(7)An Approach to Analytic Hierarchy Process by use of Fuzzy Reciprocal
Matrix
¡¡¡¡IPMU 2004 (Information Processing and Management of Uncertainty in Knowledge-Based
Systems 2004) Proceedings Vol.1,pp.303-308, 2004-7
Different types of fuzzy extensions to the Analytic Hierarchy Process (AHP)
have been proposed, using fuzzy measures or fuzzy sets. One of the most
natural uses of fuzzy sets is to employ a reciprocal matrix with fuzzy-valued
entries. Indeed, using classical AHP, there is often not enough consistency
among the data due to strong conditions bearing on the reciprocal data
matrices. Fuzzy reciprocal matrices give us flexible specifications of
pairwise preference. This paper presents an approach to using a fuzzy reciprocal
matrix in AHP, as a way of specifying fuzzy restrictions on the possible
values of the ratio judgments. Then, it can be computed to what extent
there exists a consistent standard AHP matrix which is compatible with
these restrictions. An optimal consistency index and optimal weights are
derived using a fuzzy constraint satisfaction approach.