Solving fully fuzzy linear system: A new solution concept

Abstract

Recently, the solutions of fuzzy linear systems have been considered by many researchers. Most of these studies use the same extension method as Friedman et al. (1998). The standard fuzzy arithmetic based on the extension principle does not take into account all the available information, and the obtained results are more imprecise or in some cases, even incorrect. Although the obtained solutions by these methods seem to be reasonable, however sometimes the method requires lengthy procedures and is computationally not efficient. These highlighted problematic points could be our motivation for achieving a new approach to solve fully fuzzy linear systems. To this end, we are going to solve the fully fuzzy linear systems, by using the transmission-average-based fuzzy operations that have been introduced by Abbasi et al. (2015).To this purpose, a computational procedure is going to be proposed to solve these types of equations that meet the defects of previous techniques, especially the embedding method that causes a high dimensional real (non-fuzzy) system to solve. In addition, the necessary conditions for the existence and uniqueness of the fuzzy solution are also going to be presented. For more illustration and investigation, it is shown that the solution of the proposed method is more realistic in comparison to other methods of solving such fuzzy linear systems.