(6) A fuzzy constraint-based approach to the Analytic Hierarchy Process
Shin-ichi Ohnishi, Didier Dubois, Henri Prade, Takahiro Yamanoi
Uncertainty and Intelligent Information Systems, Chapter 16, pp.217-227, 2008-9
There exist many kinds of extensions of AHP 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 preference 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 radio 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. Moreover we show an example of our approach in the last part of the paper.
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