Extracting concepts from fuzzy relational context families

Fuzzy relational formal concept analysis (FRCA) mines collections of fuzzy concept lattices from fuzzy relational context families, which are special datasets made of fuzzy formal contexts and fuzzy relations between objects of different types. Mainly, FRCA consists of the following procedures: first, an initial fuzzy relational context family is transformed into a collection of fuzzy formal contexts; second, a fuzzy concept lattice is generated from each fuzzy formal context by using one of the techniques existing in the literature. The principal tools to transform a fuzzy context family into a set of fuzzy formal contexts are the so-called fuzzy scaling quantifiers, which are particular fuzzy quantifiers based on the concept of evaluative linguistic expression. FRCA can be applied whenever information needs to be extracted from multirelational datasets including vagueness, and it can be viewed as an extension of both relational concept analysis and fuzzy formal concept analysis. This article contributes to the development of fuzzy relational concept analysis by achieving the following goals. First of all, we present and study a new class of fuzzy quantifiers, called t-scaling quantifiers, to extract fuzzy concepts from fuzzy relational context families. Subsequently, we provide an algorithm to generate, given a t-scaling quantifier, a collection of fuzzy concept lattices from a special fuzzy relational context family, which is composed of a pair of fuzzy formal contexts and a fuzzy relation between their objects. After that, we introduce an ordered relation on the set of all t-scaling quantifiers, which allows us to discover a correspondence among fuzzy concept lattices deriving from different t-scaling quantifiers. Finally, we discuss how the results obtained for t-scaling quantifiers can be extended to the class of fuzzy scaling quantifies. Therefore, this analysis highlights the main differences between t-scaling and fuzzy quantifiers.