nach oben

Soft Computing

Erschienen in:

12.02.2016 | Methodologies and Application

Fuzzy quasi-interpolation solution for Fredholm fuzzy integral equations of second kind

verfasst von: M. Amirfakhrian, K. Shakibi, R. Rodríguez López

Erschienen in: Soft Computing | Ausgabe 15/2017

Einloggen

Aktivieren Sie unsere intelligente Suche, um passende Fachinhalte oder Patente zu finden.

search-config

KI-gestützte Suche

Aus

Abstract

In this paper, we intend to offer a new approach to solve Fredholm fuzzy integral equation of the second kind by the concept of source distance and fuzzy quasi-interpolation. The error estimation of the proposed method is proved in terms of the fuzzy modulus of continuity which will be introduced in this paper. Finally some examples have been given to emphasize acceptable accuracy of our method.

Vorheriger Artikel Endocrine-based coevolutionary multi-swarm for multi-objective workflow scheduling in a cloud system

Nächster Artikel Sparse representation-based classification using generalized weighted extended dictionary

Sie haben noch keine Lizenz? Dann Informieren Sie sich jetzt über unsere Produkte:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

über 102.000 Bücher
über 537 Zeitschriften

aus folgenden Fachgebieten:

Automobil + Motoren
Bauwesen + Immobilien
Business IT + Informatik
Elektrotechnik + Elektronik
Energie + Nachhaltigkeit
Finance + Banking
Management + Führung
Marketing + Vertrieb
Maschinenbau + Werkstoffe
Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Jetzt informieren

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

über 67.000 Bücher
über 340 Zeitschriften

aus folgenden Fachgebieten:

Bauwesen + Immobilien
Business IT + Informatik
Finance + Banking
Management + Führung
Marketing + Vertrieb
Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Jetzt informieren

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

über 67.000 Bücher
über 390 Zeitschriften

aus folgenden Fachgebieten:

Automobil + Motoren
Bauwesen + Immobilien
Business IT + Informatik
Elektrotechnik + Elektronik
Energie + Nachhaltigkeit
Maschinenbau + Werkstoffe

Jetzt Wissensvorsprung sichern!

Jetzt informieren

Abbasbandy S, Babolian E (1998) Interpolation of fuzzy data by natural splines. J Appl Math Comput 5:457–463MathSciNetMATH

Abbasbandy S (2001) Interpolation of fuzzy data by complete splines. Kor J Comput Appl Math 8:587–594MathSciNetMATH

Abbasbandy S, Amirfakhrian M (2006) A new approach to universal approximation of fuzzy functions on a discrete set of points. Appl Math Model 30:1525–1534CrossRefMATH

Abbasbandy S, Amirfakhrian M (2006) Numerical approximation of fuzzy functions by fuzzy polynomials. Appl Math Comput 174:1001–1006MathSciNetMATH

Abbasbandy S, Amirfakhrian M (2006) The nearest approximation of a fuzzy quantity in parametric form. Appl Math Comput 172:624–632MathSciNetMATH

Abbasbandy S, Babolian E (1998) Interpolation of fuzzy data by natural splines. Appl Math Comput 5:457–463MathSciNetMATH

Abbasbandy S, Ezzati R, Behforooz H (2008) Interpolation of fuzzy data by using fuzzy splines. Int J Uncertain Fuzziness Knowl Based Syst 16(7):107–115MathSciNetCrossRefMATH

Abbasbandy S, Babolian E, Alavic M (2007) Numerical method for solving linear Fredholm fuzzy integral equations of the second kind. Chaos Solitons Fract 31:138–146MathSciNetCrossRefMATH

Allahviranloo T, Ghanbari M, Hosseinzadeh AA, Haghi E, Nuraei R (2011) A note on fuzzy linear systems. Fuzzy Sets Syst 177:87–92CrossRefMATH

Allahviranloo T (2005) The Adomian decomposition method for fuzzy system of linear equations. Appl Math Comput 163:553–563MathSciNetMATH

Amirfakhrian M (2012) Some approximation methods in fuzzy logic. Lambert Academic Publishing (LAP), Germany

Babolian E, Sadeghi Gohary H, Abbasbandy S (2005) Numerical solutions of linear Fredholm fuzzy integral equations of the second kind by Adomian method. Appl Math Comput 161:733–744MathSciNetMATH

Bayona V, Moscoso M, Kindelan M (2011) Optimal constant shape parameter for multiquadric based RBF-FD method. J Comput Phys 230:73847399MathSciNetCrossRefMATH

Behforooz H, Ezzati R, Abbasbandy S (2010) Interpolation of fuzzy data by using E(3) cubic splines. Int J Pure Appl Math 60(4):383–392MathSciNetMATH

Bica AM (2008) Error estimation in the approximation of the solution of nonlinear fuzzy Fredholm integral equations. Inf Sci 178:1279–1292MathSciNetCrossRefMATH

Congxin W, Ma M (1992) On embedding problem of fuzzy number spaces. Fuzzy Sets Syst 44:33–38MathSciNetCrossRefMATH

Dubois D, Prade H (1982) Towards fuzzy differential calculus. Fuzzy Sets Syst 8:225–233MathSciNetCrossRefMATH

Dehghan B, Hashemi M (2006) Iterative solution of fuzzy linear systems. Appl Math Comput 175:645–674

Fasshauer G, Zhang J (2007) On choosing optimal shape parameters for RBF approximation. Numer Alg 45:345–368MathSciNetCrossRefMATH

Friedman M, Ma M, Kandel A (1999) Numerical solutions of fuzzy differential equations and integral equations. Fuzzy Sets Syst 106:35–48MathSciNetCrossRefMATH

Goetschel R, Voxman W (1986) Elementary fuzzy calculus. Fuzzy Sets Syst 18:31–43MathSciNetCrossRefMATH

Hardy L (1978) The application of multiquadric equations and point mass anomaly models to crustal movement studies. Department of Commerce, National Oceanic and Atmospheric Administration, National Ocean Survey. Natl Geod Surv 55(76)

Hardy RL (1990) Multiquadric equation of topography and other irregular surfaces. J Geophys Res 76:1905–1915CrossRef

Jafari H, Hosseinzadeh H, Mohamadzadeh S (2010) Numerical solution of system of linear integral equations by using Legendre wavelets. Int J Open Probl Comput Sci Math 5:63–71

Kaleva O (1987) Fuzzy differential equations. Fuzzy Sets Syst 24:301–317MathSciNetCrossRefMATH

Kaleva O (1994) Interpolation of fuzzy data. Fuzzy Sets Syst 61:63–70MathSciNetCrossRefMATH

Kansa EJ (1990) Multiquadricsa scattered data approximation scheme with applications to computational fluid-dynamics. I. Surface approximation and partial dervative estimates. Comput Math Appl 19:127–145MathSciNetCrossRefMATH

Lowen R (1990) A fuzzy Lagrange interpolation theorem. Fuzzy Sets Syst 34:33–38MathSciNetCrossRefMATH

Luh Lin-Tian (2016) The mystery of the shape parameter III. Appl Comput Harmon Anal 40:186–199MathSciNetCrossRefMATH

Luh Lin-Tian (2014) The mystery of the shape parameter IV. Eng Anal Bound Elem 48:2431MathSciNetCrossRef

Nanda S (1989) On integration of fuzzy mappings. Fuzzy Sets Syst 32:95–101MathSciNetCrossRefMATH

Powell MJD (1990) Univariate multiquadric approximation: reproduction of linear polynomials. Multivar Approx Interpol 94:227–240

Sugeno M (1974) Theory of fuzzy integral and its application. Ph.D. dissertation. Tokyo Institute of Technology

Wright B (2003) Radial basis function interpolation: numerical and analytical developments. A thesis submitted to the Faculty of the Graduate School of the University of Colorado in partial fulfillment of the requirements for the degree of Doctor of Philosophy, Department of Applied Mathematics

Wu HC (2000) The fuzzy Riemann integral and it’s numerical integration. Fuzzy Sets Syst 110:1–25MathSciNetCrossRef

Wu H (2000) The fuzzy Riemann integral and its numerical integration. Fuzzy Sets Syst 110:1–25MathSciNetCrossRefMATH

Wu ZM, Schaback R (1994) Shape preserving properties and convergence of univariate multiquadric quasi-interpolation. Comput Math Appl 10:441–446MathSciNetMATH

Yue-Xing W, Lin X, Xiao-qian C (2009) The radial basis function shape parameter chosen and its application in engineering. Intell Comput Intell Syst 1:79–83

Zadeh LA (1965) Fuzzy sets. Inf Control 8:338–353

Titel: Fuzzy quasi-interpolation solution for Fredholm fuzzy integral equations of second kind
verfasst von: M. Amirfakhrian
K. Shakibi
R. Rodríguez López
Publikationsdatum: 12.02.2016
Verlag: Springer Berlin Heidelberg
Erschienen in: Soft Computing / Ausgabe 15/2017
Print ISSN: 1432-7643
Elektronische ISSN: 1433-7479
DOI: https://doi.org/10.1007/s00500-016-2065-6

Springer Professional

Abstract

Bitte loggen Sie sich ein, um Zugang zu Ihrer Lizenz zu erhalten.

Sie haben noch keine Lizenz? Dann Informieren Sie sich jetzt über unsere Produkte:

Springer Professional "Wirtschaft+Technik"

Springer Professional "Wirtschaft"

Springer Professional "Technik"

Weitere Artikel der Ausgabe 15/2017

Endocrine-based coevolutionary multi-swarm for multi-objective workflow scheduling in a cloud system

DST: days spent together using soft sensory information on OSNs—a case study on Facebook

$$k^{-}$$ k - -anonymization of multiple shortest paths

Special issue on intelligent analytics and management of mobile data and social media

Lyapunov stability-based control and identification of nonlinear dynamical systems using adaptive dynamic programming

The training set and generalization in grammatical evolution for autonomous agent navigation