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Pattern Analysis and Applications

Erschienen in:

01.05.2012 | Theoretical Advances

Imprecise information in Bayes classifier

verfasst von: Robert Burduk

Erschienen in: Pattern Analysis and Applications | Ausgabe 2/2012

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Abstract

The paper considers the problem of classification error in pattern recognition. This model of classification is primarily based on the Bayes rule and secondarily on the notion of intuitionistic or interval-valued fuzzy sets. A probability of misclassifications is derived for a classifier under the assumption that the features are class-conditionally statistically independent, and we have intuitionistic or interval-valued fuzzy information on object features instead of exact information. A probability of the intuitionistic or interval-valued fuzzy event is represented by the real number. Additionally, the received results are compared with the bound on the probability of error based on information energy. Numerical example concludes the work.

Vorheriger Artikel 2D fragmented object reconstruction with the use of the chromatic and thematic content

Nächster Artikel Preserving objects in Markov Random Fields region growing image segmentation

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Zadeh LA (1968) Probability measures of fuzzy events. J Math Anal Appl 23:421–427MATHMathSciNetCrossRef

Goguen J (1967) L-fuzzy sets. J Math Anal Appl 18(1):145–174MATHMathSciNetCrossRef

Pawlak Z (1985) Rough sets and fuzzy sets. Fuzzy Set Syst 17:99–102MATHMathSciNetCrossRef

Atanassov K (1986) Intuitionistic fuzzy sets. Fuzzy Set Syst 20:87–96MATHMathSciNetCrossRef

Atanassov K, Georgeiv C (1993) Intuitionistic fuzzy prolog. Fuzzy Set Syst 53:121–128MATHCrossRef

Szmidt E, Kacprzyk J (2002) Using intuitionistic fuzzy sets in group decision making. Control Cybern 31(4):1037–1053MATH

Szmidt E, Kacprzyk J (2003) A consensus-reaching process under intuitionistic fuzzy preference relations. Int J Intell Syst 18(7):837–852MATHCrossRef

Gerstenkorn T, Mańko J (1988) Bifuzzy probability of intuitionistic sets. Note Intuition Fuzzy Set 4:8–14

Gerstenkorn, T, Mańko J (1990) Probability of fuzzy intuitionistic sets. BUSEFAL 45:128–136

10.

Zadeh LA (1975) The concept of a linguistic variable and its application to approximate reasoning, part I. Inf Sci 8:199–249MATHMathSciNetCrossRef

11.

Dengfeng L, Chuntian C (2002) New similarity measure of intuitionistic fuzzy sets and application to pattern recognitions. Pattern Recognit Lett 23:221–225MATHCrossRef

12.

Szmidt E, Kacprzyk J (2001) Intuitionistic fuzzy sets in iteligent data analysis for medical diagnostics. LNCS 2074:263–271

13.

Szmidt E, Kacprzyk J (2004) A similarity measure of intuitionistic fuzzy sets and its application in supporting medical diagnostics reasoning. LNAI 3070:388–393

14.

Vlachos IK, Sergiadis, GD (2007) Intuitionistic fuzzy information—aplication to pattern recognition. Pattern Recognit Lett 28:197–206CrossRef

15.

De SK, Biswas R, Roy AR (2001) An application of intitionistic fuzzy sets in medical diagnosis. Fuzzy Set Syst 117:209–213MATHMathSciNetCrossRef

16.

Mitchell HB (2005) Pattern recognition using type-II fuzzy sets. Inf Sci 170:409–418CrossRef

17.

Zeng J, Liu Y-Q (2008) Type-2 fuzzy markov random fields and their application to handwritten chinese character recognition. IEEE Trans Fuzzy Syst 16(3):747–760CrossRef

18.

Bhatt RB, Gopal M (2008) FRCT: fuzzy-rough classification trees. Pattern Anal Appl 11(1):73–88MathSciNetCrossRef

19.

Mitchell HB (2003) On the Dengfang-Chuntain similarity measure and its application to pattern cecognition. Pattern Recognit Lett 24:3101–3104CrossRef

20.

Stańczyk U (2010) Rough set-based analysis of characteristic features for ANN classiifier. Lecture notes in artifical intelligence, vol 6076. Springer, Berlin, pp 565–572

21.

Okuda T, Tanaka H, Asai K (1978) A formulation of fuzzy decision problems with fuzzy information using probability measures of fuzzy events. Inf Control 38:135–147MATHMathSciNetCrossRef

22.

Antos A, Devroye LL, Gyorfi L (1999) Lower bounds for Bayes error estimation. IEEE Trans Pattern Anal Mach Intell 21:643–645CrossRef

23.

Avi-Itzhak H, Diep T (1996) Arbitrarily tight upper and lower bounds on the bayesian probability of error. IEEE Trans Pattern Anal Mach Intell 18:89–91CrossRef

24.

Hashlamoun WA, Varshney PK, Samarasooriya VNS (1994) A tight upper bound on the Bayesian probability of error. IEEE Trans Pattern Anal Mach Intell 16(2):220–224CrossRef

25.

Kittler, J (1998) Combining classifiers: a theoretical framework. Pattern Anal Appl 1:18–27CrossRef

26.

Woźniak M (2008) Experiments on linear combiners. Advances in soft computing, vol 47. Springer, Berlin, pp 445–452

27.

Kulkarni A (1978) On the mean accuracy of hierarchical classifiers. IEEE Trans Comput 27:771–776MATHMathSciNetCrossRef

28.

Kurzyński M (1988) On the multistage Bayes classifier. Pattern Recognit 21:355–365MATHCrossRef

29.

Burduk R (2010) Classification error in Bayes multistage recognition task with fuzzy observations. Pattern Anal Appl 13(1):85–91MathSciNetCrossRef

30.

Pardo L, Menendez ML (1991) Some bounds on probability of error in fuzzy discrimination problems. Eur J Oper Res 53:362–370MATHCrossRef

31.

Pardo JA, Taneja IJ (1992) On the probability of error in fuzzy discrimination Problems. Kybernetes 21(6):43–52MATHMathSciNetCrossRef

32.

Kuncheva LI (2004) Combining pattern classifier: methods and algorithms. Wiley, New YorkMATHCrossRef

33.

Tizhoosh HR (2008) Interval-valued versus intuitionistics fuzzy sets: isomorphism versus semantics. Pattern Recognit 41:1812–1813MATHCrossRef

Titel: Imprecise information in Bayes classifier
verfasst von: Robert Burduk
Publikationsdatum: 01.05.2012
Verlag: Springer-Verlag
Erschienen in: Pattern Analysis and Applications / Ausgabe 2/2012
Print ISSN: 1433-7541
Elektronische ISSN: 1433-755X
DOI: https://doi.org/10.1007/s10044-011-0201-6

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