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The Scientific World Journal
Volume 2014 (2014), Article ID 156203, 6 pages
http://dx.doi.org/10.1155/2014/156203
Research Article

The Solution of Fully Fuzzy Quadratic Equation Based on Optimization Theory

Department of Mathematics, Islamic Azad University, Science and Research Branch, Tehran, Iran

Received 16 April 2014; Accepted 17 May 2014; Published 9 June 2014

Academic Editor: Mohsen Vaez-ghasemi

Copyright © 2014 T. Allahviranloo and L. Gerami Moazam. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Firstly in this paper we introduce a new concept of the 2nd power of a fuzzy number. It is exponent to production (EP) method that provides an analytical and approximate solution for fully fuzzy quadratic equation (FFQE) : , where . To use the mentioned EP method, at first the 1-cut solution of FFQE as a real root is obtained and then unknown manipulated unsymmetrical spreads are allocated to the core point. To this purpose we find and as optimum values which construct the best spreads. Finally to illustrate easy application and rich behavior of EP method, several examples are given.