General Solutions of Fully Fuzzy Linear Systems

Abstract

We propose a method to approximate the solutions of fully fuzzy linear system (FFLS), the so-calledgeneral solutions. So, we firstly solve the 1-cut position of a system, then some unknown spreads are allocated to each row of an FFLS. Using this methodology, we obtain some general solutions which are placed in the well-known solution sets like Tolerable solution set (TSS) and Controllable solution set (CSS). Finally, we solved two examples in order to demonstrate the ability of the proposed method.

Maximal- and minimal symmetric solutions of fully fuzzy linear systems

“…Also, our proposed solutions are plotted simultaneously to compare with Dehghan's method (DHG) which is suggested in [19] and Allahviranloo's method (AM) which is proposed in [22]. For more detail see Figs.…”

“…In this section, we take an example which has been solved in [22,19] with their methods. However, we adopt the proposed method to solve it to determine four types of solutions which are as bounded solutions while two of them are the maximal symmetric solution and the minimal symmetric solution of the original FFLS.…”

“…Vroman et al suggested Cramer's rule to solve a FFLS [21], then proved that their solution is better than Buckley and Qu's solution. Recently, Allahviranloo et al [22] proposed an analytical method to obtain a solution of a FFLS by an embedding method. Their method is constructed based on obtaining a non-zero solution of the FFLS.…”

Computing the eigenvalues and eigenvectors of a fuzzy matrix

“…We illustrate the applicability of the previous results by calculating a pair of eigenvalues and eigenvectors to a particular example, choosing a matrix taken from [1,5,6] where it was solved a certain fully fuzzy linear system related. ) .…”

Uzawa method for fuzzy linear system

“…Rao and Chen [24] considered the numerical solutions of FLSs in engineering analysis. Allahviranloo et al proposed the fuzzy symmetric solutions and other algebraic solution for fuzzy linear systems [6,11], and the solutions of fully fuzzy linear systems [8,9,10,12,18,19,23]. Friedman et al [21] suggested a general model for solving a class of n × n FLSs        a 11 x 1 + a 12 x 2 + · · · + a 1n x n = y 1 ,…”