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(8) A Study on the Analytic Hierarchy Process Using a Fuzzy Reciprocal Matrix
¡¡¡¡ Information Processing and Management of Uncertainty in Knowledge-Based Systems
¡¡¡¡ (IPMU 2006),July 2-7,Paris,France,pp.1646-1651,2006-7
Analytic Hierarchy Process (AHP) is one of the most popular method in the field of decision-making today. While 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 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 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 later parts of the paper.
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