Hybrid correlated data in risk assessment
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A method for evaluating the risks in a situation has been presented where parameters in the calculation are expressed in the form of dependent fuzzy numbers and probability distributions. The procedure of risk estimation combines stochastic simulation with the execution of arithmetic operations on interactive fuzzy numbers. In order to define operations on such numbers, non-linear programming is used. Relations between the parameters presented in the form of fuzzy numbers and probability distributions are expressed by means of interval regression. The results of computations indicate that the relations between parameters have a significant impact on the ratios characterizing risk.
- BAUDRIT C., DUBOIS D., GUYONET D., Joint propagation and exploitation of probabilistic and possibilistic information in risk assessment, IEEE Transaction on Fuzzy Systems, 2006, 14 (5), 593–607.
- BUCKLEY J.J., The fuzzy mathematics of finance, Fuzzy Sets and Systems, 1987, 21 (4), 257–273.
- BUCKLEY J.J., Solving fuzzy equations in economics and finance, Fuzzy Sets and Systems, 1992, 48 (4), 289–296.
- CALZI M.L., Toward a general setting for the fuzzy mathematics of finance, Fuzzy Sets and Systems, 1990, 35 (4), 265–280.
- CHIU C.Y., PARK S.C., Fuzzy cash flow analysis using present worth criterion, England Economic, 1994, 39 (2), 113–138.
- CHOOBINEH F., BEHRENS A., Use of intervals and possibility distribution in economic analysis, Journal of the Operational Research Society, 1992, 43 (9), 907–918.
- COOPER A., FERSON S., GINZBURG L., Hybrid processing of stochastic and subjective uncertainty data, Risk Analysis, 1996, 16 (6), 785–791.
- ESOGBUE A.O., HEARNES W.E., On replacement models via a fuzzy set theoretic framework, IEEE Transactions on Systems Manufacturing and Cybernetics. Part C. Applications and Reviews, 1998, 28 (4), 549–558.
- FERSON S., GINZBURG L.R., Different methods are needed to propagate ignorance and variability, Reliability Engineering System Safety, 1996, 54, 133−144.
- FERSON S., What Monte Carlo Methods cannot do, Human and Ecological Risk Assessment, 1996 (2), 990–1007.
- GUPTA C.P., A note on transformation of possibilistic information into probabilistic information for investment decisions, Fuzzy Sets and Systems, 1993, 56 (2), 175–182.
- GUYONNET D., BOURGINE B., DUBOIS D., FARGIER H., CME B., CHILS P.J., Hybrid approach for addressing uncertainty in risk assessment, Journal of Environmental Engineering, 2003, 126, 68–76.
- HLADIK M., ČERNY M., Interval regression by tolerance analysis approach, Fuzzy Sets and Systems, 2012, 193 (1), 85–107.
- HUANG C.H., KAY H.-Y., Interval regression analysis with soft-margin reduced support vector machine, Lecture Notes in Computer Science, 2009, NLAI 5579, 826–835.
- INUIGUCHI M., FUJITA H., TANINO T., Robust interval regression analysis based on Minkowski difference, SICE 2002, Proc. 41st SICE Annual Conference, Osaka, Japan, 2002, 4, 2346–2351.
- JENG T.-J., CHUANG C.-C., SU F.-S., Support vector interval regression networks for interval regression analysis, Fuzzy Sets and Systems, 2002, 138 (2), 283–300.
- KAHRAMAN C., RUAN D., TOLGA E., Capital budgeting techniques using discounted fuzzy versus probabilistic cash flows, Information Science, 2002, 42 (1), 57–76.
- KAUFMANN A., GUPTA M.M., Introduction to fuzzy arithmetic. Theory and application, Van Nostrand Reinhold, New York 1985.
- KLIR G.J., A principle of uncertainty and information invariance, International Journal of General Systems, 1990, 17 (2), 249–275.
- KLIR G.J., YUAN B., Fuzzy Sets and Fuzzy Logic, Prentice Hall, Upper Saddle River, New Jersey, 1995.
- KUCHTA D., Fuzzy capital budgeting, Fuzzy Sets and Systems, 2000, 111 (4), 367–385.
- LEE H., TANAKA H., Lower and upper approximation models in interval regression using regression quantile techniques, European Journal of Operational Research, 1999, 116 (3), 653–666.
- LIU Y.-K., LIU B., Fuzzy random variables. A scalar expected value operator, Fuzzy Optimization and Decision Making, 2003, 2 (2), 143–160.
- MOHAMED S., MCCOWAN A.K., Modelling project investment decisions under uncertainty using possibility theory, International Journal of Project Management, 2001, 19 (4), 231–241.
- RALESCU D.A., PURI M.L., The concept of normality for fuzzy random variables, Annals of Probability, 1985, 13, 1371–1379.
- REBIASZ B., Fuzziness and randomness in investment project risk appraisal, Computers and Operations Research, 2007, 34 (1), 199–210.
- SMETS P., Constructing the pignistic probability function in a context of uncertainty, [in:] M. Henrion, E.D. Schachter, L.N. Kanal, J.F. Lemmer (Eds.), Uncertainty in Artificial Intelligence, Vol. 5, North Holland, 1990, 29–39.
- SCHAFER G., A Mathematical Theory of Evidence, Princeton University Press, Princeton, NJ, 1976.
- TANAKA H., LEE H., Fuzzy linear regression combining central tendency and possibilistic properties, Proc. 6-th IEEE International Conference on Fuzzy Sets, 1997, 1, Barcelona, Spain, 63–68.
- TANAKA H., LEE H., Interval regression analysis by quadratic programming approach, IEEE Transactions on Fuzzy Systems, 1998, 6 (4), 473–481.
- TANAKA H., WATADA J., Possibilistic linear systems and their application to the linear regression model, Fuzzy Sets and Systems, 1988, 27 (3), 275–289.
- TANAKA H., Fuzzy data analysis by possibilistic linear models, Fuzzy Sets and Systems, 1987, 24 (3), 363–375.
- TANAKA K., UEJIMA S., ASAI K., Linear regression analysis with fuzzy model, IEEE Transactions on Systems Man and Cybernetics, SMC-12, 1982 (6), 903–907.
- TRAN L., DUCKSTEIN L., Multiobjective fuzzy regression with central tendency and possibilistic properties, Fuzzy Sets and Systems, 2002, 130 (1), 21–31.
- WARD T.L., Discounted fuzzy cash flows analysis, Proc. Fall Industrial Engineering Conference, Institute of Industrial Engineers, Stanford, USA, 1985, 476–481.
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