Which Alternative for Solving Dual Fuzzy Nonlinear Equations Is More Precise?

Abstract

To answer the question stated in the title, we present and compare two approaches: first, a standard approach for solving dual fuzzy nonlinear systems (DFN-systems) based on Newton’s method, which uses 2D FN representation and second, the new approach, based on multidimensional fuzzy arithmetic (MF-arithmetic). We use a numerical example to explain how the proposed MF-arithmetic solves the DFN-system. To analyze results from the standard and the new approaches, we introduce an imprecision measure. We discuss the reasons why imprecision varies between both methods. The imprecision of the standard approach results (roots) is significant, which means that many possible values are excluded.

Keywords

• fuzzy nonlinear systems
• fuzzy arithmetic
• fuzzy calculus
• multidimensional fuzzy arithmetic
• RDM fuzzy arithmetic
• fuzzy parametric form