Piecewise linear approximation of fuzzy numbers: algorithms, arithmetic operations and stability of characteristics
Lucian Coroianu , Marek Gągolewski , Przemysław Grzegorzewski
AbstractThe 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.
|Journal series||Soft Computing, ISSN 1432-7643, (A 25 pkt)|
|Publication size in sheets||0.7|
|Keywords in English||Approximation of fuzzy numbers, Calculations on fuzzy numbers, Characteristics of fuzzy numbers, Fuzzy number, Piecewise linear approximation|
|ASJC Classification||; ;|
|Score||= 25.0, 11-07-2019, ArticleFromJournal|
|Publication indicators||= 0; : 2017 = 1.11; : 2017 = 2.367 (2) - 2017=2.204 (5)|
* presented citation count is obtained through Internet information analysis and it is close to the number calculated by the Publish or Perish system.