Classification of type-2 fuzzy sets represented as sequences of vertical slices

Granulation of information by using type-2 fuzzy sets is receiving more attention nowadays. This is due to the superior capability of type-2 fuzzy sets in handling the data uncertainty. From a theoretical perspective, a set containing type-2 fuzzy sets has no trivial geometric structure; therefore, a proper metric cannot be easily defined. As a consequence, common pattern recognition systems, which in one way or another rely on some (geo)metric structure of the input space, are not easily applicable to a space of type-2 fuzzy sets. In this paper, we study the problem of designing a classifier in the input space of type-2 fuzzy sets. Type-2 fuzzy sets are hence interpreted as (granular) patterns forming a given input dataset. By decomposing a type-2 fuzzy set into a sequence of simpler (lower type) fuzzy sets, we explore the possibility of defining and building dissimilarity and kernel-based classification systems on input spaces of type-2 fuzzy sets. Such an interpretation provided in terms of sequences allows us to conceive an effective sequence matching strategy, which can be suitably embedded into well-established pattern recognition systems. We support the methodological developments by performing experiments on synthetically generated classification problems for datasets composed of type-2 fuzzy sets, with adjustable and controlled level of difficulty. Results are promising and suggest to further investigate on the possibility of interpreting type-2 fuzzy sets as input patterns of a given data-driven inference system.