On the analytic hierarchy process and decision support based on fuzzy-linguistic preference structures

The Analytic Hierarchy Process (AHP) has received different fuzzy formulations, where two main lines of research can be identified in literature. The most popular one refers to the Extent Analysis Method, which has been subject of recent criticism, among other things, due to a number of misapplications that it may lead to. The other approach refers to the Logarithmic Least Squares Method (LLSM), which offers a constrained optimization approach for estimating fuzzy weights, but fails to generalize the original AHP proposal. The fact remains that the AHP uses linguistic evaluations as input data, where experts value pairs of alternatives/criteria with words, making it essentially fuzzy under the view that words can be represented by fuzzy sets for their respective computation. Hence, reasoning with fuzzy logic is justified by the analytical framework that it offers to design the meaning of words through membership functions and not assume a direct mapping between words and crisp numbers. In this paper we propose the fuzzy representation of linguistic preferences for the AHP, and examine its generalization by means of the fuzzy-linguistic AHP algorithm.