An algorithm for solving a system of linear equations with Z-numbers based on the neural network approach

Mathematical modeling of many natural and physical phenomena in industry, engineering sciences and basic sciences lead to linear and non-linear devices. In many cases, the coefficients of these devices, taking into account qualitative or linguistic concepts, show their complexity in the form of Z-numbers. Since Z-number involves both fuzziness and reliability or probabilistic uncertainty, it is difficult to obtain the exact solution to the problems with Z-number. In this work, a method and an algorithm are proposed for the approximate solution of a Z-number linear system of equations as an important case of such problems. The paper is devoted to solving linear systems where the coefficients of the variables and right hand side values are Z-numbers. An algorithm is presented based on a ranking scheme and the neural network technique to solve the obtained system. Moreover, two examples are included to describe the procedure of the method and results.