On the approximation of compact fuzzy sets

Y. Chalco-Cano; A. D. Bez-Snchez; H. Romn-Flores; M. A. Rojas-Medar

doi:10.1016/j.camwa.2010.11.018

On the approximation of compact fuzzy sets

Universidade Estadual de Campinas
Universidad del Bío-Bío

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

7 Scopus citations

Abstract

This paper suggests an approximation for a compact fuzzy set by a sequence of Lipschitz fuzzy sets. This approximation method involves the construction of Lipschitz fuzzy sets using the supmin convolution of a compact fuzzy set with a fuzzy zero. Considering a similar procedure, we present the approximation of a trapezoidal type fuzzy interval by a sequence of differentiable fuzzy intervals. We show some important properties of both approximations and we give some numerical examples illustrating the results.

Original language	English
Pages (from-to)	412-420
Number of pages	9
Journal	Computers and Mathematics with Applications
Volume	61
Issue number	2
DOIs	https://doi.org/10.1016/j.camwa.2010.11.018
State	Published - Jan 2011

Keywords

Compact fuzzy sets
Convolution of fuzzy sets
Fuzzy intervals
Lipschitz fuzzy sets

Access to Document

10.1016/j.camwa.2010.11.018

Cite this

@article{e91a79991a8c4c03bd70615283117875,

title = "On the approximation of compact fuzzy sets",

abstract = "This paper suggests an approximation for a compact fuzzy set by a sequence of Lipschitz fuzzy sets. This approximation method involves the construction of Lipschitz fuzzy sets using the supmin convolution of a compact fuzzy set with a fuzzy zero. Considering a similar procedure, we present the approximation of a trapezoidal type fuzzy interval by a sequence of differentiable fuzzy intervals. We show some important properties of both approximations and we give some numerical examples illustrating the results.",

keywords = "Compact fuzzy sets, Convolution of fuzzy sets, Fuzzy intervals, Lipschitz fuzzy sets",

author = "Y. Chalco-Cano and Bez-Snchez, \{A. D.\} and H. Romn-Flores and Rojas-Medar, \{M. A.\}",

year = "2011",

month = jan,

doi = "10.1016/j.camwa.2010.11.018",

language = "English",

volume = "61",

pages = "412--420",

journal = "Computers and Mathematics with Applications",

issn = "0898-1221",

number = "2",

}

TY - JOUR

T1 - On the approximation of compact fuzzy sets

AU - Chalco-Cano, Y.

AU - Bez-Snchez, A. D.

AU - Romn-Flores, H.

AU - Rojas-Medar, M. A.

PY - 2011/1

Y1 - 2011/1

N2 - This paper suggests an approximation for a compact fuzzy set by a sequence of Lipschitz fuzzy sets. This approximation method involves the construction of Lipschitz fuzzy sets using the supmin convolution of a compact fuzzy set with a fuzzy zero. Considering a similar procedure, we present the approximation of a trapezoidal type fuzzy interval by a sequence of differentiable fuzzy intervals. We show some important properties of both approximations and we give some numerical examples illustrating the results.

AB - This paper suggests an approximation for a compact fuzzy set by a sequence of Lipschitz fuzzy sets. This approximation method involves the construction of Lipschitz fuzzy sets using the supmin convolution of a compact fuzzy set with a fuzzy zero. Considering a similar procedure, we present the approximation of a trapezoidal type fuzzy interval by a sequence of differentiable fuzzy intervals. We show some important properties of both approximations and we give some numerical examples illustrating the results.

KW - Compact fuzzy sets

KW - Convolution of fuzzy sets

KW - Fuzzy intervals

KW - Lipschitz fuzzy sets

UR - https://www.scopus.com/pages/publications/78651250483

U2 - 10.1016/j.camwa.2010.11.018

DO - 10.1016/j.camwa.2010.11.018

M3 - Article

AN - SCOPUS:78651250483

SN - 0898-1221

VL - 61

SP - 412

EP - 420

JO - Computers and Mathematics with Applications

JF - Computers and Mathematics with Applications

IS - 2

ER -

On the approximation of compact fuzzy sets

Abstract

Keywords

Access to Document

Other files and links

Fingerprint

Cite this