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

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 solu...

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Veröffentlicht in:	Soft computing (Berlin, Germany) Germany), 2011-02, Vol.15 (2), p.351-361
1. Verfasser:	Ban, Adrian I.
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Sprache:	eng
Schlagworte:	Approximation Artificial Intelligence Computational Intelligence Control Engineering Fuzzy sets Fuzzy systems Invariance Mathematical analysis Mathematical Logic and Foundations Mathematical programming Mechatronics Original Paper Robotics Scale invariance Valuation
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description	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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subjects	Approximation Artificial Intelligence Computational Intelligence Control Engineering Fuzzy sets Fuzzy systems Invariance Mathematical analysis Mathematical Logic and Foundations Mathematical programming Mechatronics Original Paper Robotics Scale invariance Valuation
title	Remarks and corrections to the triangular approximations of fuzzy numbers using α-weighted valuations
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