?url_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Adc&rft.relation=https%3A%2F%2Fpure.iiasa.ac.at%2Fid%2Feprint%2F4847%2F&rft.title=Artificial+Neural+Network+Representations+for+Hierarchical+Preference+Structures&rft.creator=Stam%2C+A.&rft.creator=Sun%2C+M.&rft.creator=Haines%2C+M.&rft.description=In+this+paper+we+introduce+two+artificial+neural+network+formulations+that+can+be+used+to+assess+the+preference+ratings+from+the+pairwise+comparison+matrices+of+the+Analytic+Hierarchy+Process.+First%2C+we+introduce+a+modified+Hopfield+network+that+can+determine+the+vector+of+preference+ratings+associated+with+a+positive+reciprocal+comparison+matrix.+The+dynamics+of+this+network+are+mathematically+equivalent+to+the+power+method%2C+a+widely+used+numerical+method+for+computing+the+principal+eigenvectors+of+square+matrices.+However%2C+this+Hopfield+network+representation+is+incapable+of+generalizing+the+preference+patterns%2C+and+consequently+is+not+suitable+for+approximating+the+preference+ratings+if+the+pairwise+comparison+judgments+are+imprecise.+Second%2C+we+present+a+feed-forward+neural+network+formulation+that+does+have+the+ability+to+accurately+approximate+the+preference+ratings.+We+use+a+simulation+experiment+to+verify+the+robustness+of+the+feed-forward+neural+network+formulation+with+respect+to+imprecise+pairwise+judgments.+From+the+results+of+these+experiment%2C+we+conclude+that+feed-forward+neural+network+formulation+appears+to+be+a+powerful+tool+for+analyzing+discrete+alternative+multicriteria+decision+problems+with+imprecise+or+fuzzy+ratio-scale+preference+judgments.&rft.publisher=RR-97-012.+Reprinted+from+Computers+%26+Operations+Research%2C+23(12)+%5BDecember+1996%5D.&rft.date=1996&rft.type=Monograph&rft.type=PeerReviewed&rft.format=text&rft.language=en&rft.rights=cc_by&rft.identifier=https%3A%2F%2Fpure.iiasa.ac.at%2Fid%2Feprint%2F4847%2F1%2FRR-97-12.pdf&rft.identifier=++Stam%2C+A.+%3Chttps%3A%2F%2Fpure.iiasa.ac.at%2Fview%2Fiiasa%2F1588.html%3E%2C+Sun%2C+M.%2C+%26+Haines%2C+M.+%3Chttps%3A%2F%2Fpure.iiasa.ac.at%2Fview%2Fiiasa%2F1305.html%3E++(1996).++Artificial+Neural+Network+Representations+for+Hierarchical+Preference+Structures.+++IIASA+Research+Report+(Reprint).+IIASA%2C+Laxenburg%2C+Austria%3A+RR-97-012.+Reprinted+from+Computers+%26+Operations+Research%2C+23(12)+%5BDecember+1996%5D.+++++