8-9 October 2020 • Burgas, Bulgaria

Submission: 15 May 2020 • Notification: 31 May 2020 • Final Version: 15 June 2020

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

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Title of paper: The Inclusion–Exclusion principle for general IF-states
Daniela Kluvancová
Faculty of Natural Sciences, Matej Bel University, Tajovského 40, 974 01, Banská Bystrica, Slovakia
daniela.kluvancovaAt sign.pngumb.sk
Presented at: 11th International Workshop on Intuitionistic Fuzzy Sets, Banská Bystrica, Slovakia, 30 Oct. 2015
Published in: "Notes on IFS", Volume 21, 2015, Number 5, pages 24–32
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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.
Keywords: IF-set, IE-pair, Inclusion–Exclusion principle, Riesz space, Representation theorem.
AMS Classification: 03E72.
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