Fuzzy Weights Representation of AHP for Inner Dependence among Alternatives

The Analytic Hierarchy Process (AHP) proposed by T. L. Saaty has been widely used in decision making. Inner dependence method AHP is used for cases in which criteria or alternatives are not independent enough and using the original AHP or inner dependence AHP may cause results to lose reliability because the comparison matrix is not necessarily sufficiently consistent. In such cases, fuzzy representation for weighting criteria or alternatives using results from sensitivity analysis is useful. We present local weights of normal AHP alternatives via fuzzy sets, and then calculate modified fuzzy weights. We also get overall weights of alternatives based on certain assumptions. Results show the fuzziness of inner dependence AHP if the comparison matrix is not sufficiently consistent and individual alternatives do not have enough independence.