Pattern Recognition with Fuzzy Objective Function Algorithms
Citations
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14,054 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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9,057 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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8,432 citations
6,601 citations
References
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2,375 citations
"Pattern Recognition with Fuzzy Obje..." refers background in this paper
...Many algebraically oriented papers with the flavor of lattice theory and multivalued logic have concerned themselves with extensions of Zadeh's original structure: among the most extensive are those of Goguen(47) and Klaua(66)-see (45) for a more complete discussion and literature survey....
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2,187 citations
2,024 citations
"Pattern Recognition with Fuzzy Obje..." refers background in this paper
...(ii) Show that leu; ih ) = hf(u, u), the normalized entropy of DeLuca and Termini(32) at (16....
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...Shortly thereafter, Deluca and Termini(32) gave the following definition for the normalized entropy of a finite fuzzy set....
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...For a, (3 E IR, (i) Show that F(aU + (3W; c) = (a 2 + 2a(3 + e(32)/e....
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1,988 citations
"Pattern Recognition with Fuzzy Obje..." refers background or methods in this paper
...There are two reasons to do so: under certain special conditions, A may be included as a theoretical variable for optimization, as in the modification of Gustafson and Kessel(54) discussed in S22; and in any case, A is an algorithmic variable for the fuzzy c-means methods based on (TILl)....
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...8b) arise naturally in two generalizations of 1m: the fuzzy "covariance" algorithm of Gustafson and Kessel(54); and the fuzzy c-varieties algorithms of Bezdek et al....
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...1), but has been briefly discussed in (54)....
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...Mathematical realization of this idea in (54) is accomplished by considering the class of inner product norms induced on /RP by symmetric, positive-definite matrices in Vpp• Let us denote by A a c- tuple of such matrices, A = (A 1....
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...Gustafson and Kessel(54) proposed an interesting modification of the fuzzy c-means algorithms of SII which attempts to recognize the fact that different clusters in the same data set X may have differing geometric shapes (cf....
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1,697 citations