Abstract
Our aim is to design a pattern classifier using fuzzy relational calculus (FRC) which was initially proposed by Pedrycz (Pattern Recognition 23 (1/2), 121–146, 1990). In the course of doing so, we first consider a particular interpretation of the multidimensional fuzzy implication (MFI) to represent our knowledge about the training data set. Subsequently, we introduce the notion of a fuzzy pattern vector to represent a population of training patterns in the pattern space and to denote the antecedent part of the said particular interpretation of the MFI. We introduce a new approach to the computation of the derivative of the fuzzy max-function and min-function using the concept of a generalized function. During the construction of the classifier based on FRC, we use fuzzy linguistic statements (or fuzzy membership function to represent the linguistic statement) to represent the values of features (e.g., feature F 1 is small and F 2 is big) for a population of patterns. Note that the construction of the classifier essentially depends on the estimate of a fuzzy relation ℜ between the input (fuzzy set) and output (fuzzy set) of the classifier. Once the classifier is constructed, the nonfuzzy features of a pattern can be classified. At the time of classification of the nonfuzzy features of the test patterns, we use the concept of fuzzy masking to fuzzify the nonfuzzy feature values of the test patterns. The performance of the proposed scheme is tested on synthetic data. Finally, we use the proposed scheme for the vowel classification problem of an Indian language.
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J. C. Bezdek, S. K. Pal (eds.), Fuzzy Models for Pattern Recognition: Methods that Search for Structures in Data (IEEE, New York, 1992)
G. Bortolan, R. Degani, Ranking of fuzzy alternatives in electrocardiography, in Fuzzy Information, Knowledge Representation and Decision, Analysis, ed. by E. Sanchez, M. M. Gupta (Pergamon, Oxford, 1983), pp. 397–402
G. Bortolan, R. Degani, K. Hirota, W. Pedrycz Classification of ECG Signals-utilization of fuzzy pattern matching, in Proceedings International Workshop Fuzzy System (Applic, Iizuka, 1988)
M. K. Chakraborty, Some aspects of [0, 1] fuzzy relations and a few suggestions toward its use. Approx. Reas. Expert Syst. pp. 139–157 (1985)
R. Degani, G. Bortolan, Computerized electrocardiogram diagnosis: Fuzzy approach, in Encyclopedia of Systems and Control. (Pergamon, Oxford, 1987)
R. Degani, G. Bortolan, Fuzzy numbers in computerized electrocardiography. Fuzzy Sets Syst. 24, 345–362 (1987)
A. Dinola, W. Pedrycz, S. Sessa, E. Sanchez, Fuzzy relation equations theory as a basis of fuzzy modeling: An overview. Fuzzy Sets Syst. 40, 415–429 (1991)
D. Dubois, M. C. Jaulent, Techniques for extracting fuzzy regions, in First IFSA Congress, vol. II (Mallorca, Spain, 1985), 1–6 July
S. Gottwald, Approximately solving fuzzy relation equations: Some mathematical results and some heuristic proposals. Fuzzy Sets Syst. 66, 175–193 (1994)
H. Hellendoorn, The generalized modus ponens considered as a fuzzy relation. Fuzzy Sets Syst. 48, 29–48 (1992)
K. Hirota, Fuzzy robot vision and fuzzy controlled robot, in NATO ASI CIM, ed. by I.B. Turksen (Springer, Berlin, 1988)
K. Hirota, K. Iwami, W. Pedrycz, FCM-AD (fuzzy cluster means with additional ata) and its application to aerial images, in Proc. II IFSA Congress, vol. II (Tokyo, Japan, 1987), pp. 729–732
T. L. Huntsberger, C. L. Jacobs, R. L. Canon, Iterative fuzzy image segmentation. Pattern Recognit. 18, 131–138 (1985)
T. L. Huntsberger, C.H. Rangarajan, S.N. Jayaramurthy, Representation of uncertainty in computer vision using fuzzy sets. IEEE Trans. Comput. C–2, 145–156 (1986)
N. Ikoma, W. Pedrycz, K. Hirota, Estimation of fuzzy relational matrix by using probabilistic descent method. Fuzzy Sets Syst. 57, 335–349 (1993)
W. J. Kickert, H. Koppleaar, Application of fuzzy set theory to syntactic pattern recognition of handwritten capitals. IEEE Trans. Syst. Man Cybern. SMC–6, 148–151 (1986)
A. Kumar, A real-time system for pattern recognition of human sleep stages by fuzzy systems analysis. Pattern Recognit. 9, 43–46 (1977)
E. T. Lee, Proximity measure for the classification of geometric figures. J. Cybern. 2, 43–59 (1972)
M. Mizumoto, Extended fuzzy reasoning, in Approximate Reasoning in Expert Systems, ed. by M. M. Gupta, A. Kandel, W. Bandler, J. B. Kiszka (North-Holland, Amsterdam, 1985), pp. 71–85
R. Di Mori, Computerized Models of Speech Using Fuzzy Algorithms (Plenum, New York, 1983)
R. Di Mori, P. Laface, Use of fuzzy algorithms for phonetic and phonetic labeling of continuous speech. IEEE Trans. Pattern Anal. Machine Intell. 2, 136–148 (1980)
S. V. Ovchinnikov, T. Riera, On fuzzy classifications. Fuzzy Sets Syst. 49, 119–132 (1992)@@@@
Y. H. Pao, Adaptive Pattern Recognition and Neural Networks (Addison Wesley Publishing Company, Boston, 1989)
W. Pedrycz, Numerical and applications aspects of fuzzy relational equation. Fuzzy Sets Syst. 11, 1–18 (1983)
W. Pedrycz, Applications of fuzzy relational equations for methods of reasoning in presence of fuzzy data. Fuzzy Sets Syst. 16, 163–174 (1985a)
W. Pedrycz, On generalized fuzzy relational equations and their applications. J. Math. Anal. Appl. 107, 520–536 (1985b)
W. Pedrycz ECG Signal classification with the aid of linguistic classifier, in Proceedings XIV International Conference Medicine Biomedical Engineering, (Spain, 1985c) pp. 11–16 Aug
W. Pedrycz, Approximate solution of Fuzzy relational equations. Fuzzy Sets Syst. 28, 183–201 (1988)
W. Pedrycz, Fuzzy sets in pattern recognition methodology and methods. Pattern Recogn. 23(1/2), 121–146 (1990)
W. Pedrycz, Processing of relational structures: Fuzzy relational equations. Fuzzy Sets Syst. 40, 77–106 (1991)
W. Pedrycz, Genetic algorithms for learning in fuzzy relational structures. Fuzzy Sets Syst. 69(1), 37–52 (1995)
L. Saitta, P. Tarasso, Fuzzy characteristics of coronary disease. Fuzzy Sets Syst. 5, 245–258 (1981)
A. Seif, J. Aguilar-Martin, Multi-group classification using fuzzy correlation. Fuzzy Sets Syst. 3, 109–122 (1980)
M. Shimura, Applications of fuzzy set theory to pattern recognition. J. JAACE 19, 243–248 (1975)
P. K. Simpson, Fuzzy min-max neural network-Part 1: Classification. IEEE Trans. Neural Networks 13, 776–786 (1992)
P. Siy, C. S. Chen, Fuzzy logic for handwritten numerical character recognition. IEEE Trans. Syst. Man Cybern SMC–4, 570–575 (1974)
M. Sugeno, T. Takagi, Multidimensional fuzzy reasoning. Fuzzy Sets Syst. 9, 313–325 (1983)
Y. Tsukamoto, An approach to fuzzy reasoning method, in Advance in Fuzzy Set Theory and Applications, ed. by M. M. Gupta, R. K. Ragade, R. R. Yager (North-Holland, Amsterdam, 1979), pp. 137–149
H. F. Wang, Numerical analysis on fuzzy relation equations with various operators. Fuzzy Sets Syst. 53, 155–166 (1993)
W. U. Wangming, Fuzzy reasoning and fuzzy relational equations. Fuzzy Sets Syst. 20, 67–78 (1986)
S. Watanabe, Pattern Recognition: Human and Mechanical (Wiley, New York, 1985)
M. A. Woodbury, J. Clive, Clinical pure types as fuzzy partition. J. Cybern. 3, 111–121 (1974)
L. A. Zadeh, Theory of Approximate Reasoning, in Machine Intelligence, ed. by D. Michie, L. I. Mikulich, J. E. Hayes (Ellis Horwood, Chichester, 1970), pp. 149–194
L. A. Zadeh, K. S. Fu, K. Tanaka, M. Shimura (eds.), Fuzzy Sets and Their Applications to Cognitive and Decision Processes (Academic, New York, 1975)
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Ray, K.S. (2012). Pattern Classification Based on Conventional Interpretation of MFI. In: Soft Computing Approach to Pattern Classification and Object Recognition. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-5348-2_2
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