Approximation of fuzzy numbers by using multi-knots piecewise linear fuzzy numbers1

In this paper, the problem of approximating general fuzzy number by using multi-knots piecewise linear fuzzy number is studied. First, r - s-knots piecewise linear fuzzy numbers are defined, and the conceptions of the I-nearest r - s-knots piecewise linear approximation and the II-nearest r - s-knots piecewise linear approximation are introduced for a general fuzzy number. Then, most importantly, we set up the methods to get the I-nearest r - s-knots piecewise linear approximation and the II-nearest r - s-knots piecewise linear approximation for a general fuzzy number. And then, we investigate some properties of the new approximation operators. Finally, we also present specific examples to show the effectiveness, usability and advantages of the methods proposed in this paper, and compare the methods with some other approximation algorithms.