Learning-based similarity measurement for fuzzy sets

The work described in this paper proposes a method for the measurement of similarity, viewed from the decision maker’s perspective. At first, an algorithm is presented that generalizes 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, constructs a generalized fuzzy set. If the initial 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, and therefore of the two fuzzy sets, and can be used as 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 learning and at the convergence state. This proposal for similarity seems to be in better agreement with experimental findings in human similarity judgment than approaches based on pointwise distance metrics. Q 1998 John Wiley & Sons, Inc.