Submit your research to the International Journal "Notes on Intuitionistic Fuzzy Sets". Contact us at nifs.journal@gmail.com

Call for Papers for the 27th International Conference on Intuitionistic Fuzzy Sets is now open!
Conference: 5–6 July 2024, Burgas, Bulgaria • EXTENDED DEADLINE for submissions: 15 APRIL 2024.

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

From Ifigenia, the wiki for intuitionistic fuzzy sets and generalized nets
Revision as of 16:13, 23 April 2019 by Vassia Atanassova (talk | contribs)
(diff) ← Older revision | Latest revision (diff) | Newer revision → (diff)
Jump to navigation Jump to search
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
Download:  PDF (185 Kb  Kb, Info)
Abstract: In paper [4] 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.
Citations:

The list of publications, citing this article may be empty or incomplete. If you can provide relevant data, please, write on the talk page.