New solutions of LR fuzzy linear systems using ranking functions and ABS algorithms

Minimal Solution of Singular LR Fuzzy Linear Systems

“…(1) Ghanbari and Mahdavi-Amiri [24] considered the LR fuzzy linear system (FLRLS) of the form $\begin{array}{c}A\tilde{x}=\tilde{b},\end{array}$ where A is a m × n crisp matrix, the unknown vector $\tilde{x}={false({\tilde{x}}_{\mathrm{normal1}},\dots ,{\tilde{x}}_{n}false)}^T$ consists of n fuzzy numbers, and the constant $\tilde{b}={false({\tilde{b}}_{\mathrm{normal1}},\dots ,{\tilde{b}}_{m}false)}^T$ is a vector consisting of n LR fuzzy numbers. They convert the LR fuzzy linear system (6) into the corresponding crisp linear system $\begin{array}{c}Ax=b,\end{array}$ and the constrained least-square problem $\begin{array}{c}\left(\begin{array}{cc}{B}^{+}& -B^{-}\\ -B^{-}& B^{+}\end{array}\right)\left(\begin{array}{c}\alpha \\ \beta \end{array}\right)=\left(\begin{array}{c}{b}^l\\ b^r\end{array}\right),\hspace{1em}\left(\begin{array}{c}\alpha \\ \beta \end{array}\right)>\mathrm{0},\end{array}$ where [ B + ] and [ B − ] are determined as follows:…”

“…Ghanbari et al [24, 25] give the exact and approximated solutions of fuzzy LR linear systems. They give new algorithms using a least-squares model and the ABS approach.…”

Analyzing the solution of a system of fuzzy linear equations by a fuzzy distance

“…There are some works that use parametric functions to solve the systems of linear fuzzy equations (Amirfakhrian 2007(Amirfakhrian , 2010bVroman et al 2007), and some recent works have been done for solving linear system of fuzzy equations (Ghanbari and Mahdavi-Amiri 2010;Horck 2008;Muzzioli and Reynaerts 2007).…”

General solution of full row rank linear systems of equations using a new compression ABS model

“…In addition, ABS methods provide a unification of the field of finitely terminating methods for the solution of linear systems of equations. ABS methods were introduced by Abaffy, Broyden, and Spedicato initially for solving a determined or underdetermined linear system and later extended for linear least squares, nonlinear equations, optimization problems, Diophantine equations, and fuzzy linear systems [1,11,13]. These extended ABS algorithms offer some new approaches that are better than classical ones under several respects.…”