Abstract
Fuzzy integral provides a powerful tool for fusing multiple sources of information or evidence to give an evaluation that expresses the level of confidence (or preference) in a particular hypothesis (or decision). However, the computational framework of the fuzzy integral is not suitable for sequential decision making tasks, since it assumes that the sources of information have been readily available prior to information fusion. In a sequential decision making task, information is progressively accumulated, while decisions are made at various time instants. In this paper, we reformulate the computational framework of the fuzzy integral in order to translate its framework into a successive one. To this end, three issues have been encountered: (i) how to collect the richest information for sequential decision making, (ii) how to efficiently preserve the constantly increasing amount of incoming information, and (iii) how to build up an effective computational scheme in order to gratify the requirement of real-time decision making. The derived scheme, called the Gaussian successive fuzzy integral scheme, was closely examined to validate its feasibility in real-time sequential multi-decision making on the basis of incremental information gathering.
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Barcusa, A., Montibeller, G.: Supporting the allocation of software development work in distributed teams with multi-criteria decision analysis. Omega 36(3), 464–475 (2008)
Beck, J.M., Ma, W.J., Kiani, R., Hanks, T., Churchland, A.K., Roitman, J., Shadlen, M.N., Latham, P.E., Pouget, A.: Probabilistic population codes for bayesian decision making. Neuron 60(6), 1142–1152 (2008)
Bellman, R.E., Zadeh, L.A.: Decision-making in a fuzzy environment. Manag. Sci. 17, B141–B164 (1970)
Bozdag, C.E., Kahraman, C., Ruan, D.: Fuzzy group decision making for selection among computer integrated manufacturing systems. Comput. Ind. 51, 13–29 (2003)
Büyüközkan, G., Feyzioğlu, O., Ruan, D.: Fuzzy group decision-making to multiple preference formats in quality function deployment. Comput. Ind. 58(5), 392–402 (2007)
Chen, S.Y.: Theory of fuzzy optimum selection for multistage and multiobjective decision making systems. J. Fuzzy Math. 2(1), 163–174 (1994)
Chen, S.Y., Fu, G.T.: Combining fuzzy iteration model with dynamic programming to solve multiobjective multistage decision making problems. Fuzzy Sets Syst. 152, 499–512 (2005)
Cherng, S., Fang, C.Y., Chen, C.P., Chen, S.W.: Critical motion detection of nearby moving vehicles in a vision-based driver assistance system. IEEE Trans. Intell. Transp. Syst. 10(1), 70–82 (2009)
Chung, Y.C., Wang, J.M., Chen, S.W.: Progressive Background Image Generation. IPPR Conf. Comput. Vis., Graphics and Image (2002)
Comak, E., Polat, K., Günes, S., Arslan, A.: A new medical decision making system: Least square support vector machine (LSSVM) with fuzzy weighting pre-processing. Expert Syst. Appl. 32(2), 409–414 (2007)
Demirtas, E.A., Üstün, Ö.: An integrated multiobjective decision making process for supplier selection and order allocation. Omega 36(1), 76–90 (2008)
Esogbue, A.O., Bellman, R.E.: Fuzzy dynamic programming and its extensions. TIMS/Stud Manag. Sci. 20, 147–167 (1984)
Fan, Z.P., Ma, J., Jiang, Y.P., Sun, Y.H., Ma, L.: A goal programming approach to group decision making based on multiplicative preference relations and fuzzy preference relations. Eur. J. Oper. Res. 174(1), 311–321 (2006)
Freeman, J.A., Skapura, D.M.: Neural Networks: Algorithms, Applications, And Programming Techniques. Addison-Wesley, New York (1992)
Fu, G.: A fuzzy optimization method for multicriteria decision making: An application to reservoir flood control operation. Expert Syst. Appl. 34(1), 145–149 (2008)
Grabisch, M.: Fuzzy integral in multicriteria decision making. Fuzzy Sets Syst. 69, 279–298 (1995)
Grabisch, M., Sugeno, M., Murofushi, T.: Fuzzy Measures and Integrals: Theory and Applications, Springer-Verlag. New York, Inc., Secaucus (2000)
Greco, S., Matarazzo, B., Slowinski, R.: Rough sets theory for multicriteria decision analysis. Eur. J. Oper. Res. 129, 1–47 (2001)
Guy, T.V., Wolpert, D.H., Karny, M.: Decision Making with Imperfect Decision Makers. Springer-Verlag, Berlin (2012)
Herrera-Viedma, E., Chiclana, F., Herrera, F., Alonso, S.: Group decision making model with incomplete fuzzy preference relations based on additive consistency. IEEE Trans. Syst. Man Cybern. Part B 37(1), 176–189 (2007)
Iwamoto, S., Sniedovich, M.: Sequential decision making in fuzzy environment. Math. Anal. Appl. 222, 208–224 (1998)
Jansson, J., Gustafsson, F.: A framework and automotive application of collision avoidance decision making. Automatica 44, 2347–2351 (2008)
Kaburlassos, V.G., Petridis, V.: Learning and decision-making in the framework of fuzzy lattices. In: Jain, L.C., Kacprzyk, J. (eds.) Studies in Fuzziness and Soft Computing, pp. 55–94. Physica-Verlag Company, Heidelberg (2002)
Kacprzyk, J.: A branch-and-bound algorithm for the multistage control of a fuzzy system in fuzzy environment. Kybernetes 8, 139–147 (1979)
Kacprzyk, J., Esogbue, A.O.: Fuzzy dynamic programming: main developments and applications. Fuzzy Sets Syst. 81, 31–45 (1996)
Kacprzyk, J., Zadrożny, S., Fedrizzi, M., Nurmi, H.: On group decision making, consensus reaching, voting and voting paradoxes under fuzzy preferences and a fuzzy majority: A survey and some perspectives. In: Bustince, H., et al. (eds.) Fuzzy Sets and Their Extensions: Representation, Aggregation and Models. Springer, Berlin (2008)
Kahraman, C., Ruan, D., Dogan, I.: Fuzzy group decision-making for facility location selection. Inf. Sci. 157, 135–153 (2003)
Keller, J.M., Krishnapuram, R.: Evidence aggregation networks for fuzzy logic inference. IEEE Trans. Neural Netw. 3(5), 761–769 (1992)
Klir, G.J., Yuan, B.: Fuzzy Sets and Fuzzy Logic. Theory and Applications, pp. 177–178. Prentice Hall, Upper Saddle River (1997)
Lee, D.S.: Effective Gaussian mixture learning for video background subtraction. IEEE Trans. Pattern Anal. Mach. Intell. 27(5), 827–832 (2005)
Li, L., Lai, K.K.: Fuzzy dynamic programming approach to hybrid multiobjective multistage decision-making problems. Fuzzy Sets Syst. 117(1), 13–25 (2001)
Li, G.D., Yamaguchi, D., Nagai, M.: A grey-based decision-making approach to the supplier selection problem. Math. Comput. Model. 46(3–4), 573–581 (2007)
Luenberger, D.G., Ye, Y.: Linear and Nonlinear Programming, 3rd edn. Springer Science and Business Media, Berlin (2008)
Rasmy, M.H., Lee, S.M., Abd El-Wahed, W.F.: An expert system for multi-objective decision making: application of fuzzy linguistic preferences and goal programming. Fuzzy Sets Syst. 127(2), 209–220 (2002)
Sugeno, M.: Fuzzy Measures and Fuzzy Integrals: A Survey, pp. 89–102. Fuzzy Automatic and Decision Processes, North Holland (1977)
Teacy, W.T.L., Chalkiadakis, G., Rogers, A., Jennings, N.R.: Sequential decision making with untrustworthy service providers. In: Proceedings of the 7th Int’l Joint Conference on Autonomous Agents and Multiagent Systems, vol. 2, pp. 755–762 (2008)
Wang, Z., Li, K.W., Wang, W.: An approach to multi-attribute decision making with interval-valued intuitionistic fuzzy assessments and incomplete weights. Inf. Sci. 179(17), 3026–3040 (2009)
Yunjun, H., Xiangdong, Y., Dan, W.: Lagrangian relaxation based feasible solution algorithm. In: 24th Chinese Conference on Control and Decision, 23–25 May 2012, pp. 875–878
Peng, D.H., Gao, C.Y., Zhai, L.L.: Multi-criteria group decision making with heterogeneous information based on ideal points concept. Int. J. Comput. Intell. Syst. 6(4), 616–625 (2013)
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This work was supported by the NSC, R.O.C., under Contract NSC-99-2221-E-003-019 -MY2.
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Luo, AC., Chen, SW. & Fang, CY. Gaussian Successive Fuzzy Integral for Sequential Multi-decision Making. Int. J. Fuzzy Syst. 17, 321–336 (2015). https://doi.org/10.1007/s40815-015-0028-1
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DOI: https://doi.org/10.1007/s40815-015-0028-1