Abstract: In this manuscript we study a fuzzy initial value problem (FIVP) which describes an autocorrelated evolutive process. For this, we use the -correlated derivative (-derivative) concept on fuzzy-number-valued functions. This approach lets us establish a relationship between the diameter of the FIVP solution and its derivative. Moreover, we notice how the derivative influences the interactivity of the process by computing the measure of possibilistic interactivity of the FIVP solution. We analyze a population growth model, namely, the Logistic model, with our approach and compare the results with another approach that uses the generalized derivative of Hukuhara (gH-derivative). Finally, we conclude that in fuzzy differential equations describing locally -correlated fuzzy processes, the use of the interactive derivative is more adequate than the gH-derivative for a fuzzy number-valued function Ver menos