Fuzzy Riemann Integral via Interactivity

In this paper, we present the notion of fuzzy γ-Riemann integration based on the notion of summation of interactive fuzzy numbers. The parameter γ plays the role of controlling the uncertainty of the corresponding integral for which coincides with the usual notion of fuzzy Riemann (FR) integration when γ = 1. The existence of the γ-Riemann integral of a function is connected to the existence of its usual FR integral. We also show that the proposed integral shares similar properties to the FR integral.