Alternative Forms of Aggregation in the Analytic Hierarchy Process: Ordered Weighted Averaging Operators

The analytic hierarchy process (AHP) methodology was introduced by Thomas Saaty and has had numerous applications in a wide range of contexts. In a common three-level hierarchy, AHP involves the aggregation of criterion importance weights (or priorities) and the performance scores (or priorities) of alternatives as the sum of the products of weights and scores for each alternative. The multiplicative AHP (MAHP) involves the multiplicative aggregation of performance scores raised to the power of the criterion weights and has been seen by many individuals (notably, Freerk Lootsma and John Barzilai) as an alternative more desirable structure. It is suggested that alternative forms of aggregation of performance scores and criterion weights might be more useful, in particular the ordered weighted averaging (OWA) operator introduced by Ronald Yager. The choice of weights in an OWA operator may be guided by a linguistic quantifier involving the importance weights associated with each criterion. The geometric ordered weighted averaging (GOWA) operator is also considered as a possibility for aggregation in the MAHP. An example is given relating to the location of a Green Bridge Link (for public transport and non-motorized modes of transport) in Brisbane, Queensland, Australia. The four approaches (alternatives) to the identified site of the Green Bridge (Dutton Park) are a Full Busway, Boggo Road, Cornwall Street, and Kent Street.