The Experts below are selected from a list of 264 Experts worldwide ranked by ideXlab platform
Zarita Zainuddin - One of the best experts on this subject based on the ideXlab platform.
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triangular type 2 fuzzy neural networks version of the stone Weierstrass Theorem
Fuzzy Systems and Knowledge Discovery, 2013Co-Authors: Saeed Panahian Fard, Zarita ZainuddinAbstract:The universal approximation capability of type-2 fuzzy neural networks plays an important role in the approximation theory of type-2 fuzzy neural networks. In this study, we propose a triangular type-2 fuzzy number by using the interval type-2 triangular fuzzy number as introduced in our previous work. Moreover, we introduce some triangular type-2 fuzzy operations. Then, we use these concepts to construct three layer feedforward triangular type-2 fuzzy neural networks. Furthermore, we establish a main Theorem that shows the universal approximation capability of these networks. The main Theorem can be regarded as the triangular type-2 fuzzy neural networks version of the Stone-Weierstrass Theorem.
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FSKD - Triangular type-2 fuzzy neural networks version of the Stone-Weierstrass Theorem
2013 10th International Conference on Fuzzy Systems and Knowledge Discovery (FSKD), 2013Co-Authors: Saeed Panahian Fard, Zarita ZainuddinAbstract:The universal approximation capability of type-2 fuzzy neural networks plays an important role in the approximation theory of type-2 fuzzy neural networks. In this study, we propose a triangular type-2 fuzzy number by using the interval type-2 triangular fuzzy number as introduced in our previous work. Moreover, we introduce some triangular type-2 fuzzy operations. Then, we use these concepts to construct three layer feedforward triangular type-2 fuzzy neural networks. Furthermore, we establish a main Theorem that shows the universal approximation capability of these networks. The main Theorem can be regarded as the triangular type-2 fuzzy neural networks version of the Stone-Weierstrass Theorem.
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Interval type-2 fuzzy neural networks version of the Stone-Weierstrass Theorem
Neurocomputing, 2011Co-Authors: Saeed Panahian Fard, Zarita ZainuddinAbstract:The main purpose of this study is to state conditions that guarantee an interval type-2 triangular fuzzy (IT2TF) neural network can approximate continuous IT2TF functions. To make a more efficient calculation with IT2TF numbers, the sum and the product of two IT2TF numbers are constructed. These concepts are used in the definition of IT2TF polynomials. Moreover, the present study provides a mathematical framework to show that IT2TF polynomials are a compact Hausdroff space. Based on this concept we establish an interval type-2 fuzzy neural networks version of the Stone-Weierstrass Theorem which enables approximation by a special class of IT2TF neural networks on the set of all monotonic and continuous IT2TF functions. Finally, a numerical example is given to illustrate the results.
Saeed Panahian Fard - One of the best experts on this subject based on the ideXlab platform.
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triangular type 2 fuzzy neural networks version of the stone Weierstrass Theorem
Fuzzy Systems and Knowledge Discovery, 2013Co-Authors: Saeed Panahian Fard, Zarita ZainuddinAbstract:The universal approximation capability of type-2 fuzzy neural networks plays an important role in the approximation theory of type-2 fuzzy neural networks. In this study, we propose a triangular type-2 fuzzy number by using the interval type-2 triangular fuzzy number as introduced in our previous work. Moreover, we introduce some triangular type-2 fuzzy operations. Then, we use these concepts to construct three layer feedforward triangular type-2 fuzzy neural networks. Furthermore, we establish a main Theorem that shows the universal approximation capability of these networks. The main Theorem can be regarded as the triangular type-2 fuzzy neural networks version of the Stone-Weierstrass Theorem.
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FSKD - Triangular type-2 fuzzy neural networks version of the Stone-Weierstrass Theorem
2013 10th International Conference on Fuzzy Systems and Knowledge Discovery (FSKD), 2013Co-Authors: Saeed Panahian Fard, Zarita ZainuddinAbstract:The universal approximation capability of type-2 fuzzy neural networks plays an important role in the approximation theory of type-2 fuzzy neural networks. In this study, we propose a triangular type-2 fuzzy number by using the interval type-2 triangular fuzzy number as introduced in our previous work. Moreover, we introduce some triangular type-2 fuzzy operations. Then, we use these concepts to construct three layer feedforward triangular type-2 fuzzy neural networks. Furthermore, we establish a main Theorem that shows the universal approximation capability of these networks. The main Theorem can be regarded as the triangular type-2 fuzzy neural networks version of the Stone-Weierstrass Theorem.
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Interval type-2 fuzzy neural networks version of the Stone-Weierstrass Theorem
Neurocomputing, 2011Co-Authors: Saeed Panahian Fard, Zarita ZainuddinAbstract:The main purpose of this study is to state conditions that guarantee an interval type-2 triangular fuzzy (IT2TF) neural network can approximate continuous IT2TF functions. To make a more efficient calculation with IT2TF numbers, the sum and the product of two IT2TF numbers are constructed. These concepts are used in the definition of IT2TF polynomials. Moreover, the present study provides a mathematical framework to show that IT2TF polynomials are a compact Hausdroff space. Based on this concept we establish an interval type-2 fuzzy neural networks version of the Stone-Weierstrass Theorem which enables approximation by a special class of IT2TF neural networks on the set of all monotonic and continuous IT2TF functions. Finally, a numerical example is given to illustrate the results.
B. Banaschewski - One of the best experts on this subject based on the ideXlab platform.
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f-Rings and the Stone-Weierstrass Theorem
Order, 2001Co-Authors: B. BanaschewskiAbstract:Using an appropriate notion of separating subring, it is shown that the classical Stone-Weierstrass Theorem for compact Hausdorff spaces is ultimately a result about f -rings. As an application the constructively valid Stone-Weierstrass Theorem for compact completely regular frames is obtained.
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A constructive proof of the Stone-Weierstrass Theorem
Journal of Pure and Applied Algebra, 1997Co-Authors: B. Banaschewski, Christopher J. MulveyAbstract:Abstract A constructive version of the Stone-Weierstrass Theorem is proved, allowing a globalisation of the Gelfand duality Theorem to any Grothendieck topos to be established elsewhere.
E. Lowen-colebunders - One of the best experts on this subject based on the ideXlab platform.
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A Stone–Weierstrass Type Theorem for an Unstructured Set – with Applications
Applied Categorical Structures, 2000Co-Authors: H. L. Bentley, M. Hušek, E. Lowen-colebundersAbstract:A general version of the Stone–Weierstrass Theorem is presented – one which involves no structure on the domain set of the real valued functions. This Theorem is similar to the ‘Stone–Weierstrass Theorem’ which appears in the book by Gillman and Jerison, but instead of involving the concept of stationary sets the one presented here involves stationary filters. As a corollary to our results we obtain Nel's Theorem of Stone–Weierstrass type for an arbitrary topological space. Finally, an application is made to the setting of Cauchy spaces.
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A Stone-Weierstrass Type Theorem for an Unstructured Set - with Applications
Applied Categorical Structures, 2000Co-Authors: H. L. Bentley, M. Hušek, E. Lowen-colebundersAbstract:A general version of the Stone–Weierstrass Theorem is presented – one which involves no structure on the domain set of the real valued functions. This Theorem is similar to the ‘Stone–Weierstrass Theorem’ which appears in the book by Gillman and Jerison, but instead of involving the concept of stationary sets the one presented here involves stationary filters. As a corollary to our results we obtain Nel's Theorem of Stone–Weierstrass type for an arbitrary topological space. Finally, an application is made to the setting of Cauchy spaces.
N. V. Rao - One of the best experts on this subject based on the ideXlab platform.
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The Stone-Weierstrass Theorem Revisited
The American Mathematical Monthly, 2005Co-Authors: N. V. RaoAbstract:(2005). The Stone-Weierstrass Theorem Revisited. The American Mathematical Monthly: Vol. 112, No. 8, pp. 726-729.