By Ludmila I. Kuncheva
ISBN-10: 379081850X
ISBN-13: 9783790818505
ISBN-10: 3790824720
ISBN-13: 9783790824728
Fuzzy units have been first proposed through Lotfi Zadeh in his seminal paper [366] in 1965, and ever on account that were a middle of many discussions, fervently widespread and condemned. either proponents and competitors ponder the argu ments unnecessary simply because none of them might step again from their territory. And stiH, discussions burst out from a unmarried sparkle like a convention pa in step with or a message on a few fuzzy-mail newsgroup. here's an excerpt from an electronic mail messagepostedin1993tofuzzy-mail@vexpert. dbai. twvien. ac. at. via anyone who signed "Dave". , . . . Why then the "logic" in "fuzzy logic"? i do not believe an individual has effectively used fuzzy units for logical inference, nor do i believe an individual wiH. In my admittedly neophyte opinion, "fuzzy good judgment" is a misnomer, an oxymoron. (1 will be extremely joyful to be confirmed improper on that. ) . . . I carne to the bushy literature with an open brain (and open wal let), excessive hopes and prepared curiosity. i'm greatly disiHusioned with "fuzzy" in line with se, yet I did take place throughout a few super fascinating issues alongside the way in which. " Dave, thank you for the great quote! Enthusiastic at the floor, are usually not many people suspicious deep down? In a few books and journals the notice fuzzy is religiously kept away from: fuzzy set concept is considered as a second-hand affordable trick whose target is not anything else yet to devalue stable classical theories and open up find out how to lazy ignorants and newcomers.
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Additional info for Fuzzy Classifier Design
Sample text
Dependent features. dJ's is the normal distribution. In the one-dimensional case, the normal distribution denoted p(XIWi) '" N(mi, (where x, mi, Si E ~), and is defined by sn, 1 p(XIWi) = . /iC y27rSi exp { ( 1 --2 x - mi -Si )2} where mi is the mean and Si is the standard deviation for class multidimensional case, P(XIWi) '" N(mi, Si) is 1 Remember this function for later L. I. 3) , Wi. For the 38 3. 4) where mi E lRn is the mean vector for class Wi, and Si is the covariance matrix. The normal distribution is the most natural assumption reflecting the following situation: there is an "ideal prototype" (a point in lRn ) of class Wi and alI class members are distorted versions of it.
However, these will count when the classifier is a part of an adaptive system. The word "adaptive" is sometimes misused in the neural network literature. By "adaptive" we mean a classifier whose parameters are subject to adjustment during the operation of the system. That is, the classifier is equipped with a tun ing routine that changes the parameter values as new data is being processed. Notice that these changes take place in the real application, out of the control of the designer. In summary: as advocated by many authors [252, 237, 12], simple models should be tried first.
The input x is considered similar to that prototype, in whose bin it is located. The class labeI of the bin's prototype becomes the class labeI of x . The histogram classifier is both time and memory consuming, and, besides, critically depends on how large our data set is. The number of bins acts as a smoothing factor: the more bins we have, the noisier the approximation of the discriminant function. 9). 2 Nonparametric classifiers 47 Fig. 8. 8 % with resubstitution fb.... • Do' m - '" _1 .. ~ Q '* •II l' r- ~ ~~ -...
Fuzzy Classifier Design by Ludmila I. Kuncheva
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