Operating with Fuzzy Probability Estimates in Decision Making Processes with Risk

Oleg Uzhga-Rebrov, Galina Kuleshova

Abstract


This paper considers different techniques of operating with fuzzy probability estimates of relevant random events in decision making tasks. The recalculation of posterior probabilities of states of nature based on the information provided by indicator events is performed using a fuzzy version of Bayes’ theorem. The choice of an optimal decision is made on the basis of fuzzy expected value maximisation.


Keywords:

Comparison of fuzzy numbers; fuzzy arithmetic; fuzzy expected value; restricted fuzzy arithmetic

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References


J. Benčina, “Fuzzy Decision Trees as a Decision-Making Framework in the Public Sector,” Yugoslav J. of Operation Research, vol. 2, 2011, pp. 205– 224.

J.J. Buckley, Fuzzy Probability and Statistics. Springer-Verlag, Berlin, Heidelberg, 2006, 270 p.

C.H. Cheng, “A new approach for ranking fuzzy number by distance method,” Fuzzy Sets and Systems, vol. 95, 1998, pp. 303–317.

L.Q. Dat, V.F. Yu, Ch.-Y Chen, “An Improved Ranking Method for Fuzzy Numbers using Left and Right Indices,” in 2nd Int. Conference on Computer Design and Engineering, (ICCDE 2012), vol. 49, 2012, pp. 85–94.

M. Hanss, Applied Fuzzy Arithmetic. An Introduction with Engineering Applications. Springer, Berlin, Heidelberg, 2005, 256 p.

X. He, U. Deng, “An Area-Based Approach to Ranking Fuzzy Numbers in Fuzzy Decision Making,” J. of Computational Information Systems, vol. 7, 2011, pp. 3333–3342.

D. Palash, B. Hrishikesh, A. Tazil, “Fuzzy Arithmetic with and without α-cut method: A Comparative Study,” Int. J. of Latest Trends in Computing, vol. 2, issue 1, 2011, pp. 99–107.

G. Parvigiani, L.Y.T., Inone, Decision Theory. Principles and Approaches. John Wiley &Sons, Ltd, 2009, 404 p.

P.Ph.B. Rao, N.R., Shankar. “Ranking Fuzzy Numbers with an Area Method Using Circumcenter of Centroids,” Fuzzy Information and Engineering, vol. 5, issue 1, 2013, pp. 3–18.

F. Herrera and E. Herrera-Viedma, “Linquistic decision analysis: steps for solving decision problem under linquistic information,” Fuzzy Sets and Systems, vol. 115, issue 1, October 2000, pp.67-82.

E. Triantaphulou and Chi-Tun Lin. “Development and Evaluation of Five Fuzzy Multiattribute Decision-Making Methods,” Int. J. of Approximate Reasoning, vol. 14, 1996, pp. 281–310.

О. I. Uzhga-Rebrov, Upravlenije neopredelennostjami. Chastj 4. Kombinirovanije neopredelennostej, Rēzekne, RA Izdevniecība, 2014, 408 p. (In Russian).

Y.-M. Wang, J.-B. Jang, D.-L. Xu and K.S. Chin, “On the centroids of fuzzy numbers,” Fuzzy Sets and Systems, vol. 157, issue 7, 2006, pp. 919–926.


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