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| Title of paper:
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On the Cartesian product of intuitionistic fuzzy sets
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| Author(s):
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| Glad Deschrijver
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| Fuzziness and Uncertainty Modelling, Department of Applied Mathematics and Computer Science, Ghent University, Krijgslaan 281, S9, B-9000 Gent, Belgium
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| Glad.Deschrijver@rug.ac.be (corresponding author)
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| Etienne Kerre
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| Fuzziness and Uncertainty Modelling, Department of Applied Mathematics and Computer Science, Ghent University, Krijgslaan 281, S9, B-9000 Gent, Belgium
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| Etienne.Kerre@rug.ac.be
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| Presented at:
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5th International Conference on Intuitionistic Fuzzy Sets, held on 22-23 September 2001 in Sofia, Bulgaria.
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| Published in:
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Conference proceedings, Notes on Intuitionistic Fuzzy Sets, Volume 7, Number 3, pages 14-22
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| Download:
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 PDF (152 Kb, File info)
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| Abstract:
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Cartesian products of intuitionistic fuzzy sets have been defined using the min-max and the product-probabilistic sum operations. In this paper we introduce and analyse the properties of a generalized Cartesian product of intuitionistic fuzzy sets using a general triangular norm and conorm. In particular we investigate the emptiness, the commutativity, the distributivity, the interaction with respect to generalized unions and intersections, the distributivity with respect to the difference, the monotonicity and the cutting in terms of level-sets.
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| Keywords:
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Intuitionistic fuzzy sets, Generalized Cartesian product
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| References:
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- Atanassov K. T., Intuitionistic fuzzy sets, VII ITKR's Session, So¯a, June 1983 (Deposed in Central Sci. - Techn. Library of Bulg. Acad. of Sci., 1697/84) (in Bulgarian)
- Atanassov K. T., Intuitionistic Fuzzy Sets: Theory and Applications, Physica-Verlag Heidelberg New York, 1999
- Kerre E. E. (ed.), Introduction to the Basic Principles of Fuzzy Set Theory and some of its Applications, Communication and Cognition, Gent, 1993 (second revised edition)
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