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Estimation of Consistency of Fuzzy Pairwise Comparison Matrices using a Defuzzification Method

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Advances in Dynamical Systems and Control

Part of the book series: Studies in Systems, Decision and Control ((SSDC,volume 69))

Abstract

A definition of consistency of a fuzzy pairwise comparison matrix (FPCM) is developed in the paper. It is supposed that FPCM elements are fuzzy sets with membership functions of any shape. Such FPCMs may be a result of evaluation of decision alternatives by a group of experts when aggregating individual expert judgments made in traditional crisp scales. A comparative analysis of suggested definition with other known definitions of consistent FPCM is done. Usage of suggested definition makes it possible to evaluate the admissibility of inconsistency of expert judgments when calculating weights of decision alternatives and to reveal intransitive expert judgments.

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References

  1. Saaty, T.L., Vargas, L.G.: Decision Making with the Analytic Network Process: Economic, Political, Social and Technological Applications with Benefits, Opportunities, Costs and Risks. Springer, New York (2006)

    MATH  Google Scholar 

  2. Ramanathan, R., Ramanathan, U.: A qualitative perspective to deriving weights from pairwise comparison matrices. Omega 38(3–4), 228–232 (2010)

    Google Scholar 

  3. Tsyganok, V.: Investigation of the aggregation effectiveness of expert estimates obtained by the pairwise comparison method. Math. Comput. Model. 52(3), 538–544 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  4. Jalao, E.R., Wu, T., Shunk, D.: An intelligent decomposition of pairwise comparison matrices for large-scale decisions. Eur. J. Op. Res. 238(1), 270–280 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  5. Durbach, I., Lahdelma, R., Salminen, P.: The analytic hierarchy process with stochastic judgements. Eur. J. Op. Res. 238(2), 552–559 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  6. Koczkodaj, W.W., Szybowski, J.: Pairwise comparisons simplified. Appl. Math. Comput. 253, 387–394 (2015)

    MathSciNet  MATH  Google Scholar 

  7. Pankratova, N.D., Nedashkovskaya, N.I.: Models and methods of analysis of hierarchies. Theory Appl. Kiev, p. 371 (2010). (in ukrainian)

    Google Scholar 

  8. Pankratova, N., Nedashkovskaya, N.: The method of estimating the consistency of paired comparisons. Int. J. Inf. Technol. Knowl. 7(4), 347–361 (2013)

    Google Scholar 

  9. Nedashkovskaya, N.I.: Method of consistent pairwise comparisons when estimating decision alternatives in terms of qualitative criterion. Syst. Res. Inf. Technol. 4, 67–79 (2013). Access mode: http://journal.iasa.kpi.ua/article/view/33943 (in ukrainian)

  10. Buckley, J.J.: Fuzzy hierarchical analysis. Fuzzy Sets Syst. 17(3), 233–247 (1985)

    Article  MathSciNet  MATH  Google Scholar 

  11. Mikhailov, L.: Deriving priorities from fuzzy pairwise comparison judgements. Fuzzy Sets Syst. 134(3), 365–385 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  12. Wang, Y.M., Chin, K.S.: Fuzzy analytic hierarchy process: a logarithmic fuzzy preference programming methodology. Int. J. Approx. Reason. 52(4), 541–553 (2011)

    Article  MATH  Google Scholar 

  13. Wang, J., Lan, J., Ren, P., Luo, Y.: Some programming models to derive priority weights from additive interval fuzzy preference relation. Knowl.-Based Syst. 27, 69–77 (2012)

    Article  Google Scholar 

  14. Sugihara, K., Ishii, H., Tanaka, H.: Interval priorities in AHP by interval regression analysis. Eur. J. Op. Res. 158, 745–754 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  15. Wang, Y.M., Yang, J.B., Xu, D.L.: A two-stage logarithmic goal programming method for generating weights from interval comparison matrices. Fuzzy Sets Syst. 152, 475–498 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  16. Wang, Y.M., Elhag, T.M.S.: A goal programming method for obtaining interval weights from an interval comparison matrix. Eur. J. Op. Res. 177, 458–471 (2007)

    Article  MATH  Google Scholar 

  17. Z.S, Xu, Chen, J.: Some models for deriving the priority weights from interval fuzzy preference relations. Eur. J. Op. Res. 184(1), 266–280 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  18. Liu, F., Zhang, W.G., Fu, J.H.: A new method of obtaining the priority weights from an interval fuzzy preference relation. Inf. Sci. 185(1), 32–42 (2012)

    Article  MATH  Google Scholar 

  19. Chang, D.Y.: Applications of the extent analysis method on fuzzy AHP. Eur. J. Op. Res. 95(3), 649–655 (1996)

    Article  MATH  Google Scholar 

  20. Pankratova, N., Nedashkovskaya, N.: Methods of evaluation and improvement of consistency of expert pairwise comparison judgements. Int. J. Inf. Theor. Appl. 22(3), 203–223 (2015)

    Google Scholar 

  21. Liu, F.: Acceptable consistency analysis of interval reciprocal comparison. Matrices Fuzzy Sets Syst. 160, 2686–2700 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  22. Liu, F., et al.: Consistency analysis of triangular fuzzy reciprocal preference relations. Eur. J. Op. Res. 235, 718–726 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  23. Ross, T.J.: Fuzzy Logic with Engineering Applications, 3rd edn, p. 606. Wiley, New York (2010)

    Book  Google Scholar 

  24. Nedashkovskaya, N.I.: The M_Outflow method for finding the most inconsistent elements of a pairwise comparison matrix. System analysis and information technologies: materials of international scientific and technical conference SAIT 2015 (June 22–25, Kyiv). – 95 p. Access mode: http://sait.kpi.ua/books/

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Authors and Affiliations

  1. Institute for Applied System Analysis, National Technical University of Ukraine “Kyiv Polytechnic Institute”, Peremogy ave., 37, build, 35, 03056, Kyiv, Ukraine

    Nataliya D. Pankratova & Nadezhda I. Nedashkovskaya

Authors
  1. Nataliya D. Pankratova
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  2. Nadezhda I. Nedashkovskaya
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Correspondence to Nataliya D. Pankratova .

Editor information

Editors and Affiliations

  1. Lomonosov Moscow State University, Moscow, Russia

    Victor A. Sadovnichiy

  2. Kyiv Polytechnic Institute, National Technical University of Ukraine, Kiev, Ukraine

    Mikhail Z. Zgurovsky

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Pankratova, N.D., Nedashkovskaya, N.I. (2016). Estimation of Consistency of Fuzzy Pairwise Comparison Matrices using a Defuzzification Method. In: Sadovnichiy, V., Zgurovsky, M. (eds) Advances in Dynamical Systems and Control. Studies in Systems, Decision and Control, vol 69. Springer, Cham. https://doi.org/10.1007/978-3-319-40673-2_20

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  • DOI: https://doi.org/10.1007/978-3-319-40673-2_20

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-40672-5

  • Online ISBN: 978-3-319-40673-2

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