| Title of paper:
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The Inclusion–Exclusion principle for general IF-states
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| Author(s):
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| Daniela Kluvancová
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| Faculty of Natural Sciences, Matej Bel University, Tajovského 40, 974 01, Banská Bystrica, Slovakia
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| daniela.kluvancova@umb.sk
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| Presented at:
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11th International Workshop on Intuitionistic Fuzzy Sets, Banská Bystrica, Slovakia, 30 Oct. 2015
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| Published in:
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"Notes on IFS", Volume 21, 2015, Number 5, pages 24–32
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| Download:
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 PDF (180 Kb, Info)
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| Abstract:
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Any real state on intuitionistic fuzzy sets (IF-sets) can be represented by integrals. L. Ciungu in [3] proved that for any real state on IF-sets and for a pair of binary operations which satisfy some special conditions holds an Inclusion–Exclusion principle. In [10], J. Považan proved that also any state on IF-sets with values from the arbitrary Riesz space we can represented by integrals. But could we consider Inclusion–Exclusion principle for any IF-state? In this paper we will prove this property for general case in very similar way as for real.
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| Keywords:
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IF-set, IE-pair, Inclusion–Exclusion principle, Riesz space, Representation theorem.
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| AMS Classification:
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03E72.
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| References:
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- Atanassov, K. (1986) Intuitionistic fuzzy sets. Fuzzy sets and systems, 20, 87–96.
- Boccuto, A., B. Riečan & M. Vrábelová. (2009) Kurzweil–Henstock Integral in Riesz spaces. Bentham Science Publishers Ltd.
- Ciungu, L.C., J. Klemenová & B. Riečan. (2012) A New Point of View to the Inclusion–Exclusion principle. Proc. of 6th IEEE International Conference of Intelligent Systems IS, Varna, Bulgaria, 142–144.
- Ciungu, L.C. & B. Riečan. (2009) General form of probability on IF-sets. Fuzzy logic and applications, Proc.8th Int.Workshop WILF, Lecture Notes in Artificial Intelligence, 101–107.
- Ciungu, L.C. & B. Riečan. (2014) The Inclusion–Exclusion principle for IF-states. Iranian Journal of Fuzzy systems, 11(2), 17–25.
- Grzegorzewski, P. & E. Mrówka. (2002) Probability on intuitionistic fuzzy events. Soft Methods in Probability, Statistics and Data Analysis, 105–115.
- Grzegorzewski, P. (2011) The Inclusion–Exclusion principle on IF-sets. Information Sciences, 181, 536–546.
- Kuková, M. & M. Navara. (2013) Principles of inclusion and exclusion for fuzzy sets. Fuzzy sets and systems, 232, 98–109.
- Petrovičová, J. & B. Riečan. (2010) On the Łukasiewicz probability theory on IF-sets. Tatra Mountains Mathematical Publications, 46, 125–146.
- Považan, J. (2014) Representation theorem of general states on IF-sets. Intelligent systems, 322, 141–147.
- Riečan, B. (2003) A descriptive definition of probability on intuitionistic fuzzy sets. In: Proc. EUSFLAT, 236–266.
- Riečan, B. (2014) A general point of view to Inclusion–Exclusion property. In: Modern Approaches in Fuzzy Sets, Intuitionistic Fuzzy Sets, Generalized Nets and Related Topics, 1, 171–180.
- Riečan, B. & T. Neubrunn. (1998) Integral, Measure and Ordering. Ister Science, Bratislava.
- Riečan, B. (2006) On a problem of Radko Mesiar: General form of IF-probabilities. Fuzzy Sets and Systems, 157, 1485–1490.
- Riečan, B. (2004) Representation of probabilities on IFS events. Advances in Soft Computing, Soft Methodology and Random Information Systems, 243–246.
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