A consistency test for rational weights in multi-criterion decision analysis with fuzzy pairwise comparisons

We present some results and extensions of the use of fuzzy pairwise comparisons in multi-criterion decision analysis. We address the problem encountered in earlier articles by van Laarhoven and Pedrycz (1983) and Boender et al. (1989) in which normalized weights derived from estimates based on ratio scales can exhibit an irrational ordering. We derive conditions for a rational ordering and illustrate that the irrational ordering is the result of relative preferences provided by the decision makers. We provide a test for consistency that will insure a rational ordering of the normalized weights when using the methods of van Laarhoven and Pedrycz, and Boender et al. for normalization. (C) 1997 Elsevier Science B.V.