Approximation by Shepard type pseudo-linear operators and applications to Image Processing

Recently, it has been shown that sum and product are not the only operations that can be used in order to define concrete approximation operators. Several other operations provided by fuzzy sets theory can be used. In the present paper, pseudo-linear approximation operators are investigated from the...

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Veröffentlicht in:	International Journal of Approximate Reasoning Jg. 50; H. 1; S. 21 - 36
Hauptverfasser:	Bede, Barnabás, Schwab, Emil Daniel, Nobuhara, Hajime, Rudas, Imre J.
Format:	Journal Article Tagungsbericht
Sprache:	Englisch Japanisch
Veröffentlicht:	Amsterdam Elsevier Inc 2009 Elsevier BV Elsevier
Schlagworte:	Applied Mathematics Applied sciences Approximation Artificial Intelligence Computer science; control theory; systems Exact sciences and technology Image Processing Learning and adaptive systems Pattern recognition. Digital image processing. Computational geometry Pseudo-analysis Pseudo-linear approximation Shepard operators Software Theoretical Computer Science Pseudo-analysis Approximation Shepard operators Pseudo-linear approximation Image Processing Image processing Linear approximation Minimax method Fuzzy set Artificial intelligence Linear operator
ISSN:	0888-613X, 1873-4731
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Abstract	Recently, it has been shown that sum and product are not the only operations that can be used in order to define concrete approximation operators. Several other operations provided by fuzzy sets theory can be used. In the present paper, pseudo-linear approximation operators are investigated from the practical point of view in Image Processing. We study max–min, max–product Shepard type approximation operators together with Shepard operators based on pseudo-operations generated by an increasing continuous generator. It is shown that in several cases these outperform classical approximation operators based on sum and product operations.
AbstractList	Recently, it has been shown that sum and product are not the only operations that can be used in order to define concrete approximation operators. Several other operations provided by fuzzy sets theory can be used. In the present paper, pseudo-linear approximation operators are investigated from the practical point of view in Image Processing. We study max–min, max–product Shepard type approximation operators together with Shepard operators based on pseudo-operations generated by an increasing continuous generator. It is shown that in several cases these outperform classical approximation operators based on sum and product operations.
Author	Schwab, Emil Daniel Nobuhara, Hajime Bede, Barnabás Rudas, Imre J.
Author_xml	– sequence: 1 givenname: Barnabás surname: Bede fullname: Bede, Barnabás email: bede.barna@bgk.bmf.hu, bedeb@utpa.edu organization: Department of Mathematics, University of Texas–Pan American, Edinburg, TX 78541, USA – sequence: 2 givenname: Emil Daniel surname: Schwab fullname: Schwab, Emil Daniel organization: Department of Mathematical Sciences, The University of Texas at El Paso, 500 West University, El Paso, TX 79968, USA – sequence: 3 givenname: Hajime surname: Nobuhara fullname: Nobuhara, Hajime organization: Department of Intelligent Interaction Technologies, Graduate School of Systems and Information Engineering, University of Tsukuba Tenoudai 1-1-1, Tsukuba Science City, Ibaraki 305-8573, Japan – sequence: 4 givenname: Imre J. surname: Rudas fullname: Rudas, Imre J. organization: Department of Intelligent Engineering Systems, Budapest Tech Polytechnical Institution, Bécsi út 96/b H1034, Hungary
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Keywords	Pseudo-analysis Approximation Shepard operators Pseudo-linear approximation Image Processing Image processing Linear approximation Minimax method Fuzzy set Artificial intelligence Linear operator
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SubjectTerms	Applied Mathematics Applied sciences Approximation Artificial Intelligence Computer science; control theory; systems Exact sciences and technology Image Processing Learning and adaptive systems Pattern recognition. Digital image processing. Computational geometry Pseudo-analysis Pseudo-linear approximation Shepard operators Software Theoretical Computer Science
Title	Approximation by Shepard type pseudo-linear operators and applications to Image Processing
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