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 antishifting mechanisms, the optimal transfer price becomes a maximising α-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. OECD, 2017). It means that transfer prices are not attained to a unique true arm's length price, but rather to a range of observable parameter prices with different degrees of appropriateness with respect to the arm's length condition. In the case of a tax audit, the tax authority has to assess if the transfer prices applied by the MNE satisfy the arm's length condition, or if the deviations from the core of the arm's length range represent evidences of profit shifting. This is no more than an ambiguous decision to be taken by the tax authority, thus it implies in additional uncertainties for the MNE.This paper derives a model for optimal tax-induced transfer pricing subjected to a fuzzy arm's length parameter. We apply fuzzy numbers, which were first proposed by (Zadeh et al., 1965) and developed further by several researchers (Zimmermann, 1991;Klir & Yuan, 1995;Verdegay, 1982), thus to model the impact of the uncertainty that is intrinsic to the arm's length parameter over the profit-maximisation strategy. Our model follows the concealment costs approach that is traditional in profit shifting literature (Allingham & Sandmo, 1972;Kant, 1988;Hines Jr & Rice, 1994), however we design it in a generalised tax condition, which allows for the maximisation analysis without constraints on the shifting direction. The model takes the arm's length parameter as a fuzzy number, therefore the maximisation object is also a fuzzy object.Baseline analysis shows that the solution of the fuzzy maximisation object under usual conditions is a α-cut of the fuzzy arm's length parameter, and any adjustments on the transfer price up to the optimal level provide a profit-shifting gain for the MNE. Nonetheless, we show that the MNE may completely disregard the arm's length parameter if the probability of tax audits is sufficiently low. It means that it is profitable to choose any maximising transfer price if the MNE has low chances of being audited, even if the maximising transfer price is considered a completely non-arm's length price. In this sense, we derive the necessary and sufficient conditions to prevent this extreme shifting case.The remaining of this paper is structured as follows. Section 2 presents the basic notions of fuzzy sets and fuzzy numbers. Section 3 derives the general model. Section 4 solves the fuzzy ma...