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On the probability of error in fuzzy discrimination problems

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Pardo Llorente, Julio Ángel and Taneja, I.J. (1992) On the probability of error in fuzzy discrimination problems. Kybernetes, 21 (6). pp. 43-52. ISSN 0368-492X

Official URL: http://www.emeraldinsight.com/journals.htm?issn=0368-492X&volume=21&issue=6&articleid=1663924&articletitle=On+the+Probability+of+Error+in+Fuzzy+Discrimination+Problems


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Abstract

The decision rule which minimizes the probability of error, in the discrimination problem, is the Bayes decision rule which assigns x to the class with the highest a posteriori probability. This rule leads to a partial probability of error which is given by P(e)(x) = 1-max p(C(i)/x) for each x is-an-element-of X. Prior to observing X, the probability of error associated with X is defined as P(e) = E(X)[P(e)(x)]. Tanaka, Okuda and Asai formulated the discrimination problem with fuzzy classes and fuzzy information using the probability of fuzzy events and derived a bound for the average error probability, when the decision in the classifier is made according to the fuzzified Bayes method. The aim is to obtain bounds for the average error probability in terms of (alpha,beta)-information energy, when the decision in the classifier is made according to the fuzzified Bayes method.


Item Type:Article
Uncontrolled Keywords:information energy; Bayesian discrimination; fuzzy information system; fuzzy partition; orthogonality; lower bounds on probability of error; fuzzy discrimination; a posteriori probability
Subjects:Sciences > Mathematics > Bayesian statistical decision theory
ID Code:17943
Deposited On:24 Jan 2013 11:50
Last Modified:24 Jan 2013 11:50

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