# Approximation of Fuzzy Numbers by Using $$\alpha$$-$$\beta$$-knots Piecewise Linear Fuzzy Numbers

Conference paper
Part of the Advances in Intelligent Systems and Computing book series (AISC, volume 1074)

## Abstract

In this paper, the problems of approximating general fuzzy number by using $$\alpha$$$$\beta$$–knots piecewise linear fuzzy number are studied. Firstly, $$\alpha$$$$\beta$$–knots piecewise linear fuzzy number are defined, and the conceptions of nearest $$\alpha -\beta -$$knots piecewise linear approximation and nearest $$\{0,\alpha ,1\}$$$$\{0,\beta ,1\}$$–knots piecewise linear approximation are introduced for a general fuzzy number. Then, it is also the most important work of this paper that for a general fuzzy number, we obtain a formula to get the nearest $$\alpha -\beta$$–knots piecewise linear approximation and the nearest $$\{0,\alpha ,1\}-\{0,\beta ,1\}$$–knots piecewise linear approximation using weighted metric as a criterion. And then, we give specific example to show more reasonable and effective of the methods proposed by us.

## Keywords

Approximations Membership functions Fuzzy numbers $$\alpha$$$$\beta$$–knots piecewise linear fuzzy numbers

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