学术报告-George Tintera

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2018-06-20 08:51:00

学术报告

    题      目:Row by Row Determination of Ranking in the Analytical Hierarchy Process

报  告  人:George Tintera 教授  (邀请人:叶颀)

                     Texas A&M University-Corpus Christi


时      间:2018-06-20 10:30--11:30

地      点:学院401

报告人简介:

       George Tintera教授是美国的计算数学专家,现任教与美国Texas A&M大学Corpus Christi分校,并担任其数学与统计系的系主任,Tintera教授在国际发表多篇论文,并获得美国多项科研经费。


摘      要:

    Positive reciprocal matrices (where aji = 1/aij and aij > 0 for each i,j) are at the heart of Saaty’s Analytical Hierarchy Process. When such matrices are consistent, the principal eigenvector, v, determines rankings expressed implicitly in the matrix (aij = vi/vj) . Gass and Rapcsak used singular value decomposition to resolve inconsistencies in positive reciprocal matrices. The “best” ranking expressed implicitly by an inconsistent matrix is the eigenvector of the rank one approximation to that matrix. As an alternative, we consider the rankings determined by each row of an inconsistent matrix. Each row determines a consistent, positive reciprocal matrix, and hence a ranking vector. We show how a combination of those ranking vectors gives the “best” ranking as determined by Gass and Rapcsak without use of the singular value decomposition.