Fully fuzzy linear systems with trapezoidal and hexagonal fuzzy numbers

We study fully fuzzy linear systems with trapezoidal and hexagonal fuzzy numbers. The existence and uniqueness of the solution for such systems have been investigated in the literature under some restrictions on the coefficients matrix on one hand, and on the multiplication of fuzzy numbers on the other hand. Almost all researchers approximated the multiplication of two fuzzy numbers when they used the arithmetic α-cut\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\alpha -cut$$\end{document}. Using this approach, the multiplication of two positive fuzzy numbers need not be positive and in other times leads to a fuzzy number that is not of the same type. The aim of the current research is to solve trapezoidal and hexagonal fuzzy linear systems using the exact multiplication definition of α-cut\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\alpha -cut$$\end{document} and under certain conditions on the coefficients matrices to insure that the solution is a set of positive fuzzy numbers that are trapezoidal and hexagonal, respectively. We illustrate the proposed method using a number of numerical examples. We compare the numerical results with a well-known method to show the advantages of the proposed method.