In practical application of AHP, non-deterministic factors are frequently encountered. This paper employs uncertainty theory to deal with non-deterministic factors in problems of ranking alternatives. The concepts of uncertainty comparison matrix and uncertainty weights are proposed in this paper. It also gives the uncertain variable method to calculate uncertainty weights from uncertainty comparison matrices, which can be either consistent or inconsistent. The proposed uncertain variable method (UVM) is also applicable to interval comparison matrices and fuzzy comparison ma-trices when they are transformed into uncertainty comparison matrices using linear uncertainty distribution or zigzag uncertainty distribution. The proposed approach is computationally efficient as it consists of solving only inverse uncertainty distribution. At the end of this paper, five numerical examples are given to illustrate the method.
J. Barzilai and F. A. Lootsma, “Power Relation and Group Aggregation in the Multiplicative AHP and SMART,” Journal of Multi-Criteria Decision Analysis, Vol. 6, No. 3, 1997, pp. 155-165.
C. G. E. Bonder, J. G. de Graan and F. A. Lootsma, “Multicretia Decision Analysis with Fuzzy Pairwise Comparisons,” Fuzzy Sets and Systems, Vol. 29, No. 2, 1989, pp. 133-143. doi:10.1016/0165-0114(89)90187-5
T. L. Saaty and L. G. Vargas, “Uncertainty and Rank Order in the Analytic Hierarchy Process,” European Journal of Operational Research, Vol. 32, No. 1, 1987, pp. 107-117. doi:10.1016/0377-2217(87)90275-X
Y.-M. Wang, J.-B. Yang and D.-L. Xu, “A Two-Stage Logarithmic Goal Programming Method for Generating Weights from Interval Comparison Matrices,” Fuzzy Sets and Systems Vol. 152, No. 3, 2005, pp. 475-498.
Y.-M. Wang, J.-B. Yang and D.-L. Xu, “Interval Weight Generation Approaches Based on Consistency Test and Interval Comparison Matrices,” Applied Mathematics and Computation, Vol. 167, No. 1, 2005, pp. 252-273.
H. Ishibuchi and H. Tanaka, “Multiobjective Programming in Optimization of the Interval Objective Function,” European Journal of Operational Research, Vol. 48, No. 2, 1990, pp. 219-225.