The Additive and the Multiplicative AHP

  • Freerk A. Lootsma
Part of the Applied Optimization book series (APOP, volume 8)


The Analytic Hierarchy Process (AHP) of Saaty (1980) is a widely used method for MCDA, presumably because it elicitates preference information from the decision makers in a manner which they find easy to understand. The basic step is the pairwise comparison of two so-called stimuli, two alternatives under a given criterion, for instance, or two criteria. The decision maker is requested to state whether he/she is indifferent between the two stimuli or whether he/she has a weak, strict, strong, or very strong preference for one of them. The original AHP has been criticized in the literature because the algorithmic steps do not properly take into account that the method is based upon ratio information. The shortcomings can easily be avoided in the Additive and the Multiplicative AHP to be discussed in the present chapter. The Additive AHP is the SMART procedure with pairwise comparisons on the basis of difference information. The Multiplicative AHP with pairwise comparisons on the basis of ratio information is a variant of the original AHP. There is a logarithmic relationship between the Additive AHP (SMART) and the Multiplicative AHP. Both versions can easily be fuzzified. The reasons why we deviate from the original AHP will be explained at the end of this chapter.


Fuzzy Logic Analytic Hierarchy Process Criterion Weight Final Grade Indifference Curve 
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Copyright information

© Springer Science+Business Media Dordrecht 1997

Authors and Affiliations

  • Freerk A. Lootsma
    • 1
  1. 1.Delft University of TechnologyThe Netherlands

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