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

Lucian Coroianu , Marek Gągolewski , Przemysław Grzegorzewski

Abstract

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.
Author Lucian Coroianu - [Universitatea din Oradea]
Lucian Coroianu,,
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, Marek Gągolewski (FMIS / DIE) - [Systems Research Institute (IBS PAN) [Polska Akademia Nauk (PAN)]]
Marek Gągolewski,,
- Department of Integral Equations
- Instytucie Badań Systemowych
, Przemysław Grzegorzewski (FMIS / DIE) - [Systems Research Institute (IBS PAN)]
Przemysław Grzegorzewski,,
- Department of Integral Equations
- Instytut Badan Systemowych
Journal seriesSoft Computing, ISSN 1432-7643, (A 25 pkt)
Issue year2019
Pages1-15
Publication size in sheets0.7
Keywords in EnglishApproximation of fuzzy numbers, Calculations on fuzzy numbers, Characteristics of fuzzy numbers, Fuzzy number, Piecewise linear approximation
ASJC Classification2608 Geometry and Topology; 2614 Theoretical Computer Science; 1712 Software
DOIDOI:10.1007/s00500-019-03800-2
URL https://link.springer.com/article/10.1007/s00500-019-03800-2
Languageen angielski
Score (nominal)25
ScoreMinisterial score = 25.0, 11-07-2019, ArticleFromJournal
Publication indicators Scopus Citations = 0; Scopus SNIP (Source Normalised Impact per Paper): 2017 = 1.11; WoS Impact Factor: 2017 = 2.367 (2) - 2017=2.204 (5)
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