Refined Fuzzy Profile Matching

A profile describes a set of properties, e.g. a set of skills a person may have or a set of skills required for a particular job. Profile matching aims to determine how well a given profile fits to a requested profile and vice versa. Fuzzyness is naturally attached to this problem. The filter-based matching theory uses filters in lattices to represent profiles, and matching values in the interval [0,1], so the lattice order refers to subsumption between the concepts in a profile. In this article the lattice is extended by additional information in form of weighted extra edges that represent partial quantifiable relationships between these concepts. This gives rise to fuzzy filters, which permit a refinement of profile matching. Another way to introduce fuzzyness is to treat profiles as fuzzy sets. In the present paper we combine these two aproaches. Extra edges may introduce directed cycles in the directed graph of the ontology, and the structure of a lattice is lost. We provide a construction grounded in formal concept analysis to extend the original lattice and remove the cycles such that matching values determined over the extended lattice are exactly those resulting from the use of fuzzy filters in case of crisp profiles. For fuzzy profiles we show how to modify the weighting construction while eliminating the directed cycles but still regaining the matching values. We also give sharp estimates for the growth of the number of vertices in this construction.