# Pattern Recognition with Fuzzy Objective Function Algorithms

##### Citations

23,590 citations

13,346 citations

### Cites background or methods from "Pattern Recognition with Fuzzy Obje..."

...A generalization of the FCM algorithm was proposed by Bezdek [1981] through a family of...

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...The book by Bezdek [1981] is a good source for material on fuzzy clustering....

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8,432 citations

7,999 citations

### Cites methods from "Pattern Recognition with Fuzzy Obje..."

...Another popular technique, similar in spirit to k-means clustering, is fuzzy k-means clustering (Bezdek, 1981; Dunn, 1974)....

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...Another popular technique, similar in spirit to k-means clustering, is fuzzy k-means clustering (Bezdek, 1981; Dunn, 1973)....

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...In the second step, the vertex points are associated to nc clusters by using fuzzy k-means clustering (Bezdek, 1981; Dunn, 1973) (Section IV....

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6,278 citations

### Cites background from "Pattern Recognition with Fuzzy Obje..."

...In syntactic pattern recognition, a formal analogy is drawn between the structure of patterns and the syntax of a language....

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##### References

12,936 citations

### "Pattern Recognition with Fuzzy Obje..." refers methods in this paper

...Fisher(38) first used it to exemplify linear discriminant analysis....

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...The Iris data have been used as a test set by at least a dozen authors, including Fisher, (38) Kendall, (64) Friedman and Rubin,'40) Wolfe,(117) Scott and Symons,<95) and Backer....

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10,516 citations

### "Pattern Recognition with Fuzzy Obje..." refers background in this paper

...(42) Texts on general pattern recognition include those of Bongard,(2S) Patrick,IH1) Tou and Wilcox,(04) Tou and Gonzalez,(l03) and Duda and Hart....

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10,453 citations

### "Pattern Recognition with Fuzzy Obje..." refers background or methods in this paper

...In fact, the efficiency of the 1-NN classifier is asymptotically less than twice the theoretically optimal Bayes risk: Cover and Hart showed in (29) that...

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...4) can be improved: the tighter upper bound derived in (29) is...

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...In particular, no analysis such as Cover and Hart's(29) has been formulated for fuzzy classifier designs; whether fuzzy classifiers such as {hb}PCM in (S26) and {!Jh-NP in (S27) have nice asymptotic relations to {fjb} or others remains to be discovered....

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5,254 citations

5,132 citations

### "Pattern Recognition with Fuzzy Obje..." refers background or methods in this paper

...1e) is quite involved; and sizes of local error (el), loop error (ed, and a measure of closeness for matrices in Ven (1IU(1+1) - u(1)11> must be chosen....

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...Clustering, for example, is ably represented by the books of Anderberg,(1) Tryon and Bailey,(I09) and Hartigan....

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...l that groups together (1,3) and (10, 3) and minimizes Iw( U, v)....

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...X = {(1, 1), (1, 3), (10, 1), (10, 3), (5, 2)}....

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...[Answer {(1, 1), (1, 3)} u {(5, 2)} u {(la, 1), (10, 3))....

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