In performing pair-wise comparisons through the AHP technique, T.L. Saaty has introduced the fundamental scale of absolute numbers ranging from 1 to 9 that was claimed to be accurate through various experiments conducted. However, many researchers, have opted to use fuzzy numbers that were claimed to be more accurate since they cater for the fuzziness in one's judgments. May I have some comments from those who are familiar with the AHP on the strengths and weaknesses of both the fundamental scale of absolute numbers and the fuzzy numbers. Thank you.
Hello,
for a discussion of different scale types in AHP see Ishizaka & Labib (2011): "Review of the main developments in the Analytic Hierarchy Process", Expert Systems with Applications, 38(11), pp. 14336-14345.
Hi aminuddin, the main purpose using fuzzy number is to handle any uncertainties that may occur during the collection of expert's judgement. As we know, experts are human, they usually comfortable using linguistic term in expressing any judgement. It is difficult for us to map a precise real number to the associated linguistic term. So, the solution is by using fuzzy number where the mapping of linguistic term to numeric is considered as not precise number or just approximation since different experts may have different judgement for a same linguistic term. Hope this will help you. Good luck!
Dear all, Saaty is the strongest detractor of fuzzyfying judgments (see attachement). The fuzzy extension of AHP have their own problems but more important is that one of my students get no differences when using classic AHP Chang Extent Analysis Fuzzy Extension of AHP in order to select the best option in a sample of literature reported papers, remaining differences only in ranking all the set of alternatives.
I forgot to attach the Saaty opinion in my last post. Please apologize me
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