| Title of paper:
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On some methods of study of states on interval valued fuzzy sets
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| Author(s):
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| Alžbeta Michalíková
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Faculty of Natural Sciences, Matej Bel University, Tajovskeho 40, Banská Bystrica, Slovakia
Mathematical Institute, Slovak Academy of Sciences, Dumbierska 1, Banská Bystrica, Slovakia
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| alzbeta.michalikova@umb.sk
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| Beloslav Riečan
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| Published in:
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Notes on Intuitionistic Fuzzy Sets, Volume 24 (2018), Number 4, pages 5–12
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| DOI:
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https://doi.org/10.7546/nifs.2018.24.4.5-12
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| Download:
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 PDF (171 Kb Kb, Info)
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| Abstract:
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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.
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| Keywords:
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IF-set, IV -set, State, Central limit theorem.
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| AMS Classification:
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03E72
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| References:
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- 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.
- Butnariu, D., & Klement, E. P. (1993). Triangular norm-based measures. Triangular Norm-Based Measures and Games with Fuzzy Coalitions, Springer, Dordrecht, 37–68.
- 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.
- 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.
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- Riečan, B., & Mundici, D. (2002). Probability on MV-algebras. Handbook of Measure Theory. E. Pap Ed. Elsevier Science, Amsterdam, Chapter 21, 869–910.
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| Citations:
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