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Intelligent Decision Technologies 2016 pp 371–380Cite as

Ranking Alternatives by Pairwise Comparisons Matrix with Fuzzy Elements on Alo-Group

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Part of the book series: Smart Innovation, Systems and Technologies ((SIST,volume 57))

Abstract

The decision making problem considered in this paper is to rank n alternatives from the best to the worst, using the information given by the decision maker in the form of an n by n pairwise comparisons matrix. Here, we deal with a pairwise comparisons matrix with fuzzy elements (PCF matrix). Fuzzy elements of the pairwise comparisons matrix are applied whenever the decision maker is not sure about the value of his/her evaluation, or, the elements of the PCF matrix are aggregated crisp evaluations in a group decision making problem. We investigate pairwise comparisons matrices with elements from an abelian linearly ordered group (alo-group) over a real interval. We propose a method starting from construction of fuzzy elements of a reciprocal PCF matrix, calculating its consistency and resulting into computation of the priority vector associated to the ranking of the alternatives. Illustrating examples are presented and discussed.

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References

  1. Bilgic, T., Turksen, I.B.: Measurement of membership functions: theoretical and empirical work. In: Dubois, D., Prade, H. (eds.) Fundamentals of Fuzzy Sets, pp. 195–227. Kluwer Academic Publishers, New York (2000)

    Google Scholar 

  2. Bourbaki, N.: Algebra II. Springer, Heidelberg-New York-Berlin (1998)

    MATH  Google Scholar 

  3. Cavallo, B., D’Apuzzo, L., Squillante, M.: About a consistency index for pairwise comparison matrices over a divisible alo-group. Int. J. Intell. Syst. 27, 153–175 (2012)

    Article  Google Scholar 

  4. Cavallo, B., D’Apuzzo, L.: A general unified framework for pairwise comparison matrices in multicriteria methods. Int. J. Intell. Syst. 24(4), 377–398 (2009)

    Article  MATH  Google Scholar 

  5. Cavallo, B., D’Apuzzo, L.: Deriving weights from a pairwise comparison matrix over an alo-group. Soft Comput. 16, 353–366 (2012)

    Article  MATH  Google Scholar 

  6. Leung, L.C., Cao, D.: On consistency and ranking of alternatives in fuzzy AHP. Eur. J. Oper. Res. 124, 102–113 (2000)

    Article  MATH  Google Scholar 

  7. Mahmoudzadeh, M., Bafandeh, A.R.: A new method for consistency test in fuzzy AHP. J. Intell. Fuzzy Syst. 25(2), 457–461 (2013)

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  9. Mikhailov, L.: A fuzzy approach to deriving priorities from interval pairwise comparison judgements. Eur. J. Oper. Res. 159, 687–704 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  10. Ohnishi, S., Dubois, D., et al.: A fuzzy constraint based approach to the AHP. In: Uncertainty and Intelligent Information Systems, pp. 217–228. World Sci., Singapore, 2008 (2008)

    Google Scholar 

  11. Ramik, J.: Isomorphisms between fuzzy pairwise comparison matrices. Fuzzy Optim. Decis. Making 14, 199–209 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  12. Ramik, J.: Pairwise comparison matrix with fuzzy elements on alo-group. Inf. Sci. 297, 236–253 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  13. Ramik, J., Korviny, P.: Inconsistency of pairwise comparison matrix with fuzzy elements based on geometric mean. Fuzzy Sets Syst. 161, 1604–1613 (2010)

    Article  MATH  Google Scholar 

  14. Salo, A.A.: On fuzzy ratio comparison in hierarchical decision models. Fuzzy Sets Syst. 84, 21–32 (1996)

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

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Acknowledgments

This research has been supported by GACR project No. 14-02424S.

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Authors and Affiliations

  1. Faculty of Business Administration in Karviná, Silesian University in Opava, Univerzitní nám. 76, 733 40, Karviná, Czech Republic

    Jaroslav Ramík

Authors
  1. Jaroslav Ramík
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Correspondence to Jaroslav Ramík .

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Editors and Affiliations

  1. Gdynia Maritime University, Gdynia, Poland

    Ireneusz Czarnowski

  2. Artificial Intelligence Department, Universidad Politécnica de Madrid, Madrid, Spain

    Alfonso Mateos Caballero

  3. KES International, Shoreham-by-sea, UK

    Robert J. Howlett

  4. University of Canberra, Canberra, Australia

    Lakhmi C. Jain

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© 2016 Springer International Publishing Switzerland

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Ramík, J. (2016). Ranking Alternatives by Pairwise Comparisons Matrix with Fuzzy Elements on Alo-Group. In: Czarnowski, I., Caballero, A.M., Howlett, R.J., Jain, L.C. (eds) Intelligent Decision Technologies 2016. Smart Innovation, Systems and Technologies, vol 57. Springer, Cham. https://doi.org/10.1007/978-3-319-39627-9_32

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  • DOI: https://doi.org/10.1007/978-3-319-39627-9_32

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-39626-2

  • Online ISBN: 978-3-319-39627-9

  • eBook Packages: EngineeringEngineering (R0)

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