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Greenhouse gases emission inventories are computed with rather low precision. Moreover, their uncertainty distributions may be asymmetric. This should be accounted for in the compliance and trading rules. In this paper we model the uncertainty of inventories as intervals or using fuzzy numbers. The latter allows us to better shape the uncertainty distributions. The compliance and emission trading rules obtained generalize the results for the symmetric uncertainty distributions that were considered in the earlier papers by the present authors (Nahorski et al., Water Air & Soil Pollution. Focus 7(4-5):539-558, ; Nahorski and Horabik, , J Energy Eng 134(2):47-52, ). However, unlike in the symmetric distribution, in the asymmetric fuzzy case it is necessary to apply approximations because of nonlinearities in the formulas. The final conclusion is that the interval uncertainty rules can be applied, but with a much higher substitutional noncompliance risk, which is a parameter of the rules. [ABSTRACT FROM AUTHOR]