This paper proposes a model of optimal tax-induced transfer pricing with a fuzzy arm's length parameter. Fuzzy numbers provide a suitable structure for modelling the ambiguity that is intrinsic to the arm's length parameter. For the usual conditions regarding the anti-shifting mechanisms, the optimal transfer price becomes a maximising $\alpha$-cut of the fuzzy arm's length parameter. Nonetheless, we show that it is profitable for firms to choose any maximising transfer price if the probability of tax audit is sufficiently low, even if the chosen price is considered a completely non-arm's length price by tax authorities. In this case, we derive the necessary and sufficient conditions to prevent this extreme shifting strategy