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

Authors:
Adrian I. Ban
Affiliations:
University of Oradea, Department of Mathematics and Informatics, Universitatii 1, 410087, Oradea, Romania
Venue:
Soft Computing - A Fusion of Foundations, Methodologies and Applications
Year:
2011

Citing 0
Cited 3

Metric properties of the nearest extended parametric fuzzy number and applications

International Journal of Approximate Reasoning
Trapezoidal approximation and aggregation

Fuzzy Sets and Systems
Nearest interval, triangular and trapezoidal approximation of a fuzzy number preserving ambiguity

International Journal of Approximate Reasoning

Quantified Score

Hi-index	0.00

Visualization

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.