Piecewise Linear Approximation of Fuzzy Numbers Preserving the Support and Core

2014 ◽  
pp. 244-253 ◽  
Author(s):  
Lucian Coroianu ◽  
Marek Gagolewski ◽  
Przemyslaw Grzegorzewski ◽  
M. Adabitabar Firozja ◽  
Tahereh Houlari
Keyword(s):  
Linear Approximation ◽  
Fuzzy Numbers ◽  
Piecewise Linear ◽  
Piecewise Linear Approximation

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

2019 ◽  
Vol 23 (19) ◽  
pp. 9491-9505 ◽  
Author(s):  
Lucian Coroianu ◽  
Marek Gagolewski ◽  
Przemyslaw Grzegorzewski
Keyword(s):  
Linear Approximation ◽  
Fuzzy Numbers ◽  
Piecewise Linear ◽  
Piecewise Linear Approximation ◽  
Arithmetic Operations

Approximation of fuzzy numbers by using multi-knots piecewise linear fuzzy numbers1

2020 ◽  
Vol 39 (3) ◽  
pp. 3597-3615
Author(s):  
Guixiang Wang ◽  
Chenjie Shen ◽  
Yanyan Wang
Keyword(s):  
Approximation Algorithms ◽  
Linear Approximation ◽  
Fuzzy Number ◽  
Fuzzy Numbers ◽  
Piecewise Linear ◽  
Piecewise Linear Approximation ◽  
Approximation Operators ◽  
Set Up

In this paper, the problem of approximating general fuzzy number by using multi-knots piecewise linear fuzzy number is studied. First, r - s-knots piecewise linear fuzzy numbers are defined, and the conceptions of the I-nearest r - s-knots piecewise linear approximation and the II-nearest r - s-knots piecewise linear approximation are introduced for a general fuzzy number. Then, most importantly, we set up the methods to get the I-nearest r - s-knots piecewise linear approximation and the II-nearest r - s-knots piecewise linear approximation for a general fuzzy number. And then, we investigate some properties of the new approximation operators. Finally, we also present specific examples to show the effectiveness, usability and advantages of the methods proposed in this paper, and compare the methods with some other approximation algorithms.

Nearest piecewise linear approximation of fuzzy numbers

2013 ◽  
Vol 233 ◽  
pp. 26-51 ◽  
Author(s):  
Lucian Coroianu ◽  
Marek Gagolewski ◽  
Przemyslaw Grzegorzewski
Keyword(s):  
Linear Approximation ◽  
Fuzzy Numbers ◽  
Piecewise Linear ◽  
Piecewise Linear Approximation

scholarly journals Approximations of Fuzzy Numbers by Using r-s Piecewise Linear Fuzzy Numbers Based on Weighted Metric

Mathematics ◽  
2022 ◽  
Vol 10 (1) ◽  
pp. 145
Author(s):  
Haojie Lv ◽  
Guixiang Wang
Keyword(s):  
Linear Approximation ◽  
Fuzzy Number ◽  
Best Approximation ◽  
Fuzzy Numbers ◽  
Piecewise Linear ◽  
Piecewise Linear Approximation ◽  
Important Research ◽  
Weighted Distance ◽  
Evaluation Standard ◽  
The Best Approximation

Using simple fuzzy numbers to approximate general fuzzy numbers is an important research aspect of fuzzy number theory and application. The existing results in this field are basically based on the unweighted metric to establish the best approximation method for solving general fuzzy numbers. In order to obtain more objective and reasonable best approximation, in this paper, we use the weighted distance as the evaluation standard to establish a method to solve the best approximation of general fuzzy numbers. Firstly, the conceptions of I-nearest r-s piecewise linear approximation (in short, PLA) and the II-nearest r-s piecewise linear approximation (in short, PLA) are introduced for a general fuzzy number. Then, most importantly, taking weighted metric as a criterion, we obtain a group of formulas to get the I-nearest r-s PLA and the II-nearest r-s PLA. Finally, we also present specific examples to show the effectiveness and usability of the methods proposed in this paper.

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