Fuzzy Logistic Differential Equation with a Piecewise Constant Argument: Solution Representation, Stability, and Economic Applications

In this study, a fuzzy logistic differential equation with a piecewise constant argument is proposed to describe growth processes in which the state evolves continuously while saturation information is updated at discrete times. The model is formulated under granular differentiability, with uncertainty represented through the fuzzy initial state. Using horizontal membership functions, the fuzzy problem is reduced to a family of scalar differential equations with piecewise constant arguments, providing a basis for the solution representation and qualitative analysis. Existence, uniqueness, positivity, fuzzy reconstruction, stability, convergence, and oscillatory behavior are investigated, with rigorous proofs established for the main results. The proposed framework is then applied to technology adoption and market penetration under periodically revised information, and numerical examples are provided to illustrate the principal dynamical behaviors.