Admissible and Bayes decisions with fuzzy-valued losses

References

[1] Blackwell D.A., Girshick M. A., Theory of Games and Statistical Decisions, Wiley Publications in Statistics. New York, J. Wiley & Sons, London, Chapman & Hall, 1954, xi+355 pp.Suche in Google Scholar

[2] Wald A., “Statistical decision functions”, Ann. Math. Statist., 20:2 (1949), 165-205.10.1007/978-1-4612-0919-5_22Suche in Google Scholar

[3] Rockafellar R.T., Convex Analysis, Princeton Univ. Press, Princeton, New Jersey, 1970, xviii + 451 pp.10.1515/9781400873173Suche in Google Scholar

[4] Shvedov A.S., Probability Theory and Mathematical Statistics: Intermediate Level, M.: Izd. dom Vysshey shkoly ekonomiki, 2016 (in Russian), 280 pp.10.12737/18865Suche in Google Scholar

[5] Shvedov A.S., “Estimation of means and covariances of fuzzy random variables”, Prikladnaya ekonometrika, 42 (2016), 121138 (in Russian).Suche in Google Scholar

[6] Shvedov A.S., “Fuzzy mathematical programming: a brief review”, Problemy upravleniya, 2017, №3, 2-10.Suche in Google Scholar

[7] Ekeland I., Temam R., Convex Analysis and Variational Problems, North-Holland Publ. Comp., Amsterdam, Oxford, 1976, 399 pp.Suche in Google Scholar

[8] Berger J.O., Statistical Decision Theory and Bayesian Analysis, 2nd ed., N.Y.: Springer, 2010, 617 pp.Suche in Google Scholar

[9] Freeling A.N.S., “Fuzzy sets and decision analysis”, IEEE Trans. Systems Man Cybernet., 10:7 (1980), 341-354.10.1109/TSMC.1980.4308515Suche in Google Scholar

[10] Gil M.A., López-Díaz M., “Fundamentals and Bayesian analysis of decision problems with fuzzy-valued utilities”, Int. J. Approx. Reasoning, 15 (1996), 203-224.10.1016/S0888-613X(96)00073-4Suche in Google Scholar

[11] Hryniewicz O., “Bayes statistical decisions with random fuzzy data - an application in reliability”, Reliab. Engineer. & System Safety, 151 (2016), 20-33.10.1016/j.ress.2015.08.011Suche in Google Scholar

[12] Hryniewicz O., Kaczmarek K., Nowak P., “Bayes statistical decisions with random fuzzy data - an application for the Weibull distribution”, Eksploatacja I Niezawodnosc - Maintenance and Reliability, 17:4 (2015), 610-616.10.17531/ein.2015.4.18Suche in Google Scholar

[13] Jain R., “Decision making in the presence of fuzzy variables”, IEEE Trans. Systems Man Cybernet., 6 (1976), 698-703.10.1109/TSMC.1976.4309421Suche in Google Scholar

[14] Kahraman C., Kabak Ö., Fuzzy statistical decision making, Switzerland: Springer, 2016,356 pp.10.1007/978-3-319-39014-7Suche in Google Scholar

[15] Lehmann E.L., Casella G., Theory of point estimation, N.Y.: Springer, 1997,589 pp.Suche in Google Scholar

[16] López-DíazM., GilM.A., “Reversing the order of integration in iterated expectations of fuzzy random variables, and statistical applications”, J. Statist. Plan. Infer., 74 (1998), 11-29.10.1016/S0378-3758(98)00100-1Suche in Google Scholar

[17] Pratt J.W., Raiffa H., Schlaifer R., Introduction to Statistical Decision Theory, Cambridge (Mass.): The MIT Press, 1995,875 pp.Suche in Google Scholar

[18] Robert C.P., The Bayesian Choice: from Decision-Theoretic Foundations to Computational Implementation, 2nd ed., N.Y.: Springer, 2007, 602 pp.Suche in Google Scholar

[19] Rukhin A.L., “Admissibility: Survey of a concept in progress”, Int. Stat. Review, 63:1 (1995), 95-115.10.2307/1403779Suche in Google Scholar

[20] Tong R.M., Bonissone P.P., “A linguistic approach to decision making with fuzzy sets”, IEEE Trans. Systems Man Cybernet., 10:11 (1980), 716723.10.1109/TSMC.1980.4308391Suche in Google Scholar

[21] Viertl R., Statistical Methods for Fuzzy Data, Chichester: Wiley, 2011,256 pp.10.1002/9780470974414Suche in Google Scholar

[22] Watson S.R., Weiss J.J., Donnell M.L., “Fuzzy decision analysis”, IEEE Trans. Systems Man Cybernet., 9:1 (1979), 1-9.10.1109/TSMC.1979.4310067Suche in Google Scholar

[23] Whalen T., “Decision making under uncertainty with various assumptions about available information”, IEEE Trans. Systems Man Cybernet., 14:6 (1984), 888-900.10.1016/B978-1-4832-1450-4.50081-XSuche in Google Scholar

[24] Zadeh L.A., “Fuzzy sets”, Information and Control, 8 (1965), 338-353.10.21236/AD0608981Suche in Google Scholar

[25] Zhen Z., Runtong Z., Yan P., Yihong R., Jie W., “Fuzzy valuation-based system for Bayesian decision problems”, J. ofIntell. & Fuzzy Systems, 30 (2016), 2319-2329.10.3233/IFS-152002Suche in Google Scholar