The research on requirements specification for self-adaptive systems has a growing interest in the academy and the industry. As a result, currently there exists different proposals for the specification of requirements for self-adaptive systems. Despite the momentum that this area has received in recent years, in the works reported in the literature we have identified shortcomings. We propose a new framework to represent the requirements of self-adaptive systems. This framework seeks to manage uncertainty and to be sufficiently expressive for self-adaptive systems, including the representation of all the relevant concepts. The concepts, represented in different views to be used in a 5-stage process. Specifically, we present: (i) a discussion of the challenges and problems encountered in the literature; (ii); our proposal to solve these challenges; and (iii) a case study of the problem and its application.