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Some Properties of Binary Classifier with Fuzzy-Valued Loss Function

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Computer Recognition Systems 4

Part of the book series: Advances in Intelligent and Soft Computing ((AINSC,volume 95))

Abstract

In this paper we present some prosperities of binary classifier with fuzzyvalued loss function. The loss function in our case is dependent on the stage of the decision tree or depends on the node of the decision tree. The decision rules of a two-stage binary classifier minimize the mean risk, that is the mean value of the fuzzy loss function. In the paper the effect of a loss function on the value of the separation point of decision regions is presented. In this paper we will are not going to study the impact of the choice of ranking of fuzzy numbers method on the results of the classification.

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References

  1. Adamo, J.M.: Fuzzy Decision Trees. Fuzzy Sets and Sys. 4, 207–219 (1980)

    Article  MATH  MathSciNet  Google Scholar 

  2. Baas, S., Kwakernaak, H.: Rating and Ranking of Multi-Aspect Alternatives Using Fuzzy Sets. Automatica 13, 47–58 (1997)

    Article  MathSciNet  Google Scholar 

  3. Berger, J.: Statistical Decision Theory and Bayesian Analysis. Springer, New York (1993)

    Google Scholar 

  4. Bortolan, G., Degani, R.: A review of some methods for ranking fuzzy subsets. Fuzzy Sets and Systems 80, 167–176 (1985)

    MathSciNet  Google Scholar 

  5. Campos, L., González, A.: A Subjective Approach for Ranking Fuzzy Numbers. Fuzzy Sets and Sys. 29, 145–153 (1989)

    Article  MATH  Google Scholar 

  6. Jain, R.: Decision-Making in the Presence of Fuzzy Variables. IEEE Trans. Sys. Man and Cyber. 6, 698–703 (1976)

    Article  MATH  Google Scholar 

  7. Kurzyński, M.: Decision Rules for a Hierarchical Classifier. Pat. Rec. Let. 1, 305–310 (1983)

    Article  MATH  Google Scholar 

  8. Kurzyński, M.: On the Multistage Bayes Classifier. Pat. Rec. 21, 355–365 (1988)

    Article  MATH  Google Scholar 

  9. Viertl, R.: Statistical Methods for Non-Precise Data. CRC Press, Boca Raton (1996)

    Google Scholar 

  10. Wang, X., Kerre, E.E.: Reasonable properities for the ordering of fuzzy quantities (I). Fuzzy Sets and Systems 118, 375–385 (2001)

    Article  MATH  MathSciNet  Google Scholar 

  11. Wang, X., Kerre, E.E.: Reasonable properities for the ordering of fuzzy quantities (II). Fuzzy Sets and Systems 118, 387–405 (2001)

    Article  MATH  MathSciNet  Google Scholar 

  12. Yager, R.: A Procedure for Ordering Fuzzy Subsets of the Unit Interval. Inf. Scien. 22, 143–160 (1981)

    Article  MathSciNet  Google Scholar 

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Burduk, R. (2011). Some Properties of Binary Classifier with Fuzzy-Valued Loss Function. In: Burduk, R., Kurzyński, M., Woźniak, M., Żołnierek, A. (eds) Computer Recognition Systems 4. Advances in Intelligent and Soft Computing, vol 95. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-20320-6_23

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  • DOI: https://doi.org/10.1007/978-3-642-20320-6_23

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-20319-0

  • Online ISBN: 978-3-642-20320-6

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