Abstract
Software product line engineering relies on systematic reuse and mass customisation to reduce the development time and cost of a software system family. The extractive adoption of a product line requires to extract variability information from the description of a collection of existing software systems to model their variability. With the increasing complexity of software systems, software product line engineering faces new challenges including variability extraction and modelling. Extensions of existing boolean variability models, such as multi-valued attributes or UML-like cardinalities, were proposed to enhance their expressiveness and support variability modelling in complex product lines. In this paper, we propose an approach to extract complex variability information, i.e., involving features as well as multi-valued attributes and cardinalities, in the form of logical relationships. This approach is based on Formal Concept Analysis and Pattern Structures, two mathematical frameworks for knowledge discovery that bring theoretical foundations to complex variability extraction algorithms. We present an application on product comparison matrices representing complex descriptions of software system families. We show that our method does not suffer from scalability issues and extracts all pertinent relationships, but that it also extracts numerous accidental relationships that need to be filtered.