Abstract
A logical approach to the fuzzification of binary (mathematical) morphology is presented. The fuzzy dilation and fuzzy erosion are introduced independently, and are based on the fuzzy logical operators’ conjunctor’ and’ implicator’ In this way, duality relationships are not forced from the very beginning. It is shown that by choosing suitable fuzzy logical operators, all classical duality and other relationships can be preserved. Following a similar line of reasoning, it is possible to assure the idempotence of the fuzzy closing and fuzzy opening.
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References
Bandemer H. and Näther W., Fuzzy Data Analysis, Theory and Decision Library, Series B: Mathematical and statistical methods, Kluwer Academic Publishers, Dordrecht, 1992.
Bloch I., Normes et conormes triangulaires: un outil général pour la génération de morphologies mathématiques floues, Télécom Paris 93D001.
Bloch I. and Maître H., Constructing fuzzy mathematical morphology: alternative ways, Proceedings of the Second IEEE Conference on Fuzzy Systems (San Francisco, CA., USA), 1993, pp. 1303–1308.
Bloch I. and Maître H., Fuzzy mathematical morphologies: a comparative study, Télécom Paris 94D001.
De Baets B., Oplossen van vaagrelationele vergelijkingcn: een ordetheoretische benadering, Ph.D. thesis, University of Gent, 1995.
De Baets B., Model implicators and their characterization, Proceedings of the First ICSC International Symposium on Fuzzy Logic (Zürich, Switzerland) (Steele N., ed.), ICSC Academic Press, 1995, pp. A42–A49.
De Baets B., Idempotent closing and opening operations in fuzzy mathematical morphology, Proceedings of the Joint Third International Symposium on Uncertainty Modeling and Analysis and Annual Conference of the North American Fuzzy Information Processing Society College Park, MD, USA) (Ayyub B., ed.), IEEE Computer Society Press, Los Alamitos, 1995, pp. 228–233.
De Baets B. and Kerre E., Fuzzy inclusions and the inverse problems, Proceedings of the Second European Congress on Intelligent Techniques and Soft Computing (Zimmermann H.-J., ed.), vol. 2, ELITE, Aachen, 1994, pp. 940–945.
De Baets B., Kerre E. and Gupta M., The fundamentals of fuzzy mathematical morphology. Part 1: Basic concepts, Int. J. General Systems 23 (1994), 155–171.
De Baets B., Kerre E. and Gupta M., The fundamentals of fuzzy mathematical morphology. Part 2: Idempotence, convexity and decomposition, Int. J. General Systems 23 (1995), 307–322.
De Baets B. and Mesiar R., Residual implicators of continuous t-norms, Proceedings of the Fourth European Congress on Intelligent Techniques and Soft Computing (Aachen, Germany) (Zimmermann H.-J., ed.), vol. 1, ELITE, 1996, pp. 27–31.
De Baets B. and Mesiar R,, Metrics and T-equalities, J. Math. Anal. Appl. (1996), submitted.
De Baets B., Tsiporkova E. and Mesiar R., Conditioning in possibility theory with strict order norms, Fuzzy Sets and Systems (1996), submitted.
De Cooman G. and Kerre E., Order norms on bounded partially ordered sets, J. Fuzzy Mathematics 2 (1994), 281–310.
Fodor J., Contrapositive symmetry of fuzzy implications, Fuzzy Sets and Systems 69 (1995), 141–156.
Haralick R., Sternberg S. and Zhuang X., Image analysis using mathematical morphology, IEEE Transactions on Pattern Analysis and Machine Intelligence 9 (1987), 532–550.
Schweizer B. and Sklar A., Associative functions and abstract semi-grvups, Publ. Math. Debrecen 10 (1963), 69–84.
Serra J., Image Analysis and Mathematical Morphology, Academic Press, London, 1982.
Sinha D. and Dougherty E., Fuzzification of set inclusion: theory and applications, Fuzzy Sets and Systems 55 (1993), 15–42.
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De Baets, B. (1998). A Fuzzy Morphology: a Logical Approach. In: Uncertainty Analysis in Engineering and Sciences: Fuzzy Logic, Statistics, and Neural Network Approach . International Series in Intelligent Technologies, vol 11. Springer, Boston, MA. https://doi.org/10.1007/978-1-4615-5473-8_4
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DOI: https://doi.org/10.1007/978-1-4615-5473-8_4
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