The purpose of this paper is twofold. Firstly, we would like to comment on the study of similarity measures carried out by Pappis and Karacapilidis (1993). Their definition of 'approximate equality' of fuzzy sets is modified and relevant properties related to this correlated definition are listed. Secondly, a new class of similarity measures, extracted from the work of Bandler and Kohout (1980) on fuzzy power sets, is presented. The properties of the concept of approximate equality corresponding to these similarity measures are discussed, and involve a study of implication operators.