Before answering whether APF is a Project Management methodology, it is necessary to understand what this is. To this end, we can say that project management methodologies are structured processes to turn a vision into reality. Additionally, the development and definition of its processes seek to meet the general objectives of a project; that is, a temporary effort undertaken to create a product, service or exclusive result.
Prince2, Scrum, PMBoK pmi or ABNT NBR ISO 21500 are examples of Project Management methodologies.
The Analysis of Function Points and their applicability
Function Point Analysis (APF) is a method of measuring the functional size of software. Additionally, APF is applicable to the measurement of improvement or development projects; that is, it is not limited to measuring product software, also measuring the application.Dai, you already see the first relevant point.
APF is not limited to projects. That is, its applicability includes the measurement of applications or even continuous development operations outside the scope of a project.
APF in the context of a Project Management methodology
Although there are several methodologies of Project Management, all lend the general theory of administration principles of planning, monitoring and control. Additionally, they discuss how project resources should be used over time, in a budget for producing results.
This is where there is an intercession between project management methodologies and function point analysis. The measurement process, as well as the measurement result, helps bring visibility to various aspects of the project, such as scope and requirements.
As you can see, APF is not a Project Management methodology. However it plays an important role as an applied technique in the context of projects. The association between functional size and other quantities, such as effort, cost, number of defects, enables the generation of useful indicators to Project Management for monitoring productivity and quality. The productivity indicator is heistly used for generating estimates (based on function points) for the project.
However, APF applications are not limited to estimates. In agile development methodologies such as Scrum, APF's role is to monitor performance at a higher level. That is, APF fulfills a role of evaluating the operational capacity in the organization of a product roadmap and evaluating the use of that capability in the follow-up to this roadmap, while estimates under a Sprint may well use a metric or use different metrics, functional or not, internal to the team or not, but of a much finer granularity than that of the APF.