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Table 8
Fuzzy evaluation matrix for the alternatives
C1 C2 C3 C4 C5 C6 C7 C8 C9
A1 (6.33, 8.33, 9.67) (5, 6.67, 8) (5, 7, 8.67) (4.33, 6, 7.33) (5.67, 7.67, 9.33) (6.33, 8, 9.33) (6.33, 8, 9.33) (6.33, 8.33, 9.67) (3.67, 5.67, 7.67)
A2 (5.67, 7.67, 9) (5.67, 7.67, 9) (6, 6.67, 7) (2.33, 3.33, 4.67) (5, 7, 8.33) (5.67, 7.67, 9.33) (3, 4, 5.33) (3, 3.33, 4) (3, 5, 7)
A3 (1.67, 3.67, 5.67) (2.33, 4.33, 6.33) (3.67, 5.67, 7.67) (5, 7, 8.67) (6.33, 8.33, 9.67) (3.67, 5.67, 7.67) (5, 7, 8.67) (4.33, 6.33, 8.33) (6.33, 8.33, 9.67)
A4 (2.33, 4.33, 6.33) (2.33, 4.33, 6.33) (4.33, 6.33, 8) (6.33, 8.33, 9.67) (3, 5, 7) (5.67, 7.67, 9.33) (4.33, 6.33, 8.33) (5, 7, 8.67) (5.67, 7.67, 9.33)
A5 (7.67, 9.33, 10) (5.67, 7.67, 9) (5, 7, 8.67) (7, 9, 10) (8.33, 9.67, 10) (2, 3.67, 5.67) (7, 9, 10) (6.33, 8.33, 9.67) (6.33, 8.33, 9.67)
Table 9
Separation measures of A i from the fuzzy best and fuzzy worst values
A 1 (17.2, 27.19, 46.41) (2.9, 6.66, 11.57)
A 2 (24.34, 37.2, 61.1) (4.78, 7, 14.14)
A 3 (18.09, 31.15, 61.08) (2.98, 8.23, 12.6)
A 4 (17.41, 29.03, 54.42) (2.86, 7.36, 11.35)
A 5 (16.31, 25.95, 45.95) (2.64, 6.66, 12.67)
Table 10
, , and
values
(16.31, 25.95, 45.95)
(24.34, 37.2, 61.1)
(2.64, 6.66, 11.35)
(4.78, 8.23, 14.14)
Table 11
Integrated fuzzy VIKOR–AHP analysis results
Q i Rank order
A 1 (-2.46, 0.05, 3.96) 0.29 2
A 2 (-1.89, 0.61, 5.48) 1.00 5
A 3 (-2.42, 0.73, 5.11) 0.94 4
A 4 (-2.47, 0.36, 4.41) 0.56 3
A 5 (-2.54, 0, 4.19) 0.27 1
Results of the integrated fuzzy VIKOR– AHP analysis results are in Table 11. The ranking of the
alternatives in descending order are A 5 , A 1 , A 4 , A 3 , and A 2 , that is based on the crisp Q i index values.
The best alternative is found to be A 5 . The second best alternative is A 1 .
6. Concluding remarks
In this paper, an integrated fuzzy VIKOR–AHP methodology is developed for the selection of the
best contractor in one of Iran construction industry projects. VIKOR is a multi-criteria decision
making technique which provides a compromise solution, providing a maximum group utility for the
majority and a minimum of an individual regret for the opponent. In fuzzy VIKOR, linguistic
evaluations of the experts can easily be converted to fuzzy numbers which are allowed to be used in
calculations. In this study, weights of the selection criteria are determined based on a fuzzy AHP
approach in order to allow both pairwise comparisons and the utilization of linguistic variables.
Despite the demanding nature of the pairwise comparisons approach, as it is considered to offer
maximum insight and consistency, we choose modifying the existing fuzzy VIKOR methodology
with the weights of the extent analysis.
References
Alarcón, L.F. & Mourgues, C. (2002). Performance modeling for contractor selection. Journal of
Management in Engineering, 18 (2), 52–60 ASCE.