Maximal- and minimal symmetric solutions of fully fuzzy linear systems

  • Authors:

  • T. Allahviranloo;S. Salahshour;M. Khezerloo

  • Affiliations:

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

  • Venue:
  • Journal of Computational and Applied Mathematics
  • Year:
  • 2011

Quantified Score

Hi-index 7.29

Visualization

Abstract

In this paper, we shall propose a new method to obtain symmetric solutions of a fully fuzzy linear system (FFLS) based on a 1-cut expansion. To this end, we solve the 1-cut of a FFLS (in the present paper, we assumed that the 1-cut of a FFLS is a crisp linear system or equivalently, the matrix coefficient and right hand side have triangular shapes), then some unknown symmetric spreads are allocated to each row of a 1-cut of a FFLS. So, after some manipulations, the original FFLS is transformed to solving 2n linear equations to find the symmetric spreads. However, our method always give us a fuzzy number vector solution. Moreover, using the proposed method leads to determining the maximal- and minimal symmetric solutions of the FFLS which are placed in a Tolerable Solution Set and a Controllable Solution Set, respectively. However, the obtained solutions could be interpreted as bounded symmetric solutions of the FFLS which are useful for a large number of multiplications existing between two fuzzy numbers. Finally, some numerical examples are given to illustrate the ability of the proposed method.