16-17 May 2019 • Sofia, Bulgaria

Submission: 21 February 2019Notification: 11 March 2019Final Version: 1 April 2019

Issue:On some methods of study of states on interval valued fuzzy sets

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Title of paper: On some methods of study of states on interval valued fuzzy sets
Author(s):
Alžbeta Michalíková
Faculty of Natural Sciences, Matej Bel University, Tajovskeho 40, Banská Bystrica, Slovakia
Mathematical Institute, Slovak Academy of Sciences, Dumbierska 1, Banská Bystrica, Slovakia
alzbeta.michalikovaAt sign.pngumb.sk
 Beloslav Riečan 
Published in: Notes on Intuitionistic Fuzzy Sets, Volume 24 (2018), Number 4, pages 5–12
DOI: https://doi.org/10.7546/nifs.2018.24.4.5-12
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Abstract: In this paper the state on interval valued fuzzy sets is studied. Two methods are considered: a representation of a state by a Kolmogorov probability and an embedding to an MV-algebra. The Butnariu–Klement representation theorem for interval valued fuzzy sets as a relation between probability measure and state is presented.
Keywords: IF-set, IV -set, State, Central limit theorem.
AMS Classification: 03E72
References:
  1. Atanassov, K. T. (1983). Intuitionistic Fuzzy Sets, VII ITKR Session, Sofia, 20-23 June 1983 (Deposed in Centr. Sci.-Techn. Library of the Bulg. Acad. of Sci., 1697/84) (in Bulgarian). Reprinted: Int. J. Bioautomation, 2016, 20(S1), S1–S6.
  2. Butnariu, D., & Klement, E. P. (1993). Triangular norm-based measures. Triangular Norm-Based Measures and Games with Fuzzy Coalitions, Springer, Dordrecht, 37–68.
  3. Ciungu, L., & Riečan, B. (2009). General form of probabilities on IF-sets. In: Di Gesu, V., Pal, S. K., & Petrosino, A. (eds) Fuzzy Logic and Applications. WILF 2009. Lecture Notes in Computer Science, Vol. 5571. Springer, Berlin, Heidelberg.
  4. Čunderlíková, K., & Riečan, B. (2016). On Two Formulations of the Representation Theorem for an IF-state. In: Atanassov K. et al. (eds) Uncertainty and Imprecision in Decision Making and Decision Support: Cross-Fertilization, New Models and Applications. IWIFSGN 2016. Advances in Intelligent Systems and Computing, Vol. 559. Springer, Cham.
  5. Halmos, P. R. (1950). Measure Theory. New York.
  6. Michalíková, A., & Riečan, B. (2018). On some methods of probability. Notes on Intuitionistic Fuzzy Sets, 24(2), 76–83.
  7. Riečan, B., & Mundici, D. (2002). Probability on MV-algebras. Handbook of Measure Theory. E. Pap Ed. Elsevier Science, Amsterdam, Chapter 21, 869–910.
  8. Riečan, B., & Neubrunn, T. (2013). Integral, Measure, and Ordering (Vol. 411). Springer Science and Business Media.
  9. Zadeh, L. A. (1965). Fuzzy sets. Information and Control. 8(3), 338–353.
  10. Zadeh, L. A. (1975). The concept of a linguistic variable and its application to approximate reasoning—I. Information Sciences, 8(3), 199–249.
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