Estimation of Fuzzy Measures Using Covariance Matrices in Gaussian Mixtures
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 co...
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| Format: | Article |
| Language: | English |
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Wiley
2012-01-01
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| Series: | Applied Computational Intelligence and Soft Computing |
| Online Access: | http://dx.doi.org/10.1155/2012/402420 |
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| author | Nishchal K. Verma |
| author_facet | Nishchal K. Verma |
| author_sort | Nishchal K. Verma |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-3b49d89aa2934530b17c5f752d534a9b |
| institution | OA Journals |
| issn | 1687-9724 1687-9732 |
| language | English |
| publishDate | 2012-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Applied Computational Intelligence and Soft Computing |
| spelling | doaj-art-3b49d89aa2934530b17c5f752d534a9b2025-08-20T02:08:02ZengWileyApplied Computational Intelligence and Soft Computing1687-97241687-97322012-01-01201210.1155/2012/402420402420Estimation of Fuzzy Measures Using Covariance Matrices in Gaussian MixturesNishchal K. Verma0Department of Electrical Engineering, Indian Institute of Technology Kanpur, Kanpur 208016, IndiaThis 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.http://dx.doi.org/10.1155/2012/402420 |
| spellingShingle | Nishchal K. Verma Estimation of Fuzzy Measures Using Covariance Matrices in Gaussian Mixtures Applied Computational Intelligence and Soft Computing |
| title | Estimation of Fuzzy Measures Using Covariance Matrices in Gaussian Mixtures |
| title_full | Estimation of Fuzzy Measures Using Covariance Matrices in Gaussian Mixtures |
| title_fullStr | Estimation of Fuzzy Measures Using Covariance Matrices in Gaussian Mixtures |
| title_full_unstemmed | Estimation of Fuzzy Measures Using Covariance Matrices in Gaussian Mixtures |
| title_short | Estimation of Fuzzy Measures Using Covariance Matrices in Gaussian Mixtures |
| title_sort | estimation of fuzzy measures using covariance matrices in gaussian mixtures |
| url | http://dx.doi.org/10.1155/2012/402420 |
| work_keys_str_mv | AT nishchalkverma estimationoffuzzymeasuresusingcovariancematricesingaussianmixtures |