With increasing digitalization, Artificial Intelligence (AI) is becoming ubiquitous. AI-based systems to identify, optimize, automate, and scale solutions to complex economic and societal problems are being proposed and implemented. This has motivated regulation efforts, including the Proposal of an EU AI Act. This interdisciplinary position paper considers various concerns surrounding fairness and discrimination in AI, and discusses how AI regulations address them, focusing on (but not limited to) the Proposal. We first look at AI and fairness through the lenses of law, (AI) industry, sociotechnology, and (moral) philosophy, and present various perspectives. Then, we map these perspectives along three axes of interests: (i) Standardization vs. Localization, (ii) Utilitarianism vs. Egalitarianism, and (iii) Consequential vs. Deontological ethics which leads us to identify a pattern of common arguments and tensions between these axes. Positioning the discussion within the axes of interest and with a focus on reconciling the key tensions, we identify and propose the roles AI Regulation should take to make the endeavor of the AI Act a success in terms of AI fairness concerns.