Imprecision of the elements of fuzzy eigenvectors of pairwise comparison matrices in fuzzy AHP

Fuzzy AHP is often used in multi-criteria decision analysis. In this paper we consider an example given by Deng [I] and in particular the method used to approximate the fuzzy principle eigenvector of the fuzzy pairwise comparison matrices. We show Nigel Steele Computational Intelligence Group, School of Mathematical and Information Sciences, Coventry University, Priory Street, Coventry. CV1 5FB U.K. [email protected] 2 Background The Analytic Hierarchy Process (AHP) The analytic hierarchy process (AHP) developed by Saaty [4] is often used in multi-attribute decision analysis where the data is qualitative rather than numeric. Table 1: Values for Saaty's Analytic Hierarchy Prothat the imprecision of the fuzzy numbers cess obtained as outputs is highly correlated to I Numerical I Relative Importance using a different approximation method exhibits a similar relationship. On the basis of these results we question whether the Fuzzy AHP propagates uncertain inputs effectively to uncertain outputs. the value of the kernel of the fuzzy number. We also show that output data obtained