Bustince, H.; Barrenechea, E.; Pagola, M. Restricted equivalence functions. (English) Zbl 1110.68158 Fuzzy Sets Syst. 157, No. 17, 2333-2346 (2006). The paper deals with the treatment of images by means of fuzzy set theory, namely with the comparison of two images and with the distance measures used to order and measure the degrees of similarity by such a comparison. The paper contributes to this topic by introducing the function of restricted equivalence, and global image comparison measures. They are useful in the case of fuzzy image processing. The main contribution of this paper consists in the analysis of comparison methods constructed on the base of two automorphisms, and in the characterization of equivalence functions using implication operators. Reviewer: Milan Mareš (Praha) Cited in 36 Documents MSC: 68U10 Computing methodologies for image processing 03E72 Theory of fuzzy sets, etc. Keywords:fuzzy set; restricted equivalence functions; similarity measures; implication; aggregation; image processing PDFBibTeX XMLCite \textit{H. Bustince} et al., Fuzzy Sets Syst. 157, No. 17, 2333--2346 (2006; Zbl 1110.68158) Full Text: DOI References: [1] Bandler, W.; Kohout, L., Fuzzy power sets and fuzzy implication operators, Fuzzy Sets and Systems, 4, 13-30 (1980) · Zbl 0433.03013 [2] Beliakov, G., Definition of general aggregation operators through similarity relations, Fuzzy Sets and Systems, 114, 437-453 (2000) · Zbl 0962.03051 [3] Bezdek, J. C.; Keller, J.; Krisnapuram, R.; Pal, N. 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