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Fuzzy MCDA Without Defuzzification Based on Fuzzy Rank Acceptability Analysis

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Advances in Fuzzy Logic and Technology 2017 (EUSFLAT 2017, IWIFSGN 2017)

Part of the book series: Advances in Intelligent Systems and Computing ((AISC,volume 643))

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Abstract

Multi-criteria decision analysis (MCDA) in the fuzzy environment needs not only in implementation of functions of fuzzy variables but also inevitably leads to ranking fuzzy quantities. The use of simplification and defuzzification methods at different stages of fuzzy MCDA (FMCDA) results in a loss of information and does not meet the concept of fuzzy decision analysis that “the decision taken in the fuzzy environment must be inherently fuzzy”. In this contribution, a new approach to FMCDA is suggested, in which fuzzy criterion values and fuzzy weight coefficients are considered as fuzzy numbers (FNs) of a general type. Ranking alternatives is based on a novel methodological approach, fuzzy rank acceptability analysis (FRAA), for ranking FNs, whose use within FMCDA forms the fuzzy multicriteria acceptability analysis (FMAA) and implements a consistent approach to fuzzy decision analysis providing both ranking alternatives and the degree of confidence for each alternative to have the corresponding rank. Properties of FRAA ranking and integration of FRAA with a fuzzy extension of MAVT (FMAVT) as an example are considered and discussed along with the overestimation problem, which can arise when implementing FMCDA. The outcomes of FMAVT application for analysis of a multicriteria problem within the case study on land-use planning are considered and compared with the results by (classical) MAVT method.

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References

  1. Bellman, R.E., Zadeh, L.A.: Decision-making in a fuzzy environment. Manag. Sci. 17, 141–163 (1970)

    Article  MathSciNet  MATH  Google Scholar 

  2. Chen, S.J., Hwang, C.L.: Fuzzy Multiple Attribute Decision Making: Methods and Applications, vol. 375. Springer, Berlin (1992)

    MATH  Google Scholar 

  3. Wang, X., Ruan, D., Kerre, E.E.: Mathematics of Fuzziness Basic Issues. Springer, Berlin (2009)

    Book  MATH  Google Scholar 

  4. Pedrycz, W., Ekel, P., Parreiras, R.: Fuzzy Multicriteria Decision-Making: Models, Methods and Applications. Wiley, Chichester (2010)

    Book  Google Scholar 

  5. Belton, V., Stewart, T.: Multiple Criteria Decision Analysis: An Integrated Approach. Kluwer Academic Publishers, Dordrecht (2002)

    Book  Google Scholar 

  6. Figueira, J., Greco, S., Ehrgott, M. (eds.): Multiple Criteria Decision Analysis. State of the Art Surveys. Springer, New York (2005)

    MATH  Google Scholar 

  7. Matarazzo, B., Munda, G.: New approaches for the comparison of LR fuzzy numbers: a theoretical and operational analysis. Fuzzy Sets Syst. 118, 407–418 (2001)

    Article  MATH  Google Scholar 

  8. Yuan, Y.: Criteria for evaluating fuzzy ranking methods. Fuzzy Sets Syst. 44, 139–157 (1991)

    Article  MathSciNet  MATH  Google Scholar 

  9. Wang, X., Kerre, E.E.: Reasonable properties for the ordering of fuzzy quantities (I). Fuzzy Sets Syst. 118(3), 375–385 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  10. Wang, X., Kerre, E.E.: Reasonable properties for the ordering of fuzzy quantities (II). Fuzzy Sets Syst. 118(3), 387–405 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  11. Wang, Z.-X., Mo, Y.-N.: Ranking fuzzy numbers based on ideal solution. In: Cao, B.-Y., Zhang, C.-Y., Li, T.-F. (eds.) Fuzzy Information and Engineering. Advances in Soft Computing, vol. 54, pp. 201–209. Springer, Berlin (2009)

    Chapter  Google Scholar 

  12. Tong, R.M., Bonissone, P.P.: A linguistic approach to decision making with fuzzy sets. IEEE Trans. Syst. Man Cybern. 10, 716–723 (1980)

    Article  MathSciNet  Google Scholar 

  13. Yatsalo, L., Martinez, A.: Novel approach to ranking fuzzy numbers based on fuzzy acceptability analysis. In: Zeng, X., Lu, J., Kerre, E.E., Martinez, L., Koehl, L. (eds.) Proceedings of the 12th International FLINS2016 Conferences on Uncertainty Modelling in Knowledge Engineering and Decision Making, pp. 75–80. World Scientific, Roubaix (2016). doi:10.1142/9789813146976_0015. ISBN 978-981-316-96-9.24-26.08

  14. Basu, K.: Fuzzy revealed preference theory. J. Econ. Theory 32(2), 212–227 (1984)

    Article  MathSciNet  MATH  Google Scholar 

  15. Nakamura, Kazuo.: Preference relations on a set of fuzzy utilities as a basis for decision making. Fuzzy Sets Syst. 20(2), 147–162 (1986)

    Article  MathSciNet  MATH  Google Scholar 

  16. Delgado, M., Verdegay, J.L., Vila, M.A.: A procedure for ranking fuzzy numbers using fuzzy relations. Fuzzy Sets Syst. 26(1), 49–62 (1988)

    Article  MathSciNet  MATH  Google Scholar 

  17. Salminen, P., Lahdelma, R.: SMAA-2: stochastic multicriteria acceptability analysis for group decision making. Oper. Res. 49(3), 444–454 (2001)

    Article  MATH  Google Scholar 

  18. Yatsalo, B., Gritsyuk, S., Mirzeabasov, O.A., Vasilevskaya, M.: Uncertainty treatment within multicriteria decision analysis with the use of acceptability concept. Control Big Syst. 32, 5–30 (2011). (in Russian)

    Google Scholar 

  19. Dubois, D., Prade, H.: Operations on fuzzy numbers. Int. J. Syst. Sci. 9(6), 613–626 (1978)

    Article  MathSciNet  MATH  Google Scholar 

  20. Yatsalo, B.: A new approach to fuzzy multi-criteria acceptability analysis. In: Alonso, J.M., Bustince, H., Reformat, M. (eds.), Proceedings of the 2015 Conference of the International Fuzzy Systems Association and the European Society for Fuzzy Logic and Technology. Series AISR, vol. 89, pp. 947–952 (2015). ISBN 978-94-62520-77-6. ISSN 1951-6851 (2015)

    Google Scholar 

  21. Yatsalo, B., Martinez, L.: A novel approach to ranking fuzzy numbers based on fuzzy acceptability analysis. In: Zeng, X., Lu, J., Kerre, E.E., Martinez, L., Koehl, L. (eds.), Proceedings of the 12th International FLINS2016 Conference on Uncertainty Modelling in Knowledge Engineering and Decision Making, pp. 75–80. World Scientific, Roubaix (2016). doi:10.1142/9789813146976_0015. ISBN 978-981-316-96-9.24-26.08

  22. Yatsalo, B., Martinez, L.: Fuzzy multi-criteria acceptability analysis: a new approach to multi-criteria decision analysis under fuzzy environment. Expert Syst. Appl. 84, 262–271 (2017)

    Article  Google Scholar 

  23. Hanss, M.: Applied Fuzzy Arithmetic. Springer, Berlin (2005)

    MATH  Google Scholar 

  24. Keeney, R.L., Raiffa, H.: Decisions with Multiple Objectives: Preferences and Value Tradeoffs. Wiley, New York (1976)

    MATH  Google Scholar 

  25. Kahraman, C., Cevik Onar, S., Oztaysi, B.: Fuzzy multicriteria decision-making: a literature review. Int. J. Comput. Intell. Syst. 8(4), 637–666 (2015)

    Article  MATH  Google Scholar 

  26. Ashour, O.M., Okudan Kremer, Gl.E.: A simulation analysis of the impact of FAHP-MAUT triage algorithm on the emergency department performance measures. Expert Syst. Appl. 40(1), 177–187 (2013)

    Article  Google Scholar 

  27. Jimnez, A., Mateos, A., Sabio, P.: Dominance intensity measure within fuzzy weight oriented MAUT: an application. Omega Manag. Sci. Environ. Issues 41(2), 397–405 (2013)

    Google Scholar 

  28. Yatsalo, B., Didenko, V., Tkachuk, A., Gritsyuk, S., Mirzeabasov, O., Slipenkaya, V., Babutski, A., Pichugina, I., Sullivan, T., Linkov, I.: Multi-criteria spatial decision support system DECERNS: application to land use planning. Int. J. Inf. Syst. Soc. Change 1, 11–30 (2010)

    Article  Google Scholar 

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Authors and Affiliations

  1. Institute of Cybernetic Intelligent Systems, National Research Nuclear University MEPHI, Obninsk-Moscow, Russian Federation

    Boris Yatsalo

  2. Department of Computer Science, University of Jaen, Jaén, Spain

    Luis Martinez

Authors
  1. Boris Yatsalo
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  2. Luis Martinez
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Correspondence to Boris Yatsalo .

Editor information

Editors and Affiliations

  1. Systems Research Institute, Polish Academy of Sciences, Warsaw, Poland

    Janusz Kacprzyk

  2. Systems Research Institute, Polish Academy of Sciences, Warsaw, Poland

    Eulalia Szmidt

  3. Systems Research Institute, Polish Academy of Sciences, Warsaw, Poland

    Slawomir Zadrożny

  4. Institute of Biophysics and Biomedical Engineering, Department of Bioinformatics and Mathematical Modelling, Bulgarian Academy of Sciences, Sofia, Bulgaria

    Krassimir T. Atanassov

  5. WIT - Warsaw School of Information Technology, Warsaw, Poland

    Maciej Krawczak

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Yatsalo, B., Martinez, L. (2018). Fuzzy MCDA Without Defuzzification Based on Fuzzy Rank Acceptability Analysis. In: Kacprzyk, J., Szmidt, E., Zadrożny, S., Atanassov, K., Krawczak, M. (eds) Advances in Fuzzy Logic and Technology 2017. EUSFLAT IWIFSGN 2017 2017. Advances in Intelligent Systems and Computing, vol 643. Springer, Cham. https://doi.org/10.1007/978-3-319-66827-7_50

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  • DOI: https://doi.org/10.1007/978-3-319-66827-7_50

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-66826-0

  • Online ISBN: 978-3-319-66827-7

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