The extension principle and a decomposition of fuzzy sets

Y. Chalco-Cano; H. Román-Flores; M. Rojas-Medar; O. R. Saavedra; M. D. Jiménez-Gamero

doi:10.1016/j.ins.2007.07.007

The extension principle and a decomposition of fuzzy sets

Y. Chalco-Cano
, H. Román-Flores
, M. Rojas-Medar
, O. R. Saavedra
, M. D. Jiménez-Gamero

Department of Mathematics

Universidad de Tarapacá
Universidad del Bío-Bío
Universidade Federal do Maranhão
University of Seville

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

30 Scopus citations

Abstract

We give an algorithm to decompose a fuzzy interval u. Using this decomposition and the multilinearization of a univariate function f, we obtain an approximation of the fuzzy interval over(f, ̂) (u), where over(f, ̂) is obtained from f by applying the extension principle. We provide approximation bounds. Some numeric illustration is provided.

Original language	English
Pages (from-to)	5394-5403
Number of pages	10
Journal	Information Sciences
Volume	177
Issue number	23
DOIs	https://doi.org/10.1016/j.ins.2007.07.007
State	Published - 1 Dec 2007

Keywords

Decomposition of fuzzy sets
Extension principle
Fuzzy sets

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10.1016/j.ins.2007.07.007

Cite this

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abstract = "We give an algorithm to decompose a fuzzy interval u. Using this decomposition and the multilinearization of a univariate function f, we obtain an approximation of the fuzzy interval over(f,{\^ }) (u), where over(f,{\^ }) is obtained from f by applying the extension principle. We provide approximation bounds. Some numeric illustration is provided.",

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AU - Chalco-Cano, Y.

AU - Román-Flores, H.

AU - Rojas-Medar, M.

AU - Saavedra, O. R.

AU - Jiménez-Gamero, M. D.

PY - 2007/12/1

Y1 - 2007/12/1

N2 - We give an algorithm to decompose a fuzzy interval u. Using this decomposition and the multilinearization of a univariate function f, we obtain an approximation of the fuzzy interval over(f, ̂) (u), where over(f, ̂) is obtained from f by applying the extension principle. We provide approximation bounds. Some numeric illustration is provided.

AB - We give an algorithm to decompose a fuzzy interval u. Using this decomposition and the multilinearization of a univariate function f, we obtain an approximation of the fuzzy interval over(f, ̂) (u), where over(f, ̂) is obtained from f by applying the extension principle. We provide approximation bounds. Some numeric illustration is provided.

KW - Decomposition of fuzzy sets

KW - Extension principle

KW - Fuzzy sets

UR - https://www.scopus.com/pages/publications/34548733039

U2 - 10.1016/j.ins.2007.07.007

DO - 10.1016/j.ins.2007.07.007

M3 - Article

AN - SCOPUS:34548733039

SN - 0020-0255

VL - 177

SP - 5394

EP - 5403

JO - Information Sciences

JF - Information Sciences

IS - 23

ER -

The extension principle and a decomposition of fuzzy sets

Abstract

Keywords

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