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.
References
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)
Bourbaki, N.: Algebra II. Springer, Heidelberg-New York-Berlin (1998)
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)
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)
Cavallo, B., D’Apuzzo, L.: Deriving weights from a pairwise comparison matrix over an alo-group. Soft Comput. 16, 353–366 (2012)
Leung, L.C., Cao, D.: On consistency and ranking of alternatives in fuzzy AHP. Eur. J. Oper. Res. 124, 102–113 (2000)
Mahmoudzadeh, M., Bafandeh, A.R.: A new method for consistency test in fuzzy AHP. J. Intell. Fuzzy Syst. 25(2), 457–461 (2013)
Mikhailov, L.: Deriving priorities from fuzzy pairwise comparison judgments. Fuzzy Sets Syst. 134, 365–385 (2003)
Mikhailov, L.: A fuzzy approach to deriving priorities from interval pairwise comparison judgements. Eur. J. Oper. Res. 159, 687–704 (2004)
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)
Ramik, J.: Isomorphisms between fuzzy pairwise comparison matrices. Fuzzy Optim. Decis. Making 14, 199–209 (2015)
Ramik, J.: Pairwise comparison matrix with fuzzy elements on alo-group. Inf. Sci. 297, 236–253 (2015)
Ramik, J., Korviny, P.: Inconsistency of pairwise comparison matrix with fuzzy elements based on geometric mean. Fuzzy Sets Syst. 161, 1604–1613 (2010)
Salo, A.A.: On fuzzy ratio comparison in hierarchical decision models. Fuzzy Sets Syst. 84, 21–32 (1996)
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)
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This research has been supported by GACR project No. 14-02424S.
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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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