Issue:On IF-semistates

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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: 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.