Numerical solutions for systems of `qualitative' nonlinear algebraic equations by fuzzy logic

This paper presents a fuzzy logic approach for determining a numerical solution to a consistent system of algebraic equations F(x)=0 in which the function F(·) is not explicitly defined and may be underdetermined. Such systems arise frequently in many engineering design problems where design parameters must be chosen using qualitative information by the designer to meet a set of desired performance constraints. The proposed method also can be used for a consistent system of nonlinear equations in which F(·) is explicitly defined and may have fewer independent equations than the number of unknowns. However, this method is very computationally demanding; hence, it is not advisable to apply it to problems involving explicit functions that can be solved using other existing numerical methods. It is seen that this method works quite well and numerical solutions for such problems can be obtained, although it is much slower than Newton's method when employed to consistent, explicit nonlinear equations.