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

Vassia Atanassova: Text replacement - ""Notes on IFS", Volume" to ""Notes on Intuitionistic Fuzzy Sets", Volume"

2024-08-29T09:08:59Z

Text replacement - ""Notes on IFS", Volume" to ""Notes on Intuitionistic Fuzzy Sets", Volume"

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	\| conference = 11<sup>th</sup> [[International Workshop on Intuitionistic Fuzzy Sets]], Banská Bystrica, Slovakia, 30 Oct. 2015		\| conference = 11<sup>th</sup> [[International Workshop on Intuitionistic Fuzzy Sets]], Banská Bystrica, Slovakia, 30 Oct. 2015
	\| issue = [[Notes on Intuitionistic Fuzzy Sets/21/5\|"Notes on ~~IFS~~", Volume 21, 2015, Number 5]], pages 24–32		\| issue = [[Notes on Intuitionistic Fuzzy Sets/21/5\|"Notes on Intuitionistic Fuzzy Sets", Volume 21, 2015, Number 5]], pages 24–32
	\| file = NIFS-21-5-24-32.pdf		\| file = NIFS-21-5-24-32.pdf
	\| format = PDF		\| format = PDF

Vassia Atanassova: | conference = 11^th International Workshop on Intuitionistic Fuzzy Sets, Banská Bystrica, Slovakia, 30 Oct. 2015

2016-01-22T10:39:16Z

| conference = 11<sup>th</sup> International Workshop on Intuitionistic Fuzzy Sets, Banská Bystrica, Slovakia, 30 Oct. 2015

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	{{issue/data		{{issue/data
	\| conference =		\| conference = 11<sup>th</sup> [[International Workshop on Intuitionistic Fuzzy Sets]], Banská Bystrica, Slovakia, 30 Oct. 2015
	\| issue = [[Notes on Intuitionistic Fuzzy Sets/21/5\|"Notes on IFS", Volume 21, 2015, Number 5]], pages 24–32		\| issue = [[Notes on Intuitionistic Fuzzy Sets/21/5\|"Notes on IFS", Volume 21, 2015, Number 5]], pages 24–32
	\| file = NIFS-21-5-24-32.pdf		\| file = NIFS-21-5-24-32.pdf

Peter Vassilev at 09:56, 20 January 2016

2016-01-20T09:56:15Z

← Older revision		Revision as of 12:56, 20 January 2016
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	\| file = NIFS-21-5-24-32.pdf		\| file = NIFS-21-5-24-32.pdf
	\| format = PDF		\| format = PDF
	\| size = ~~120~~		\| size = 180
	\| 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.

Peter Vassilev: Created page with "{{PAGENAME}} {{PAGENAME}} {{PAGENAME}}..."

2016-01-20T09:55:54Z

Created page with "{{PAGENAME}} {{PAGENAME}} {{PAGENAME}}..."

New page

[[Category:Publications on intuitionistic fuzzy sets|{{PAGENAME}}]]
[[Category:Publications in Notes on IFS|{{PAGENAME}}]]
[[Category:Publications in 2015 year|{{PAGENAME}}]]
{{issue/title
| title = The Inclusion–Exclusion principle for general IF-states
| shortcut = nifs/21/5/24-32
}}
{{issue/author
| author = Daniela Kluvancová
| institution = Faculty of Natural Sciences, Matej Bel University
| address = Tajovského 40, 974 01, Banská Bystrica, Slovakia
| email-before-at = daniela.kluvancova
| email-after-at = umb.sk
}}
{{issue/data
| conference =
| issue = [[Notes on Intuitionistic Fuzzy Sets/21/5|"Notes on IFS", Volume 21, 2015, Number 5]], pages 24–32
| file = NIFS-21-5-24-32.pdf
| format = PDF
| size = 120
| 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 = 03E72.
| references =
# 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.

| citations =
| see-also =
}}

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

Vassia Atanassova: Text replacement - ""Notes on IFS", Volume" to ""Notes on Intuitionistic Fuzzy Sets", Volume"

Vassia Atanassova: | conference = 11th International Workshop on Intuitionistic Fuzzy Sets, Banská Bystrica, Slovakia, 30 Oct. 2015

Peter Vassilev at 09:56, 20 January 2016

Peter Vassilev: Created page with "{{PAGENAME}} {{PAGENAME}} {{PAGENAME}}..."

Vassia Atanassova: | conference = 11^th International Workshop on Intuitionistic Fuzzy Sets, Banská Bystrica, Slovakia, 30 Oct. 2015