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Issue:On IF-semistates: Difference between revisions

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# 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.
# 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.
# 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.
# Riečan, 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.
# Riečan, 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.
# Riečan, 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.
# Riečan, 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.
# Riečan, 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.
# Riečan, 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.
# Riečan, B. & Neubrunn, T. (1997) Integral, Measure, and Ordering, Kluwer, Dordrecht.


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Revision as of 11:17, 17 January 2017

shortcut
http://ifigenia.org/wiki/issue:nifs/22/1/27-34
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:
  1. Atanassov, K. T. (1999). Intuitionistic Fuzzy Sets: Theory and Applications. Studies in Fuzziness and Soft Computing. Physica Verlag, Heidelberg.
  2. Atanassov, K. T. (2012) On Intuitionistic Fuzzy Sets. Springer, Berlin.
  3. Cignoli L., D’Ottaviano M., & Mundici, D. (2000) Algebraic Foundations on Many-valed Reasoning, Kluwer, Dordrecht.
  4. Ciungu, L. & Riečan, B. (2009) General form of probabilities on IF-sets. Fuzzy Logic and Applications. Proc. WILF Palermo, 101–107.
  5. Ciungu L. & Riečan, B. (2010) Representation theorem for probabilities on IFS-events. Information Sciences, 180, 703–708.
  6. 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.
  7. 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.
  8. Mundici, D. (1986) Interpretation of AFC? algebras in Łukasiewicz sentential calculus. J. Funct. Anal., 56, 889– 894.
  9. Riečan, B. (2003) A descriptive definition of probability on intutionistic fuzzy sets. In: EUSFLAT’2003 (M. Wagenecht, R. Hampet eds.), 263–266.
  10. Riečan, B. (2005) On the probability on IF-sets and MV-algebras. Notes on Intuitionistic Fuzzy Sets, 11(6), 21–25.
  11. Riečan, B. (2006) On a problem of Radko Mesiar: General form of IF-probabilities. Fuzzy Sets and Systems, 152, 1485–1490.
  12. Riečan, B. (2012) Analysis of Fuzzy Logic Models. In: Intelligent Systems (V. M. Koleshko ed.) INTECH, 219–244.
  13. Riečan, B. (2015) On finitely additive IF-states. In: Intelligent Systems 2014. Proc. 7th Conf. IEEE (P. Angelov et al. eds), Springer 148–156.
  14. Riečan, B., & Mundici, D. (2002) Probability in MV-algebras. Handbook of Measure Theory (E. Pap ed.), Elsevier, Heidelberg.
  15. Riečan, B. & Neubrunn, T. (1997) Integral, Measure, and Ordering, Kluwer, Dordrecht.
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