Issue:On two formulations of the IF state representation theorem

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Title of paper: On two formulations of the IF state representation theorem Author(s): Beloslav Riečan Department of Mathematics, Faculty of Natural Sciences, Matej Bel University, Tajovského 40, 974 01 Banská Bystrica, Slovakia beloslav.riecan@umb.sk Presented at: 11th International Workshop on Intuitionistic Fuzzy Sets, Banská Bystrica, Slovakia, 30 Oct. 2015 Published in: "Notes on IFS", Volume 21, 2015, Number 5, pages 7–10 Download:  PDF (121  Kb, Info) Abstract: There are two IF-state representation theorems, [2,4]. They represent IF-state by some classical Kolmogorovian probabilities. Of course, they must be equivalent, but the formulations correspond with the constructions of the probabilities. Keywords: D-poset, Effect algebra, Multiplicative operation. AMS Classification: 03G12, 03B5D. References: Butnariu, D. & E. P. Klement (1993) Triangular Norm-Based Measures and Games with Fuzzy Coalitions. Kluwer, Dordrecht. Ciungu, L. & B. Riečan (2010) Representation theorem for probabilities on IFS-events. Information Sciences, 180, 793–798. Grzegorzewski, P.,& E. Mrowka (2002) Probability of intuitionistic fuzzy events. In: Soft Methods in Probability, Statistics and Data Analysis (P. Grzegorzewski et al. eds.), 105–115. Riečan, B. (2003) A decsriptive definition of the probability on intuitionistic fuzzy sets. In: EUSFLAT 2003 (M. Wagenecht, R. Hampet, eds.), 263–266. Riečan, B. (2006) On a problem of Radko Mesiar: General form of IF-probabilities. Fuzzy Sets and Systems, 152, 1485–1490. 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.