?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%2F4111%2F&rft.title=Stochastic+Judgments+in+the+AHP%3A+The+Measurement+of+Rank+Reversal+Probabilities&rft.creator=Stam%2C+A.&rft.creator=Duarte+Silva%2C+A.P.&rft.description=Recently%2C+the+issue+of+rank+reversal+of+alternatives+in+the+Analytic+Hierarchy+Process+(AHP)+has+captured+the+attention+of+a+number+of+researchers.+Most+of+the+research+on+rank+reversal+has+addressed+the+case+where+the+pairwise+comparisons+of+the+alternatives+are+represented+by+single+values%2C+focusing+on+mathematical+properties+inherent+to+the+AHP+methodology+that+can+lead+to+rank+reversal+if+a+new+alternative+is+added+or+an+existing+one+is+deleted.+A+second+situation%2C+completely+unrelated+to+the+mathematical+foundations+of+the+AHP%2C+in+which+rank+reversal+can+occur+is+the+case+where+the+pairwise+judgments+are+stochastic%2C+rather+than+single+values.+%0D%0A%0D%0AIf+the+relative+preference+ratings+are+uncertain%2C+one+has+judgment+intervals%2C+and+as+a+consequence+there+is+a+possibility+that+the+rankings+resulting+from+an+AHP+analysis+are+reversed%2C+i.e.%2C+incorrect.+It+is+important+for+modeler+and+decision+maker+alike+to+be+aware+of+the+likelihood+that+this+situation+of+rank+reversal+will+occur.+In+this+paper%2C+we+introduce+methods+for+assessing+the+relative+preference+of+the+alternatives+in+terms+of+their+rankings%2C+if+the+pairwise+comparisons+of+the+alternatives+are+stochastic.+%0D%0A%0D%0AWe+develop+multivariate+statistical+techniques+to+obtain+point+estimates+and+confidence+intervals+of+the+rank+reversal+probabilities%2C+and+show+how+simulation+experiments+can+be+used+as+an+effective+and+accurate+tool+for+analyzing+the+stability+of+the+preference+rankings+under+uncertainty.+This+information+about+the+extent+to+which+the+ranking+of+the+alternatives+is+sensitive+to+the+stochastic+nature+of+the+pairwise+judgments+should+be+valuable+information+into+the+decision+making+process%2C+much+like+variability+and+confidence+intervals+are+crucial+tools+for+statistical+inference.+Although+the+focus+of+our+analysis+is+on+stochastic+preference+judgments%2C+our+sampling+method+for+estimating+rank+reversal+probabilities+can+be+extended+to+the+case+of+non-stochastic+imprecise+fuzzy+judgments.+%0D%0A%0D%0AWe+provide+simulation+experiments+and+numerical+examples+comparing+our+method+with+that+proposed+previously+by+Saaty+and+Vargas+(1987)+for+imprecise+interval+judgments.&rft.publisher=WP-94-101&rft.date=1994-09&rft.type=Monograph&rft.type=NonPeerReviewed&rft.format=text&rft.language=en&rft.identifier=https%3A%2F%2Fpure.iiasa.ac.at%2Fid%2Feprint%2F4111%2F1%2FWP-94-101.pdf&rft.identifier=++Stam%2C+A.+%3Chttps%3A%2F%2Fpure.iiasa.ac.at%2Fview%2Fiiasa%2F1588.html%3E+%26+Duarte+Silva%2C+A.P.++(1994).++Stochastic+Judgments+in+the+AHP%3A+The+Measurement+of+Rank+Reversal+Probabilities.+++IIASA+Working+Paper.+IIASA%2C+Laxenburg%2C+Austria%3A+WP-94-101+++++