| Title of paper:
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On the operators and partial orderings of intuitionistic fuzzy sets
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| Author(s):
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| Evgeniy Marinov
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| Dept. of Bioinformatics and Mathematical Modelling, IBPhBME - Bulgarian Academy of Sciences, 105 Acad. Georgi Bonchev Str., 1113 Sofia, Bulgaria
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| evgeniy.marinov@biomed.bas.bg
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| Presented at:
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17th International Conference on Intuitionistic Fuzzy Sets, 1–2 November 2013, Sofia, Bulgaria
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| Published in:
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"Notes on IFS", Volume 19, 2013, Number 3, pages 25—33
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| Download:
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 PDF (202 Kb, File info)
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| Abstract:
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Atanassov’s extension of the notion of fuzzy set has proved to be an important field of real-life applications and theoretical research. In the paper [5], there was introduced a new ordering on IF-sets, the so called π-ordering, which turns out to be a key concept for this paper.
In the last section we introduce some new operators on IF-sets and investigate their properties in respect of the two base partial orderings on the class of IF-sets. The standard operators are classified according to the π-ordering as well. The theoretical basis is provided trough the investigation
of more general partial orderings on the vector space R2 and their properties are carried over the triangular representation of IF-sets.
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| Keywords:
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IF-set, π-ordering, Modal quasi-orderings, Operators on IF-sets.
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| AMS Classification:
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03E72
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| References:
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- Atanassov, K., Intuitionistic Fuzzy Sets: Theory and Applications, Springer Physica-Verlag, Heidelberg, 1999.
- Atanassov, K., On Intuitionistic Fuzzy Sets Theory, Springer Physica-Verlag, Berlin, 2012.
- Atanassov, K., V. Tasseva, E. Szmidt, J. Kacprzyk, On the geometrical interpretations of the intuitionistic fuzzy sets. In: Issues in the Representation and Processing of Uncertain and Imprecise Information. Fuzzy Sets, Intuitionistic Fuzzy Sets, Generalized Nets, and Related Topics (Eds. Atanassov K., J. Kacprzyk, M. Krawczak, E. Szmidt), EXIT, Warsaw 2005.
- Birkhoff, G. Lattice Theory, American Mathematical Society, Providence, Rhode Island, 1967.
- Marinov, E., K. Atanassov, π-ordering and index of indeterminacy for intuitionistic fuzzy sets, Proc. of 12th Int. Workshop on IFS and GN, IWIFSGN’13, Warsaw, 11 Oct. 2013 (accepted)
- Szmidt, E., J. Baldwin, New similarity measure for intuitionistic fuzzy set theory and mass assignment theory. Notes on Intuitionistic Fuzzy Sets, Vol. 9, 2003, No. 3, 60–76.
- Szmidt, E., J. Baldwin, Intuitionistic Fuzzy Set Functions, Mass Assignment Theory, Possibility Theory and Histograms. Proc. of 2006 IEEE World Congress on Computational Intelligence, 16-21 July 2006, Vancouver, Canada, 237–243.
- Zadeh, L. A. Fuzzy sets. Information and Control, Vol. 8, 1965, 338–353.
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