27 (2), 196–207.

    Article  Google Scholar 

  • DePalma, G.F. and Yau, S. S. (1975). Fractionally fuzzy grammars with application to pattern recognition, in Fuzzy Sets and their Applications to Cognitive and Decision Processes, eds. L. A. Zadeh, K.S. Fu, K. Tanaka and M. Shimura, Academic Press, NY, 329–351.

    Google Scholar 

  • Devijver, P. and Kittler, J. (1982). Pattern Recognition: A Statistical Approach, Prentice-Hall, Englewood Cliffs, NJ.

    Google Scholar 

  • Dasarathy, B.V. (1990). Nearest Neighbor (NN) Norms: NN Pattern Classification Techniques, IEEE Computer Society Press, Los Alamitos, CA.

    Google Scholar 

  • Kuncheva, L. I. and Bezdek, J. C. (1998). Nearest prototype classification: clustering, genetic algorithms or random search?, IEEE Trans. Syst. Man and Cyberns., C28 (1), 160–164.

    Article  Google Scholar 

  • Velthuizen, R. P., Hall, L. O. and Clarke, L. P. (1996). Feature extraction with genetic algorithms for fuzzy clustering, Biomed. Engineering Appl., Basis and Communications, 8 (6), 496–517.

    Google Scholar 

  • Chang, C.L. (1974). Finding prototypes for nearest neighbor classification, IEEE Trans. Computer, 23 (11), 1179–1184.

    Article  MATH  Google Scholar 

  • Blonda, P. N., Satalino, G., Baraldi, A. and De Blasi, R. (1998). Segmentation of multiple sclerosis lesions in MRI by fuzzy neural networks: FLVQ and FOSART, Proc. NAFIPS Conf., eds. J. C. Bezdek and L. O. Hall, 39–43.

    Google Scholar 

  • Bobrowski, L. and Bezdek, J. C. (1991). c-Means Clustering with the e l and e Norms, IEEE Trans. Syst.,Man and Cyberns.,21(3), 545–554.

    Google Scholar 

  • Bookstein, F. L. (1979). Fitting conic sections to scattered data, CVGIP, 9, 56–71.

    Google Scholar 

  • Bombardier, V., Jaulent, M.-C., Bubel, A. and Bremont, J. (1997). Cooperation of two fuzzy segmentation operators for digital substract angiograms analysis. Proc. Sixth IEEE Int. Conf. on Fuzzy Syst., 2, IEEE Press, Piscataway, NJ, 1057–1062.

    Google Scholar 

  • Boudraa, A. E. (1997). Automated detection of the left ventricle region in magnetic resonance images by the fuzzy c-means model, Int. J. of Cardiac Imaging, 13, 347–355.

    Article  Google Scholar 

  • Boudraa, A. E., Mallet, J. J., Besson, J. E., Bouyoucef, S. E. and Champier, J. (1993). Left ventricle automated detection method in gated isotropic ventriculography using fuzzy clustering, IEEE Trans. Med. Imaging, 12 (3), 451–465.

    Article  Google Scholar 

  • Dudani, S. A. (1976). The distance weighted k-nearest neighbor rule, IEEE Trans. Syst., Man and Cyberns., 6, 325–327.

    Google Scholar 

  • Dunn, J. C. (1974a). A fuzzy relative of the ISODATA process and its use in detecting compact well-separated clusters, J. Cyberns., 3 (3), 32–57.

    MathSciNet  Google Scholar 

  • Dunn, J. C. (1974b). A graph theoretic analysis of pattern classification via Tamura’s fuzzy relation, IEEE Trans. Syst., Man and Cybems., 4, 310–313.

    Google Scholar 

  • Dunn, J. C. (1977). Indices of partition fuzziness and the detection of clusters in large data sets, in Fuzzy Automata and Decision Processes, ed. M.M. Gupta, Elsevier, NY.

    Google Scholar 

  • Dutta, S. (1991). Approximate spatial reasoning: integrating qualitative and quantitative constraints Int. J. of Approximate Reasoning, 5, 307–331.

    Article  Google Scholar 

  • Fisher, P. F. and Pathirana, S. (1990). The evaluation of fuzzy membership of land cover classes in the suburban zone, Remote Sensing of the Environment, 34, 121–132.

    Article  Google Scholar 

  • Fisher, R. A. (1936). The use of multiple measurements in taxonomic problems, Ann. Eugenics, 7 (2), 179–188.

    Article  Google Scholar 

  • Forgy, E. (1965). Cluster analysis of multivariate data: efficiency vs interpretability of classifications, Biometrics, 21 (3).

    Google Scholar 

  • Fowlkes, E. B. and Mallows, C. L. (1983). A method of comparing two hierarchical clusterings, J. Amer. Stat. Assoc., 78, 553–569.

    Article  MATH  Google Scholar 

  • Freeman, J. (1975). The modeling of spatial relations, Computer Graphics and Image Processing, 4, 156–171.

    Article  Google Scholar 

  • Kuncheva, L. I. and Bezdek, J. C. (1999). An integrated framework for generalized nearest prototype classifier design, Int. J. Uncertainty, Fuzziness and Knowledge-Based Syst., 6 (5), 437–457.

    Article  Google Scholar 

  • Kuncheva, L. I., Bezdek, J. C. and Duin, R. (1999). Decision templates for multiple classifier fusion: An experimental comparison, Patt. Recog., in press.

    Google Scholar 

  • Kuncheva, L. I., Bezdek, J. C. and Sutton, M. A. (1998). On combining multiple classifiers by fuzzy templates, Proc. NAFIPS Cont., eds. J. C. Bezdek and L.O. Hall, 193–197.

    Google Scholar 

  • Kuncheva, L. I., Kounchev, R.K. and Zlatev, R.Z. (1995) Aggregation of multiple classification decisions by fuzzy templates, Proc. European Congress on Intelligent Techniques and Soft Computing, Aachen, Germany, 1470–1474.

    Google Scholar 

  • Kundu, S. (1995). Defining the fuzzy spatial relationship LEFT(A,B), Proc. IFSA Congress, 1, 653–656.

    Google Scholar 

  • Kwan, H. K. and Cai Y. (1994). A fuzzy neural network and its application to pattern recognition, IEEE Trans. Fuzzy Syst., 2 (3), 185–193.

    Article  Google Scholar 

  • Senay, H. (1992). Fuzzy command grammars for intelligent interface design, IEEE Trans. Syst., Man and Cyberns., 22 (5), 1124–1131.

    Article  Google Scholar 

  • Serrano-Gotarredona, T., Linares-Barranco, B. and Andreou, A. G. (1998). Adaptive Resonance Theory Microchips: Circuit Design Techniques, Kluwer, Boston, MA.

    Google Scholar 

  • Sethi, I. K. (1990). Entropy nets: from decision trees to neural networks, Proc. IEEE, 78 (10), 1605–1613.

    Article  Google Scholar 

  • Sethi, I. K. (1995). Neural implementation of tree classifiers, IEEE Trans. Syst., Man and Cyberns., 25 (8), 1243–1249.

    Article  Google Scholar 

  • Sethi, I. K. and Sarvarayudu, G.P.R. (1982). Hierarchical classifier design using mutual information, IEEE Trans. Patt. Anal. and Machine Intell., 4, 441–445.

    Article  Google Scholar 

  • Shephard, R.N. and Arabie, P. (1979). Additive clustering: representation of similarities as combinations of discrete overlapping properties, Psychological Review, 86 (2), 87–123.

    Article  Google Scholar 

  • Shi, H., Gader, P. and Chen, W. (1998). Fuzzy integral filters: properties and parallel implementations, J. of Real-Time Imaging, 2 (4), 233–241.

    Article  Google Scholar 

  • Shih, F. Y., Moh, J. and Chang, F. (1992). A new ART-based neural architecture for pattern classification and image enhancement without prior knowledge, Patt. Recog., 25 (5), 533–542.

    Article  Google Scholar 

  • Simpson, P. K. (1993). Fuzzy min-max neural networks–Part 2: Clustering, IEEE Trans. Fuzzy Syst., 1(1), 32–45.

    Google Scholar 

  • Sims, S. R. and Dasarathy, B. (1992). Automatic target recognition using a passive multisensor suite, Optical Engineering, 31 (12), 2584–2593.

    Article  Google Scholar 

  • Sin, S. K. and deFigueiredo, R. J. P. (1993). Fuzzy system design through fuzzy clustering and optimal predefuzzification, Proc. IEEE Int. Conf Fuzzy Syst., San Francisco, CA, 190–195.

    Google Scholar 

  • Sinha, D., Sinha, P., Dougherty, E. R. and Batman, S. (1997). Design and analysis of fuzzy morphological algorithms for image processing, IEEE Trans. Fuzzy Syst., 5 (4), 570–584.

    Article  Google Scholar 

  • Sinha, D. and Dougherty, E. R. (1992). Fuzzy mathematical morphology, J. Comm. Image Representation, 3 (3), 286–302.

    Article  Google Scholar 

  • Solina, F. and Bajcsy, R. (1990). Recovery of parametric models from range images: the case for superquadrics, IEEE Trans. Patt. Anal. and Machine Intell., 12 (2), 131–176.

    Article  Google Scholar 

  • Srinivasan, R., and Kinser, J. (1998). A foveating fuzzy scoring target recognition system, Patt. Recog., 31 (8), 1149–1158.

    Article  Google Scholar 

  • Srinivasan, R., Kinser, J., Schamschula, J., Shamir, J. and Caulfield, H. J. (1996). Optical syntactic pattern recognition by fuzzy scoring, Optical Lett., 21 (11), 815–817.

    Article  Google Scholar 

  • St. Clair, D. C., Bond, W. E., Rigler, A. K. and Aylward, S. (1992). An evaluation of learning performance in backpropagation and decision-tree classifier systems, Proc. ACM/SIGAPP Symp. on Applications Computers, ACM Press, 636–642.

    Google Scholar 

  • Stanley, R. J., Keller, J. M., Caldwell, C. W. and Gader, P. (1995). Automated chromosome classification limitations due to image processing, Proc. Rocky Mountain Bioengineering Symp., Copper Mountain, CO, 183–188.

    Google Scholar 

  • Suh, I. H. and Kim, T. W. (1994). Fuzzy membership function based neural networks with applications to the visual servoing of robot manipulators, IEEE Trans. Fuzzy Syst., 2 (3), 203–220.

    Article  Google Scholar 

  • SUNY Buffalo Postal Address Image Database (1989). State U. of NY at Buffalo, CS Department, Buffalo, NY.

    Google Scholar 

  • Tahani, H. and Keller, J. M. (1990). Information fusion in computer vision using the fuzzy integral, IEEE Trans. Syst., Man and Cyberns., 20 (3), 733–741.

    Article  Google Scholar 

  • Takagi, T. and Sugeno, M. (1985). Fuzzy identification of systems and its application to modeling and control, IEEE Trans. Syst., Man and Cyberns., 15 (1), 116–132.

    Article  MATH  Google Scholar 

  • Tamura, S. and Tanaka, K. (1973). Learning of fuzzy formal language, IEEE Trans. Syst., Man and Cyberns., 3, 98–102.

    Article  MATH  MathSciNet  Google Scholar 

  • Tamura, S., Higuchi, S. and Tanaka, K. (1971). Pattern classification based on fuzzy relations, IEEE Trans. Syst., Man and Cyberns., 1 (1), 61–66.

    Article  MATH  MathSciNet  Google Scholar 

  • Parizeau, M. and Plamondon, R. (1995). A fuzzy-syntactic approach to allograph modeling for cursive script recognition, IEEE Trans. Patt. Anal. and Machine Intell., 17 (7), 702–712.

    Article  Google Scholar 

  • Parizeau, M., Plamondon, R. and Lorette, G. (1993). Fuzzy shape grammars for cursive script recognition, in Advances in Structural and Syntactic Pattern Recognition, ed. H. Bunke, World Scientific, Singapore, 320–332.

    Chapter  Google Scholar 

  • Senay, H. (1992). Fuzzy command grammars for intelligent interface design, IEEE Trans. Syst., Man and Cyberns., 22 (5), 1124–1131.

    Article  Google Scholar 

  • Peeva, K. (1991). Fuzzy acceptors for syntactic pattern recognition, Int. J. Approx. Reasoning, 5, 291–306.

    Article  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

Copyright information

© 1999 Springer Science+Business Media New York

About this chapter

Cite this chapter

Bezdek, J.C., Keller, J., Krisnapuram, R., Pal, N.R. (1999). Classifier Design. In: Fuzzy Models and Algorithms for Pattern Recognition and Image Processing. The Handbooks of Fuzzy Sets Series, vol 4. Springer, Boston, MA. https://doi.org/10.1007/0-387-24579-0_4

Download citation

  • DOI: https://doi.org/10.1007/0-387-24579-0_4

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-0-387-24515-7

  • Online ISBN: 978-0-387-24579-9

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics