A kind of fuzzy weights representation for inner dependence AHP

The Analytic Hierarchy Process (AHP) was proposed by Saaty T.L. and has been widely used in decision making. Inner dependence method AHP is one technique for the case in which criteria do not have enough independency. However using original AHP or inner dependence method, the data and results often lose their reliability because the comparison matrix does not always have sufficient consistency. In these cases, fuzzy representation for weighting criteria using results from a sensitivity analysis is useful. In this paper, we first present weights of criteria of normal AHP by means of fuzzy sets, then modified fuzzy weights can be calculated. We can also have overall weights of alternatives by employing some assumptions. The results show how inner dependence AHP has fuzziness when the comparison matrix is not sufficiently consistent and each criterion has not enough independency.