RDM Based Approach To Solving Decision Making Problem Under Uncertain Environment
Keywords:
alternatives, decision making, portfolio selection, relative distance measureAbstract
The combination of fuzzy logic tools and multi criteria decision making has a great relevance in the literature. Real life decision making problem under uncertainty is usually associated with information that may be incomplete or imprecise. The information on which decisions are based is uncertainty . Decision making theory is based on several type of uncertainty and tools. Computing with word (CwW) is very effective tool for decision making. Professor Zadeh the creator of CwW idea , formulated many challenge problems. Zadeh’s flight delay problem using relative-distance-measure is discussed in [1].In this paper RDM is applied to solve real life decision making problem. A numerical example is used to illustrate the procedure of the presented approach.
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F.Herrera, E. Herrera-Viedma, J.L.Verdegay, “A Rational Consensus Model in group Decision making Using Linguistic Assessments”, Fuzzy sets and systems, vol 88, pp.31-49, 1997.
G.I.Adamopoulos, C.P.Pappis. “A fuzzy linguistic approach to a multi criteria sequencing problem”, European Journal of Operational Research, vol.92,pp.31-49, 1996.
R.C.Wang,S.J.Chuu. “Group Decision making using a fuzzy linguistic approach for evaluating the flexibility in a manufacturing system”, European Journal of Operational Research, vol.154, pp.563-572, 2004.
E. Herrera-Viedma,F.Herrera, F.Chiclana, M.Luque, “Some Issues on consistency of fuzzy preference Relations”, European Journal of Operational Research, vol.154, pp.98-109,2004.
Dongriu Wu, Jerry M. Mendel. “Linguistic summarization Using if then rules and interval Type-2 Fuzzy sets”, IEEE Transactions on Fuzzy systems, vol 19, No.1,pp.136-151, 2011.
J.Kasprzyk,R.Yager, “Linguistic summaries of data using fuzzy logic”, Int.J. General Systems,.vol.30, pp.133-154, 2001.
J.Kacprzyk,R.Yager,S.Zadrozny, “A fuzzy logic based approach to linguistic summaries of databases” In J. Appl.Math.Comput.Sci, vol.10, pp.813-834, 2000.
J.M.Mendel, D.Wu, “A Type-2 Fuzzy Approach To Linguistic Summarization Of Data”, IEEE Trans.Fuzzy Syst.vol.16,no1,2008, pp.198-212
R.A.Aliev, B.F.Aliev, L.A.Gardashova,O.H. Huseynov, “Selection of an optimal treatment method for acute periodontitis disease”, Journal of Medical Systems, Springer verlag, USA, 36(2), pp.639-46. 2012 Apr.
www.springerlink.com/index/j3127j07280871v5.pdf. Ronald R.Yager, “Human Behavioral Modeling Using Fuzzy and Dempster-Shafer Theory”,2008, pp.89-99.
Pedrycz,W. and Gomide, F., “Fuzzy Systems Engineering: Toward Human-Centric Computing”, John Wiley &Sons: New York,2007.
J.M.Mendel and D.Wu, “Perceptual reasoning for perceptual computing”, Transactions on Fuzzy systems, vol 16, No.6, 2008,. pp.1550-1564.
J.M.Mendel and D.Wu, “Perceptual reasoning using interval type-2 fuzzy sets:Properties”, in Proc.IEEE Int.Conf.Fuzzy Syst., 2008, pp.1219-1226.
Zadeh L.A, “A note on Z-numbers”, J.Inf.Sci, 181,2011, pp. 2923-2932.
Ronald R.Yager, “On Z-valuations using Zadeh`s Z-numbers,” International Journal of Intelligent Systems, 27, 2012, pp259-278.
Adam Neiwiadomski. “A type-2 Fuzzy approach to linguistic Summarization of data”, IEEE Transctions on fuzzy systems, vol. 16,n0.1, 2008,pp.198-211.
Jinsong Zhang, Lakshitha Weerakkody, David Roelant, “A Dempster-Shafer Theory based algorithm for classification of imperfect data”, IADIS European Conference Data Ming. , 2007, pp.11-16.
B. Kang, D. Wei, Y. Li, Y. Deng, A method of converting z-number to classical fuzzy number, Journal of Information & Computational Science 9(3) (2012) 703-709
A. Kaufmann, M. Gupta, Introduction to fuzzy arithmetic: Theory and application, Van Nostrand Reinhold Co: New York, 1985
G. Klir, B. Yuan. Fuzzy Sets and Fuzzy Logic: Theory and Applications, New Jersey:Prentice Hall, 1995 [21] A. Piegat., M.Plucinski. Computing with words with the use of inverse RDM models of membership functions. Int.J. Appl.Math.Comput.Sci.,2015, Vol. 25.No.3, 675-688.
Dymova, L.: Soft computing in economics and finance. Springer-Verlag, Berlin, Heidelberg, 2011.
Piegat, A.: On practical problems with the explanation of the difference between possibility and probability. Control and Cybernetics, vol.34, no.2, 2005.
Sevastjanov, P., L. Dymova, L., Bartosiewicz, P.: A framework for rule-base evidential reasoning in the interval settings applied to diagnosing type 2 diabets, Expert Systems with Applications 39, (2012),
pp.4190-4200.
Piegat, A., Landowski, M.: Is the conventional interval-arithmetic correct? Journalof Theoretical and Applied Computer Science, (2012),vol. 6, no. 2, pp.27-44.
Piegat, A., Landowski, M.: Multidimensional approach to interval uncertainty calculations. In: New Trends in Fuzzy Sets, Intuitionistic: Fuzzy Sets, Generalized Nets and Related Topics, Volume II: Applications, ed. K.T. Atanassov et al., IBS PAN SRI PAS, Warsaw, Poland, (2013), pp.137-151.
Piegat, A., Landowski, M.: Two Interpretations of Multidimensional RDM Interval Arithmetic - Multiplication and Division, International Journal of Fuzzy Systems,vol. 15 no. 4, Dec. 2013, pp.488-496.
Piegat, A., Landowski, M.: Correctness-checking of uncertain -equation solutions on example of the interval-modal method, Paper presented on Twelfth International Workshop on Intuitionistic Fuzzy Sets and Generalized Nets, October 11, 2013,Warsaw, Poland.
Bingyi Kang, Daijun Wei, Ya Li, Yong Deng, “A method of converting Z-number to classical fuzzy number,” Journal of Information & Computational Science, 9(3), 2012, pp.703-709.
Bingyi Kang, Daijun Wei, Ya Li, Yong Deng, “Decision Making Using Z-numbers under Uncertain Environment,”Journal of Information & Computational Science,8(7), 2012, pp.2807-2814.
Ch.Ch.Chou.The canonical representation of multiplication operation on triangular fuzzy numbers. Computers&Mathematics with Applications, 45,2003, pp.1601-1610.
