Weighted polygonal approximation of fuzzy numbers preserving their main characteristics

In this article we obtain an approximation of a given fuzzy number by a unique polygonal fuzzy number preserving its main characteristics such as core, support, and expected interval. For this, we consider the well-known weighted L-2 metric. We show that this weighted polygonal approximation is equivalent to a strict convex quadratic optimization problem finite dimensional with linear inequality and equality constraint. Then, we present efficient and practice solution methods illustrated with several examples. Some properties of invariance of the approximation operator are also obtained. The results presented here extend and improve the methods obtained for weighted trapezoidal approximation and piecewise linear approximation of fuzzy numbers. (C) 2021 Elsevier B.V. All rights reserved.

Automated summary

In this article, we approximate a given fuzzy number by a unique polygonal fuzzy number using the weighted L-2 metric to preserve its main characteristics. We show that this polygonal approximation is equivalent to a finite-dimensional strict convex quadratic optimization problem with linear inequality and equality constraint. We present efficient solution methods and provide several examples for illustration. We also obtain properties of invariance of the approximation operator. The results extend and improve the methods for weighted trapezoidal approximation and piecewise linear approximation of fuzzy numbers.