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A comparison study of fuzzy MADM methods in nuclear safeguards evaluation

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Abstract

Nuclear safeguards evaluation (NSE) is to verify that a State is living up to its international undertakings not to use nuclear programs for nuclear weapons purposes. The main issue in NSE is on the aggregation of expert evaluations for numerous indicators to make a final decision about the State’s nuclear activity. Fuzzy multiple attribute decision making (FMADM) methods are capable of dealing with such an issue. In this study, we propose a new FMADM methodology to solve the NSE problem. To this end, we investigate the applicability of four basic FMADM methods, namely a simple additive weighting method, a TOPSIS method, a linguistic method, and a non-compensatory method, to the NSE issue. As a result of the assessment of the basic methods, we propose a new FMADM methodology based on a new aggregation operator in which a cumulative belief structure is used to represent the expert evaluations. The basic methods and the proposed method as well are applied to an example from the literature for illustration purposes.

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References

  1. Korhonen P., Moskowitz H., Wallenius J.: Multiple criteria decision support—a review. Eur. J. Oper. Res. 63, 361–375 (1992)

    Article  Google Scholar 

  2. Dyer J.S., Fishburn P.C., Steuer R.E., Wallenius J., Zionts S.: Multiple criteria decision making, multiattribute utility theory: the next ten years. Manag. Sci. 38(5), 645–654 (1992)

    Article  Google Scholar 

  3. Pardalos, P.M., Siskos, Y., Zopounidis, C. (eds): Advances in multicriteria analysis. Kluwer Academic Publishers, Dordrecht (1995)

    Google Scholar 

  4. Yoon K., Hwang C.: Multiple attribute decision making. Springer, Heidelberg (1995)

    Google Scholar 

  5. Chen S., Hwang C.: Fuzzy multiple attribute decision making: methods and applications. Lecture notes in economics and mathematical systems. Springer, Berlin (1992)

    Google Scholar 

  6. Stewart T.J.: A critical survey of the status of multiple criteria decision making theory and practice. OMEGA 20, 569–586 (1992)

    Article  Google Scholar 

  7. Esogbue A.O.: Dynamic programming approaches. In: Pardalos, P.M., Resende, M. (eds) Handbook of Applied Optimization, pp. 78–103. Oxford University Press, New York (2002)

    Google Scholar 

  8. Zadeh L.A.: Fuzzy sets. Inf. Cont. 8, 338–353 (1965)

    Article  Google Scholar 

  9. Dubois D., Prade H., Testemale C.: Weighted fuzzy pattern matching. Fuzzy Sets Syst. 28(3), 313–331 (1988)

    Article  Google Scholar 

  10. Bellman R.E., Zadeh L.A.: Decision-making in a fuzzy environment. Manag. Sci. 17(4), B141–B164 (1970)

    Article  Google Scholar 

  11. Yager R.R.: Fuzzy decision making including unequal objectives. Fuzzy Sets Syst. 1(2), 87–95 (1978)

    Article  Google Scholar 

  12. Deng H., Yeh C.-H.: Simulation-based evaluation of defuzzification-based approaches to fuzzy multiattribute decision making. IEEE Trans. Syst. Man Cybern A Syst. Hum. 36(5), 968–977 (2006)

    Article  Google Scholar 

  13. Baas S.M., Kwakernaak H.: Rating and ranking of multiple-aspect alternatives using fuzzy sets. Automatica 13, 47–58 (1977)

    Article  Google Scholar 

  14. Dubois, D., Prade, H.: The use of fuzzy numbers in decision analysis. In: Gupta, M.M., Sanchez, E. (eds.) Fuzzy Information and Decision Processes, pp. 309–321. North-Holland, (1982)

  15. Chou S.-Y., Chang Y.-H., Shen C.Y.: A fuzzy simple additive weighting system under group decision-making for facility location selection with objective/subjective attributes. Eur. J. Oper. Res. 189(1), 132–145 (2008)

    Article  Google Scholar 

  16. Hwang C.L., Yoon K.: Multiple Attribute Decision Making: Methods and Applications. Springer, New York (1981)

    Google Scholar 

  17. Negi, D.S.: Fuzzy Analysis and Optimization, Ph. D. Thesis, Department of Industrial Engineering, Kansas State University (1989)

  18. Wu W.-Y., Lin C., Kung J.-Y., Lind C.-T.: A new fuzzy TOPSIS for fuzzy MADM problems under group decisions. J. Intell. Fuzzy Syst. 18, 109–115 (2007)

    Google Scholar 

  19. Chen T.-Y., Tsao C.-Y.: The interval-valued fuzzy TOPSIS method and experimental analysis. Fuzzy Sets Syst. 159(11), 1410–1428 (2008)

    Article  Google Scholar 

  20. Chen C.T.: Extensions of the TOPSIS for group decision-making under fuzzy environment. Fuzzy Sets Syst. 114(1), 1–9 (2000)

    Article  Google Scholar 

  21. Wang Y.J., Lee H.S.: Generalizing TOPSIS for fuzzy multiple-criteria group decision-making. Comput. Math. Appl. 53(11), 1762–1772 (2007)

    Article  Google Scholar 

  22. Saaty T.L.: A scaling method for priorities in hierarchical structures. J. Math. Psychol. 15(3), 234–281 (1977)

    Article  Google Scholar 

  23. Laarhoven P.J.M., Pedrycz W.: A fuzzy extension of Saaty’s priority theory. Fuzzy Sets Syst. 11(3), 229–241 (1983)

    Article  Google Scholar 

  24. Buckley J.J., Feuring T., Hayashi Y.: Fuzzy hierarchical analysis revisited. Eur. J. Oper. Res. 129, 48–64 (2001)

    Article  Google Scholar 

  25. Kahraman, C., Cebeci U., Ruan D.: Multi-attribute comparison of catering service companies using fuzzy AHP: The case of Turkey. Int. J. Prod. Econ. 87(2), 171–184 (2004)

    Article  Google Scholar 

  26. Chan F.T.S., Kumar N.: Global supplier development considering risk factors using fuzzy extended AHP-based approach. OMEGA 35(4), 417–431 (2007)

    Article  Google Scholar 

  27. Roy B.: Classement et choix en présence de points de vue multiples (la méthode ELECTRE). RIRO 8, 57–75 (1968) (in French)

    Google Scholar 

  28. Brans J.P., Vincke P.: A preference ranking organization method: the PROMETHEE method for MCDM. Manag. Sci. 31(6), 647–656 (1985)

    Article  Google Scholar 

  29. Figueira J.R., Greco S., Roy R., Słowinski R.: ELECTRE methods: main features and recent developments. In: Zopounidis, C., Pardalos, P.M. (eds) Handbook of Multicriteria Analysis, Applied Optimization, Vol. 103, pp. 51–90. Springer, Berlin (2010)

    Chapter  Google Scholar 

  30. F., F.: A new perspective for assessing the sustainability of countries. J. Trans. Manag. 12(4), 3–32 (2008)

    Google Scholar 

  31. Aouam T., Chang S.I., Lee E.S.: Fuzzy MADM: an outranking method. Eur. J. Oper. Res. 145(2), 317–328 (2003)

    Article  Google Scholar 

  32. Fernandez E., Lopez E., Bernal S., Coello C.A.C., Navarro J.: Evolutionary multiobjective optimization using an outranking-based dominance generalization. Comput. Oper. Res. 37(2), 390–395 (2010)

    Article  Google Scholar 

  33. Herrera F., Martínez L.: A 2-tuple fuzzy linguistic representation model for computing with words. IEEE Trans. Fuzzy Syst. 8(6), 746–752 (2000)

    Article  Google Scholar 

  34. Martinez L., Liu J., Ruan D., Yang J.-B.: Dealing with heterogeneous information in engineering evaluation processes. Inf. Sci. 177, 1533–1542 (2007)

    Article  Google Scholar 

  35. Wu Z., Chen Y.: The maximizing deviation method for group multiple attribute decision making under linguistic environment. Fuzzy Sets Syst. 158, 1608–1617 (2007)

    Article  Google Scholar 

  36. Fan Z.-P., Feng B.: A multiple attributes decision making method using individual and collaborative attribute data in a fuzzy environment. Inf. Sci. 179(20), 3603–3618 (2009)

    Article  Google Scholar 

  37. Kabak, Ö., Ruan, D.: A cumulative belief degree-based approach for missing values in nuclear safeguards evaluation, IEEE Trans. Knowl. Data Eng., (2010) IEEE computer Society Digital Library. IEEE Computer Society, http://doi.ieeecomputersociety.org/10.1109/TKDE.2010.60

  38. IAEA: Physical Model, IAEA Department of Safeguards, SRT-314 (1999)

  39. Liu J., Ruan D., Carchon R.: Synthesis and evaluation analysis of the indicator information in nuclear safeguards applications by computing with words. Int. J. Appl. Math. Comput. Sci. 12(3), 229–462 (2002)

    Google Scholar 

  40. Liu J., Ruan D., Wang H., Martinez L.: Improving nuclear safeguards evaluation through enhanced belief rule-based inference methodology. Int. J. Nucl. Knowl. Manag. 3(3), 312–339 (2009)

    Article  Google Scholar 

  41. Yager R.R.: On ordered weighted averaging aggregation operators in multicriteria decision-making. IEEE Trans. Syst. Man Cybern. 18(1), 183–190 (1988)

    Article  Google Scholar 

  42. Yager R.R.: On the inclusion of importances in OWA aggregations. In: Yager, R.R., Kacprzyk, J. (eds) The Ordered Weighted Averaging Operators: Theory and Applications, pp. 41–59. Kluwer, Boston (1997)

    Chapter  Google Scholar 

  43. Yang J.-B.: Rule and utility based evidential reasoning approach for multiattribute decision analysis under uncertainties. Eur. J. Oper. Res. 131, 31–61 (2001)

    Article  Google Scholar 

  44. Yang J.-B., Sen P.: A general multi-level evaluation process for hybrid MADM with uncertainty. IEEE Trans. Syst. Man Cybern. 24(10), 1458–1473 (1994)

    Article  Google Scholar 

  45. Yang J.-B., Singh M.G.: An evidential reasoning approach for multiple attribute decision making with uncertainty. IEEE Trans. syst. Man Cybern. 24(1), 1–18 (1994)

    Article  Google Scholar 

  46. Xu Z.: An overview of methods for determining OWA weights. Int. J. Intell. Syst. 20, 843–865 (2005)

    Article  Google Scholar 

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Authors and Affiliations

  1. Belgian Nuclear Research Centre (SCK·CEN), Boeretang 200, 2400, Mol, Belgium

    Özgür Kabak & Da Ruan

  2. Industrial Engineering Department, Istanbul Technical University, Macka, 34367, Istanbul, Turkey

    Özgür Kabak

  3. Department of Applied Mathematics and Computer Science, Ghent University, 9000, Gent, Belgium

    Da Ruan

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  1. Özgür Kabak
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  2. Da Ruan
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Correspondence to Özgür Kabak.

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Kabak, Ö., Ruan, D. A comparison study of fuzzy MADM methods in nuclear safeguards evaluation. J Glob Optim 51, 209–226 (2011). https://doi.org/10.1007/s10898-010-9601-1

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  • DOI: https://doi.org/10.1007/s10898-010-9601-1

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