Xingyu Wang (Mathematics)

Title: Reciprocal Matrices, Efficient Vectors, and their Application in Priority Setting Methodology

Department: Mathematics

Description: With lots of choices to make, it can be a difficult for an organization (person, company, government, etc) to rank several alternatives. While pair-wise comparisons are more easily made, if not necessarily accurate. Saaty proposed using pair-wise ratio comparisons arrayed as a reciprocal matrix A (entry a_ji = 1/a_ij). If such matrix satisfies the consistency condition of a_ij a_jk = a_ik, then there exists a distinct natural cardinal ordering determined by the relative values of the entries. However, in situations where human judgement is involved, consistency is not guaranteed, resulting in multiple possible vectors that could be inferred from a reciprocal matrix A. Mathematicians are choosing from among ?efficient? vectors to approximate reciprocal matrices and improve prioritization process, but it is not known yet how to generate all of them. The interests of this research are two-fold. First, using matrix methods, more deeply understand the set of efficient vectors, and second, explore heretofore novel applications, such as foreign exchange rates, other interconnected markets, and connections to social choice.

Hometown: Beijing, China

Advisor: Charles Royal Johnson

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