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# Issue:Connection between interval-valued observables and intuitionistic fuzzy observables

 shortcut http://ifigenia.org/wiki/issue:nifs/25/1/32-42
Title of paper: Connection between interval-valued observables and intuitionistic fuzzy observables
Author(s):
 Katarína Čunderlíková Mathematical Institute, Slovak Academy of Sciences, 49 Stefánikova Str., 814 73 Bratislava, Slovakia cunderlikova.lendelova@gmail.com
Published in: Notes on Intuitionistic Fuzzy Sets, Volume 25 (2019), Number 1, pages 32–42
DOI: https://doi.org/10.7546/nifs.2019.25.1.32-42
Abstract: In paper  the authors studied probability on two lattices and they showed that these two lattices are isomorphic. First lattice was the geometrical interpretation of intuitionistic fuzzy sets introduced by K. T. Atanassov and the second lattice was the geometrical interpretation of interval valued sets introduced by L. A. Zadeh. Later in papers [3, 6] authors studied intuitionistic fuzzy events and interval-valued events. They showed that these two systems are isomorphic and they illustrated the connection between intuitionistic fuzzy state and interval valued state. In this paper, we define the notion of interval valued observable and we display the connection to the intuitionistic fuzzy observable. We define the notion of interval valued mean value and dispersion and we show the relation between interval-valued distribution function and intuitionistic fuzzy distribution function, too.
Keywords: Intuitionistic fuzzy set, Interval-valued set, Intuitionistic fuzzy event, Interval-valued event, Intuitionistic fuzzy state, Interval-valued state, Intuitionistic fuzzy observable, Interval-valued observable, Isomorphism, Interval-valuedmeanvalue, Interval-valueddispersion, Interval-valued distribution function, Intuitionistic fuzzy distribution function.
AMS Classification: 03E72, 03B52, 60A86.
References:
1. Atannasov, K. (1999). Intuitionistic Fuzzy Sets: Theory and Applications. Springer Physica Verlag, Heidelberg.
2. Atanassov, K. T. (2012). On Intuitionistic Fuzzy Sets Theory. Springer, Berlin.
3. Král, P., & Riečan, B. (2010). Probabilty on interval-valued Events.Proceeding of Eleventh Int. Workshop on GNs and Second Int. Workshop on GNs, IFSs , KE, London, 9-10 July 2010, 43–47.
4. Lendelová, K., & Michalíková, A. (2005). Probability on a Lattice L1 . Proceedings East West Fuzzy Colloquium 2005, 12th Zittau Fuzzy Colloquium, September 21-23, 2005, Zittau Germany, Heft 84/2005 Nr. 2090-2131, Germany: Institut für Prozeßtechnik, Prozeßau-tomatisierung und Meßtechnik, 79–83.
5. Lendelová, K., & Riečan, B. (2004). Weak law of large numbers for IF-events. Current Issues in Data and Knowledge Engineering (Bernard De Baets et al. eds.), EXIT, Warszawa, 309–314.
6. Michal´ ıková, A., & Riečan, B. (2018). On some methods of study of states on interval-valued fuzzy sets. Notes on Intuitionistic Fuzzy Sets, 24 (4), 5–12.
7. Riečan, B. (2006). On a problem of Radko Mesiar: general form of IF-probabilities. Fuzzy Sets and Systems, 152, 1485–1490.
8. Riečan, B. (2006). On the probability and random variables on IF events. In Applied Artifical Intelligence, Proc. 7th FLINS Conf. Genova (D. Ruan et al. eds.), 138–145.
9. Riečan, B. (2012). Analysis of fuzzy logic models, Intelligent systems (V. Koleshko ed.), INTECH, 219–244.
10. Zadeh, L. A. (1975). The concept of linguistic variable and its application to approximate reasoning I. Information Sciences, 8 (3), 199–249.
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