Fuzzy set theory is a mathematical field designed to analysing and processing sets (concepts) with uncertain boundaries. Recently, researchers have investigated solutions of dynamic systems in which their parameters and/or variables have values into the class of fuzzy numbers on time scales. In this project, we propose new definitions for derivative of fuzzy functions on time scales, where the values of their range may have a special type of relationship called interactivity. Are studiedtwo forms of interactivity: via the concept of completely correlated and linearly correlated fuzzy numbers. We introduce some properties of the proposed notions of differentiability. In addition, we show the connections between these derivatives and compare them with other well-known derivatives on time scales. We also present the characterization theorem of the new derivatives in terms of the Hilger differentiability of their endpoint functions. Furthermore, we establish theorems as the fundamental theorem of calculus. Finally, we study the fuzzy differential equations (FDEs) under the concepts of proposed differentiability on time scales that have coefficients and/or initial conditions uncertain and modeled by interactive fuzzy sets. In particular, we focus on HIV dynamics with imprecise factors such as mortality rate of the virus, presenting a fuzzy solution on time scales.
News published in Agência FAPESP Newsletter about the scholarship: