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Solving inexplicit and underdetermined nonlinear systems of equations using fuzzy logic

Solutions for a system of nonlinear equations are needed quite frequently in many applications. For example, selection of design parameters in most control design problems can be posed in terms of the solution of nonlinear equations. The available methods for such solutions are based on explicit and determinate systems. This paper presents a method of solving inexplicit and/or underdetermined systems using fuzzy logic. The method is formulated using the theory of interval arithmetic and subsequently transformed into fuzzy set rules. This method is seen to be effective although it is slower than Newton's method for explicit determinate problems.