A comparative study of similarity measures. (English) Zbl 0852.04011

Summary: The purpose of this paper is twofold. Firstly, we would like to comment on the study of similarity measures carried out by C. P. Pappis and N. I. Karacapilidis [ibid. 56, 171-174 (1993; Zbl 0795.04007)]. 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 W. Bandler and L. Kohout [ibid. 4, 13-30 (1980; Zbl 0433.03013)] 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.


03E72 Theory of fuzzy sets, etc.
Full Text: DOI


[1] Bandler, W.; Kohout, L., Fuzzy power sets and fuzzy implication operators, Fuzzy Sets and Systems, 4, 13-30 (1980) · Zbl 0433.03013
[2] De Baets, B.; Kerre, E., Fuzzy relational compositions, Fuzzy Sets and Systems, 60, 109-120 (1993) · Zbl 0794.04004
[3] Pappis, C.; Karacapilidis, N., Value approximation of fuzzy systems variables, Fuzzy Sets and Systems, 39, 111-115 (1991) · Zbl 0724.93049
[4] Pappis, C.; Karacapilidis, N., A comparative assessment of measures of similarity of fuzzy values, Fuzzy Sets and Systems, 56, 171-174 (1993) · Zbl 0795.04007
[5] Schweizer, B.; Sklar, A., Probabilistic Metric Spaces (1983), Elsevier Science: Elsevier Science New York · Zbl 0546.60010
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.