Fuzzy Soft Set Approach to First-Order Separable Differential Equations

Abstract

This paper investigates first-order separable differential equations in a fuzzy soft set environment. The concept of fuzzy soft sets combines the uncertainty-handling capability of fuzzy sets with the parameter-ization feature of soft sets, making it suitable for modeling systems involving multiple sources of uncertainty. In this work, fuzzy soft differential equations with parameter-dependent coefficients are considered, and solution techniques are developed by transforming them into corresponding crisp differential equations for each parameter. The study discusses Type-1, Type-2 and Type-3 fuzzy soft differential equations and analytical solutions are obtained using classical methods such as separation of variables and integrating factor techniques. The obtained results show that fuzzy soft differential equations generate families of solutions associated with different parameters, thereby providing a richer and more flexible representation of uncertainty in dynamical systems.