Comments on "Choquet fuzzy integral-based hierarchical networks for decision analysis" [with reply]

Hocaoglu, Ali Koksal; Gader, Paul D.; Chiang, Jung-Hsien

doi:10.1109/91.811248

Cited by 7 publications

(5 citation statements)

References 3 publications

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“…Similarly, we can evaluate the rest of the derivatives. 1) Learning Process Using -Measure: We will now present an alternative formulation for the learning process with -measure as this eliminates the need for solving (11). The output expression from (47) Thus, we can see a considerable simplification with -measure, as the solution of -polynomial is not needed.…”

Section: Appendix a Formulation Of The Learning Processmentioning

confidence: 97%

From a Gaussian Mixture Model to Nonadditive Fuzzy Systems

Verma

Hanmandlu

2007

IEEE Trans. Fuzzy Syst.

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This paper presents the formulation of nonadditive generalized fuzzy model (GFM) by using the framework of the Gaussian mixture model, which provides the membership functions for the input fuzzy sets. By treating the consequent part as a function of fuzzy measures, we derive its coefficients. The defuzzified output constructed from both the premise and consequent parts of the GFM rules takes the form of Choquet integral. The computational burden involved with the solution of -measure is mitigated using -measure. This nonadditive fuzzy model is applied on two benchmark applications, and the results are found to be better than those obtained from the additive fuzzy models.Index Terms-Choquet fuzzy integral, Gaussian mixture model (GMM), generalized fuzzy model (GFM), nonadditive fuzzy systems, -measure and -measure.

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Section: Appendix a Formulation Of The Learning Processmentioning

confidence: 97%

From a Gaussian Mixture Model to Nonadditive Fuzzy Systems

Verma

Hanmandlu

2007

IEEE Trans. Fuzzy Syst.

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“…Note that for correct classification, dissimilarity measures are negative. The dissimilarity measure we use is (16) Note that (16) …”

Section: B Minimum Classification Errormentioning

confidence: 99%

“…In addition, for the gradient-descent method, heuristics must be used to insure that the monotonicity constraints of fuzzy measures are maintained. Chiang [15] proposed a method for using gradient descent to optimize Choquet integrals with respect to Sugeno -measures, but the formulas for the derivatives were incorrect [16].…”

Section: Introductionmentioning

confidence: 99%

Minimum Classification Error Training for Choquet Integrals With Applications to Landmine Detection

Méndez-Vázquez

Gader

Keller

et al. 2008

IEEE Trans. Fuzzy Syst.

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A novel algorithm for discriminative training of Choquet-integral-based fusion operators is described. Fusion is performed by Choquet integration of classifier outputs with respect to fuzzy measures. The fusion operators are determined by the parameters of fuzzy measures. These parameters are found by minimizing a minimum classification error (MCE) objective function. The minimization is performed with respect to a special class of measures, the Sugeno -measures. An analytic expression is derived for the gradient of the Choquet integral with respect to the Sugeno -measure. The new algorithm is applied to a landmine detection problem, and compared to previous techniques.Index Terms-Choquet integral, fuzzy measures, least squared error (LSE), minimum classification error (MCE), Sugeno -measure.

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“…As usual, a single CFI cannot approximate any arbitrary function yet can only its functional. Thus a popular application formation of CFI is to construct them to neural network [10][11][12][13][14][15][16]. Two classes of typical methods have been proposed for this purpose.…”

Section: Related Workmentioning

confidence: 99%

A New Approach to Enterprise Information Fusion: Choquet-Fuzzy-Integral-Based Neural Network

Wang

2007

Third International Conference on Natural Computation (ICNC 2007) Vol V

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On the basis of Enterprise Information Fusion concept, a new approach of EIF, i.e, Choquet-fuzzy-integral-based neural network is presented. In light of examining the structure characteristics of conventional neural networks, the initial size of the new neural network is determined, a learning algorithm for weight value estimation based on genetic algorithm and back propagation algorithm of neural network is given, and then using the pruning algorithm of general neural network the final size can be done. An experiment is used to verify the validation of the new neural network. And lastly, some discussions and potential trends centering around EIF methods are pointed out.

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Comments on "Choquet fuzzy integral-based hierarchical networks for decision analysis" [with reply]

Cited by 7 publications

References 3 publications

From a Gaussian Mixture Model to Nonadditive Fuzzy Systems

From a Gaussian Mixture Model to Nonadditive Fuzzy Systems

Minimum Classification Error Training for Choquet Integrals With Applications to Landmine Detection

A New Approach to Enterprise Information Fusion: Choquet-Fuzzy-Integral-Based Neural Network

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