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Issue:The Inclusion–Exclusion principle for general IF-states: Difference between revisions

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  | file            = NIFS-21-5-24-32.pdf
  | format          = PDF
  | format          = PDF
  | size            = 120
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  | abstract        = 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.
  | abstract        = 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.
  | keywords        = IF-set, IE-pair, Inclusion–Exclusion principle, Riesz space, Representation theorem.
  | keywords        = IF-set, IE-pair, Inclusion–Exclusion principle, Riesz space, Representation theorem.

Revision as of 11:56, 20 January 2016

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Title of paper: The Inclusion–Exclusion principle for general IF-states
Author(s):
Daniela Kluvancová
Faculty of Natural Sciences, Matej Bel University, Tajovského 40, 974 01, Banská Bystrica, Slovakia
daniela.kluvancova@umb.sk
Published in: "Notes on IFS", Volume 21, 2015, Number 5, pages 24–32
Download:  PDF (180  Kb, File info)
Abstract: 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.
Keywords: IF-set, IE-pair, Inclusion–Exclusion principle, Riesz space, Representation theorem.
AMS Classification: 03E72.
References:
  1. Atanassov, K. (1986) Intuitionistic fuzzy sets. Fuzzy sets and systems, 20, 87–96.
  2. Boccuto, A., B. Riečan & M. Vrábelová. (2009) Kurzweil–Henstock Integral in Riesz spaces. Bentham Science Publishers Ltd.
  3. 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.
  4. 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.
  5. Ciungu, L.C. & B. Riečan. (2014) The Inclusion–Exclusion principle for IF-states. Iranian Journal of Fuzzy systems, 11(2), 17–25.
  6. Grzegorzewski, P. & E. Mrówka. (2002) Probability on intuitionistic fuzzy events. Soft Methods in Probability, Statistics and Data Analysis, 105–115.
  7. Grzegorzewski, P. (2011) The Inclusion–Exclusion principle on IF-sets. Information Sciences, 181, 536–546.
  8. Kuková, M. & M. Navara. (2013) Principles of inclusion and exclusion for fuzzy sets. Fuzzy sets and systems, 232, 98–109.
  9. Petrovičová, J. & B. Riečan. (2010) On the Łukasiewicz probability theory on IF-sets. Tatra Mountains Mathematical Publications, 46, 125–146.
  10. Považan, J. (2014) Representation theorem of general states on IF-sets. Intelligent systems, 322, 141–147.
  11. Riečan, B. (2003) A descriptive definition of probability on intuitionistic fuzzy sets. In: Proc. EUSFLAT, 236–266.
  12. 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.
  13. Riečan, B. & T. Neubrunn. (1998) Integral, Measure and Ordering. Ister Science, Bratislava.
  14. Riečan, B. (2006) On a problem of Radko Mesiar: General form of IF-probabilities. Fuzzy Sets and Systems, 157, 1485–1490.
  15. 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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