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Published in: Soft Computing 2/2011

01-02-2011 | Original Paper

Remarks and corrections to the triangular approximations of fuzzy numbers using α-weighted valuations

Author: Adrian I. Ban

Published in: Soft Computing | Issue 2/2011

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Abstract

A recent paper was dedicated to find the nearest fuzzy triangular approximations of a fuzzy number by using α-weighted valuations. We prove, by simple examples, that the results of approximations are not always triangular fuzzy numbers and that in fact they are not fuzzy sets. We give a correct solution of the problem of approximation in a more general case, and we study the properties of identity, additivity, translation invariance, scale invariance, and monotonicity of the new approximation operator.

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Metadata
Title
Remarks and corrections to the triangular approximations of fuzzy numbers using α-weighted valuations
Author
Adrian I. Ban
Publication date
01-02-2011
Publisher
Springer-Verlag
Published in
Soft Computing / Issue 2/2011
Print ISSN: 1432-7643
Electronic ISSN: 1433-7479
DOI
https://doi.org/10.1007/s00500-010-0620-0

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