Object

Title: Piecewise Linear Approximation of Fuzzy Numbers – a Discussion on Algorithms, Arithmetic Operations and Stability of Fuzzy Number Characteristics

Subtitle:

Raport Badawczy = Research Report ; RB/1/2014

Publisher:

Instytut Badań Systemowych. Polska Akademia Nauk ; Systems Research Institute. Polish Academy of Sciences

Place of publishing:

Warszawa

Description:

32 pages ; 21 cm ; Bibliography p. 28-32

Abstract:

We discuss the solution to the problem of the piecewise linear approximation of fuzzy numbers giving outputs nearest to the inputs with respect to the Euclidean metric. A piecewise linear representation of Fuzzy Numbers is important as far as computer implementation of extension principle-based arithmetic operations is concerned. First of all, we generalize the results presented in Coroianu, Gagolewski, Grzegorzewski, Nearest piecewise linear approximation of fuzzy numbers, FSS 233 (2013), pp. 26-51. Here the n-knot piecewise linear fuzzy numbers for arbitrary n > 2 are examined instead of 1-knot fuzzy numbers. We prove some results on the existence and properties of the approximation operator. Secondly, we study the limiting behavior of the introduced approxima¬tion operator, like the stability of some fuzzy number characteristics under approximation as the number of knots tends to infinity. Finally, we provide a simulation study concerning the computer implementations of arithmetic operations on fuzzy numbers. Suggested concepts are illustrated by examples and algorithms ready for the practical use.

Relation:

Raport Badawczy = Research Report

Resource Identifier:

oai:rcin.org.pl:105537

Source:

RB-2014-01

Language:

eng

Language of abstract:

eng

Rights:

Creative Commons Attribution BY 4.0 license

Terms of use:

Copyright-protected material. [CC BY 4.0] May be used within the scope specified in Creative Commons Attribution BY 4.0 license, full text available at: ; -

Digitizing institution:

Systems Research Institute of the Polish Academy of Sciences

Original in:

Library of Systems Research Institute PAS

Projects co-financed by:

Operational Program Digital Poland, 2014-2020, Measure 2.3: Digital accessibility and usefulness of public sector information; funds from the European Regional Development Fund and national co-financing from the state budget.

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