| Title of paper:
|
On IF-semistates
|
| Author(s):
|
| Beloslav Riečan
|
Department of Mathematics, Faculty of Natural Sciences, Matej Bel University, Tajovskeho 40, 974 01 Banská Bystrica, Slovakia
Mathematical Institute of Slovak Acad. of Sciences, Stefanikova 49, SK–81473 Bratislava, Slovakia
|
| riecan@mat.savba.sk, riecan@fpv.umb.sk
|
|
| Published in:
|
"Notes on IFS", Volume 22 (2016) Number 1, pages 27—34
|
| Download:
|
 PDF (166 Kb, File info)
|
| Abstract:
|
Semistates on a family F of IF-events are considered as functions m : F → [0, 1], additive with respect to the Lukasiewicz disjunction A ⊕ B and conjunction A ⊙ B. The main result is an extension theorem extending m to an MV algebra m : M → [0, 1]. The theorem generalizes the extension theorem of IF states from F to M.
|
| Keywords:
|
IF-sets, MV-algebras, Measures.
|
| AMS Classification:
|
28C99.
|
| References:
|
- Atanassov, K. T. (1999). Intuitionistic Fuzzy Sets: Theory and Applications. Studies in Fuzziness and Soft Computing. Physica Verlag, Heidelberg.
- Atanassov, K. T. (2012) On Intuitionistic Fuzzy Sets. Springer, Berlin.
- Cignoli L., D’Ottaviano M., & Mundici, D. (2000) Algebraic Foundations on Many-valed Reasoning, Kluwer, Dordrecht.
- Ciungu, L. & Riečan, B. (2009) General form of probabilities on IF-sets. Fuzzy Logic and Applications. Proc. WILF Palermo, 101–107.
- Ciungu L. & Riečan, B. (2010) Representation theorem for probabilities on IFS-events. Information Sciences, 180, 703–708.
- Grzegorzewski, P. & Mrowka, E. (2002) Probabilitty on intuitionistic fuzzy events. In: Soft Methods in Probability, Statistics and Data Analysis (P. Grzegorzewski, et al. eds.), 105–115.
- Montagna, F. (2000) An algebraic approach to propositional fuzzy logic. J. Logic Lang. Inf. (D. Mundici et al. eds.), Special Issue on Logics of Uncertainty, 9, 91–124.
- Mundici, D. (1986) Interpretation of AFC? algebras in Łukasiewicz sentential calculus. J. Funct. Anal., 56, 889– 894.
- Riecan, B. (2003) A descriptive definition of probability on intutionistic fuzzy sets. In: EUSFLAT’2003 (M. Wagenecht, R. Hampet eds.), 263–266.
- Riecan, B. (2005) On the probability on IF-sets and MV-algebras. Notes on Intuitionistic Fuzzy Sets, 11(6), 21–25.
- Riecan, B. (2006) On a problem of Radko Mesiar: General form of IF-probabilities. Fuzzy Sets and Systems, 152, 1485–1490.
- Riecan, B. (2012) Analysis of Fuzzy Logic Models. In: Intelligent Systems (V. M. Koleshko ed.) INTECH, 219–244.
- Riecan,B. (2015) On finitely additive IF-states. In: Intelligent Systems 2014. Proc. 7th Conf. IEEE (P. Angelov et al. eds), Springer 148–156.
- Riecan, B., & Mundici, D. (2002) Probability in MV-algebras. Handbook of Measure Theory (E. Pap ed.), Elsevier, Heidelberg.
- Riecan, B. & Neubrunn, T. (1997) Integral, Measure, and Ordering, Kluwer, Dordrecht.
|
| 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.
|
|
