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Piecewise linear approximation of fuzzy numbers: Algorithms, arithmetic operations and stability of characteristics

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journal contribution
posted on 2019-01-01, 00:00 authored by L Coroianu, Marek Gagolewski, P Grzegorzewski
The problem of the piecewise linear approximation of fuzzy numbers giving outputs nearest to the inputs with respect to the Euclidean metric is discussed. The results given in Coroianu et al. (Fuzzy Sets Syst 233:26–51, 2013) for the 1-knot fuzzy numbers are generalized for arbitrary n-knot (n≥ 2) piecewise linear fuzzy numbers. Some results on the existence and properties of the approximation operator are proved. Then, the stability of some fuzzy number characteristics under approximation as the number of knots tends to infinity is considered. Finally, a simulation study concerning the computer implementations of arithmetic operations on fuzzy numbers is provided. Suggested concepts are illustrated by examples and algorithms ready for the practical use. This way, we throw a bridge between theory and applications as the latter ones are so desired in real-world problems.

History

Journal

Soft Computing

Volume

23

Issue

19

Pagination

9491 - 9505

Publisher

Springer

Location

Berlin, Germany

ISSN

1432-7643

eISSN

1433-7479

Language

eng

Publication classification

C1.1 Refereed article in a scholarly journal

Copyright notice

2019, The Author(s)