A similarity ordering of fuzzy sets based on a generalisation process

The present work proposes a method for generalising a discrete fuzzy set F, representing a model, given another discrete fuzzy set G representing new evidence. The algorithm proceeds by expressing the fuzzy sets as possibility distributions, and then by extending the focal elements of F with elements from the focal elements of G, constructing a generalised fuzzy set. If the fuzzy model is repetitively updated with the same evidence, a convergence state will be reached, the number of repetitions depending on the relative position of the two sets. This number is considered to give an indication of the conceptual proximity of the two entities represented by the fuzzy sets, and therefore provides a similarity index. This index is further complemented with a second measure, equal to the reduction of the probability assigned to the element with full membership in F, before generalisation and at the convergence state. This proposal for similarity seems to be in better agreement with experimental findings in human similarity judgement, than the approaches based on pointwise distance metrics.