Uncertainties present in the system parameters and/or external forces play a significant role in the static analysis of structures. Recently, fuzzy numbers have been used to model these uncertainties. It may be noted that when uncertainties are considered only for external loading in terms of type-1 or type-2 fuzzy numbers, the problem is converted to a fuzzy system of linear equations with crisp coefficients. In this regard, the purpose of this research is to propose a new technique to solve the fuzzy system of linear equations with crisp coefficients.
It is very interesting to propose effective techniques to solve such problems. A methodology based on the parametric forms of the type-1 and type-2 fuzzy numbers is used to convert the fuzzy system into interval systems of equations. Further, the concept of double and triple parametric forms is utilised to solve the interval systems.
The proposed technique has been successfully implemented to solve the fuzzy linear system of equations in type-1 as well as type-2 fuzzy environments. Accordingly, sample mathematical problems as well as application problems, namely 8-bar truss structure and uniform rectangular sheet structure, have been solved. Further, present results have been contrasted with the solution obtained by the existing approaches and found to be in good agreement.
To deal with the uncertainty in the external loadings, type-1 and type-2 fuzzy numbers are used here. Also, the approach presented in this work to solve the fuzzy linear system of equations shows the originality of this research.
