Triangular approximation preserving the centroid of fuzzy numbers

Abstract

In this paper, the Karush–Kuhn–Tucker theorem is used for finding the nearest triangular approximation of a fuzzy number with respect to a well-known metric, which preserves the centroid of the fuzzy number, is studied. The properties of translation invariance, scale invariance and identity of the triangular approximation operator are discussed. The main advantage is that the proposed triangular approximation operator preserves the centroid of fuzzy numbers, which is an important index for evaluating fuzzy numbers.

Keywords:

• fuzzy numbers
• triangular fuzzy numbers
• approximation
• centroid

2010 AMS Subject Classifications :

• 03E72

Acknowledgements

We thank the associate editor and two referees for giving us many valuable suggestions and comments, which improved this paper greatly. This work was supported by the Natural Science of Guangxi (Project No. 0991029).