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

International Journal of Approximate Reasoning

Volumn 50, Issue 1, 2009, Pages 21-36

  Bede, Barnabás ^a   Schwab, Emil Daniel ^b   Nobuhara, Hajime ^c   Rudas, Imre J ^d  

^a UNIVERSITY OF TEXAS PAN AMERICAN   (United States)

^b UNIVERSITY OF TEXAS AT EL PASO   (United States)

^c UNIVERSITY OF TSUKUBA   (Japan)

^d ÓBUDA UNIVERSITY   (Hungary)

Author keywords

Approximation; Image Processing; Pseudo analysis; Pseudo linear approximation; Shepard operators

Indexed keywords

DIGITAL IMAGE STORAGE; FUZZY SETS; IMAGE PROCESSING; IMAGING SYSTEMS; PROGRAMMING THEORY;

APPROXIMATION; APPROXIMATION OPERATORS; CLASSICAL APPROXIMATIONS; FUZZY SETS THEORIES; LINEAR OPERATORS; MAX PRODUCTS; MAX-MIN; PRODUCT OPERATIONS; PSEUDO-ANALYSIS; PSEUDO-LINEAR APPROXIMATION; PSEUDO-OPERATIONS; SHEPARD OPERATORS;

MATHEMATICAL OPERATORS;

EID: 58849139743     PISSN: 0888613X     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.ijar.2008.01.007     Document Type: Article

References (19)

1. Aczél J. Lectures on Functional Equations and their Applications (1966), Academic Press, New York
2. Anastassiou G.A., and Gal S.G. Approximation Theory: Moduli of Continuity and Global Smoothness Preservation (2000), Birkhäuser, Boston, Basel, Berlin
3. Bede B., Nobuhara H., Fodor J., and Hirota K. Max-product Shepard approximation operators. Journal of Advanced Computational Intelligence and Intelligent Informatics 10 (2006) 494-497
4. Bede B., Nobuhara H., Daňková M., and Di Nola A. Approximation by pseudo-linear operators. Fuzzy Sets and Systems 159 (2008) 804-820
5. DeVore R.A., and Lorentz G.G. Constructive Approximation, Polynomials and Splines Approximation (1993), Springer-Verlag, Berlin, Heidelberg
6. Kóczy L.T., and Hirota K. Approximate reasoning by linear rule interpolation and general approximation. International Journal of Approximate Reasoning 9 (1993) 197-225
7. Maslov V.P., and Samborskii S.N. Idempotent Analysis. Advances in Soviet Mathematics vol. 13 (1992), American Mathematical Society, Providence, RI
8. Mesiar R., and Rybárik J. Pan-operations structure. Fuzzy Sets and Systems 74 (1995) 365-369
9. Musielak J. Nonlinear approximation in some modular function spaces I. Math. Japonica 38 (1993) 83-90
10. Pap E. Pseudo-additive measures and their applications. In: Pap E. (Ed). Handbook of Measure Theory (2002), Elsevier Science B.V.
11. Pap E. Applications of the generated pseudo-analysis to nonlinear partial differential equations. Contemporary Mathematics 377 (2005) 239-259
12. Pap E., and Jegdić K. Pseudo-analysis and its application in railway routing. Fuzzy Sets and Systems 116 (2000) 103-118
13. Schweizer B., and Sklar A. Probabilistic Metric Spaces (1983), North-Holland, Amsterdam
14. I.J. Rudas, B. Bede, H. Nobuhara, K. Hirota, On approximation capability of pseudo-linear Shepard approximation operators, in: Proceedings of the 2006 IEEE International Conference on Fuzzy Systems, Vancouver, Canada, pp. 6642-6647.
15. Szabados J. On a problem of R. DeVore. Acta Mathematica Hungarica 27 1-2 (1976) 219-223
16. Tikk D. Notes on the approximation rate of fuzzy KH interpolators. Fuzzy Sets and Systems 138 (2003) 441-453
17. E. Trillas, C. Alsina, Introduccion a los Espacios Metricos Generalizados, Serie Universitaria 49, Fundacion Juan March, Madrid, 1978 (in Spanish).
18. Valverde L. On the structure of F-indistinguishability operators. Fuzzy Sets and Systems 17 (1985) 313-328
19. Vértesi P. Saturation of the Shepard operator. Acta Mathematica Hungararica 72 (1996) 307-317