Spline approximation for Zadeh's extensions

Y. Chalco-Cano; M. T. Misukoshi; H. Roán-Flores; A. Flores-Franulic

doi:10.1142/S0218488509005851

Spline approximation for Zadeh's extensions

Y. Chalco-Cano
, M. T. Misukoshi
, H. Roán-Flores
, A. Flores-Franulic

Department of Mathematics

Universidade Federal de Goiás
Universidad de Tarapacá

Research output: Contribution to journal › Article › peer-review

13 Scopus citations

Abstract

In this paper we show an approximation for $\hat f(u)$, where u is a fuzzy interval and $\hat f$ is obtained from a continuous function f applying the Zadeh's extension principle. In this process, we used a decomposition for u and the linear spline function for the approximation of f. A bound for the error in the approximation is given. Also, some examples are presented.

Original language	English
Pages (from-to)	269-280
Number of pages	12
Journal	International Journal of Uncertainty, Fuzziness and Knowldege-Based Systems
Volume	17
Issue number	2
DOIs	https://doi.org/10.1142/S0218488509005851
State	Published - Apr 2009

Keywords

Fuzzy sets
Spline functions
Zadeh's extension principle

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10.1142/S0218488509005851

Cite this

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title = "Spline approximation for Zadeh's extensions",

abstract = "In this paper we show an approximation for \$\textbackslash{}hat f(u)\$, where u is a fuzzy interval and \$\textbackslash{}hat f\$ is obtained from a continuous function f applying the Zadeh's extension principle. In this process, we used a decomposition for u and the linear spline function for the approximation of f. A bound for the error in the approximation is given. Also, some examples are presented.",

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AU - Chalco-Cano, Y.

AU - Misukoshi, M. T.

AU - Roán-Flores, H.

AU - Flores-Franulic, A.

PY - 2009/4

Y1 - 2009/4

N2 - In this paper we show an approximation for $\hat f(u)$, where u is a fuzzy interval and $\hat f$ is obtained from a continuous function f applying the Zadeh's extension principle. In this process, we used a decomposition for u and the linear spline function for the approximation of f. A bound for the error in the approximation is given. Also, some examples are presented.

AB - In this paper we show an approximation for $\hat f(u)$, where u is a fuzzy interval and $\hat f$ is obtained from a continuous function f applying the Zadeh's extension principle. In this process, we used a decomposition for u and the linear spline function for the approximation of f. A bound for the error in the approximation is given. Also, some examples are presented.

KW - Fuzzy sets

KW - Spline functions

KW - Zadeh's extension principle

UR - https://www.scopus.com/pages/publications/65249189304

U2 - 10.1142/S0218488509005851

DO - 10.1142/S0218488509005851

M3 - Article

AN - SCOPUS:65249189304

SN - 0218-4885

VL - 17

SP - 269

EP - 280

JO - International Journal of Uncertainty, Fuzziness and Knowldege-Based Systems

JF - International Journal of Uncertainty, Fuzziness and Knowldege-Based Systems

IS - 2

ER -

Spline approximation for Zadeh's extensions

Abstract

Keywords

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