Economic processes are naturally characterized by imprecise and uncertain relevant information. One of the main reasons is existence of an underground economy. However, in existing works, real-world imprecision and uncertainty of economic conditions are not taken into account. In this paper we consider a problem of calculation of a taxation base to assess tax burden for proportionally growing economy under uncertainty. In order to account for imprecision and uncertainty of economic processes, we use the theory of fuzzy sets. A fuzzy integral equation is used to identify an integral tax burden taking into account the contribution of the underground economy for a certain financial (tax) year. It is also assumed that dynamics of gross domestic product are modeled by fuzzy linear differential equation. An optimal value of tax burden is determined as a solution to the considered fuzzy integral equation. An example is provided to illustrate validity of the proposed study.

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