Fuzzy Fixed-Point Theory in Numerical Method for Solving Fuzzy Equations

Pratik Barot, Mohini Desai

Abstract: Fuzzy Fixed Point Theory has emerged as a powerful tool in addressing uncertainties in numerical methods for solving fuzzy equations. This theory extends classical fixed point concepts to fuzzy environments, enabling the resolution of equations where parameters and solutions are expressed as fuzzy sets rather than crisp numbers. The paper explores the application of fuzzy fixed point theory in developing numerical methods for solving fuzzy equations, with a focus on its convergence properties, stability, and computational efficiency. Techniques such as iterative methods and fuzzy differential equations are examined, demonstrating the utility of fuzzy fixed point theory in handling imprecise or vague data. The results reveal that fuzzy fixed point-based numerical methods offer robust solutions in various fields, including engineering, finance, and decision-making, where uncertainty is prevalent.

Keywords: Fuzzy Fixed Point Theory, Fuzzy Equations, Numerical Methods, Iterative Methods, Convergence, Fuzzy Differential Equations, Uncertainty, Stability, Computational Efficiency, Fuzzy Sets