From a Gaussian Mixture Model to Nonadditive Fuzzy Systems

Verma, Nishchal K.; Hanmandlu, M.

doi:10.1109/tfuzz.2006.889821

Cited by 30 publications

(6 citation statements)

References 44 publications

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“…Because of this difficulty, fuzzy logic techniques have attracted the attention of several researchers [28]- [31].…”

Section: Issues In the Building Of Modelsmentioning

confidence: 99%

“…In such a case, the consequent part has to be replaced with a fuzzy integral that leads to the non-additive fuzzy model as shown in [31]. In the TS model, fuzzy sets are independent and the resulting system is called additive fuzzy system as the output is directly related to these fuzzy sets [30].…”

Section: Interactive Fuzzy Modelingmentioning

confidence: 99%

“…As shown in [31], the use of q-measure improves the convergence of fuzzy measures in (8). In view of (10), is rewritten as (11) The defuzzified output of the model is given by Interchanging the summations, the defuzzified output takes the form of the Choquet integral (see Appendix B) (12) where it is assumed with which is the firing strength of the th rule obtained by taking the T-norm of the generalized Gaussian function.…”

Section: Properties Of Choquet Integralmentioning

confidence: 99%

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Load Forecasting Using Hybrid Models

Hanmandlu

Chauhan²

2011

IEEE Trans. Power Syst.

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110

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Abstract-This paper presents two hybrid neural networks derived from fuzzy neural networks (FNN): wavelet fuzzy neural network (WFNN) using the fuzzified wavelet features as the inputs to FNN and fuzzy neural network (FNCI) employing the Choquet integral as the outputs of FNN. The learning through FNCI is simplified by the use of q-measure and the speed of convergence of the parameters is increased by reinforced learning. The underlying fuzzy models of these hybrid networks are a modified form of fuzzy rules of Takagi-Sugeno model. The number of fuzzy rules is found from a fuzzy curve corresponding to each input-output by counting the total number of peaks and troughs in the curve. The models can forecast hourly load with a lead time of 1 h as they deal with short-term load forecasting. The results of the two hybrid networks using Indian utility data are compared with ANFIS and other conventional methods. The performance of the proposed WFNN is found superior to all the other compared methods.Index Terms-Fuzzy systems, neural networks, short-term load forecasting, wavelet transforms and Choquet integral.

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“…Because of this difficulty, fuzzy logic techniques have attracted the attention of several researchers [28]- [31].…”

Section: Issues In the Building Of Modelsmentioning

confidence: 99%

Section: Interactive Fuzzy Modelingmentioning

confidence: 99%

Section: Properties Of Choquet Integralmentioning

confidence: 99%

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Load Forecasting Using Hybrid Models

Hanmandlu

Chauhan²

2011

IEEE Trans. Power Syst.

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110

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“…Let us throw some light on the additive and non-additive fuzzy systems [29][30][31]. Conventional evaluation with multiple attributes which are independent is based on the concept of additive fuzzy systems where importance of each attribute is given a weight.…”

Section: Introductionmentioning

confidence: 99%

“…As the large number of input variables is increased for the purpose of fusion, the computational complexity grows exponentially [31,51] with the λ-measure. To overcome this problem a new fuzzy measure known as Q-Measure is introduced in [52].…”

Section: Introductionmentioning

confidence: 99%

Estimation of Fuzzy Measures Using Covariance Matrices in Gaussian Mixtures

Verma

2012

Applied Computational Intelligence and Soft Computing

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This paper presents a novel computational approach for estimating fuzzy measures directly from Gaussian mixtures model (GMM). The mixture components of GMM provide the membership functions for the input-output fuzzy sets. By treating consequent part as a function of fuzzy measures, we derived its coefficients from the covariance matrices found directly from GMM and the defuzzified output constructed from both the premise and consequent parts of the nonadditive fuzzy rules that takes the form of Choquet integral. The computational burden involved with the solution of λ-measure is minimized using Q-measure. The fuzzy model whose fuzzy measures were computed using covariance matrices found in GMM has been successfully applied on two benchmark problems and one real-time electric load data of Indian utility. The performance of the resulting model for many experimental studies including the above-mentioned application is found to be better and comparable to recent available fuzzy models. The main contribution of this paper is the estimation of fuzzy measures efficiently and directly from covariance matrices found in GMM, avoiding the computational burden greatly while learning them iteratively and solving polynomial equations of order of the number of input-output variables.

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