Mathematical Sciences: Consensus & Mathematical Programming in Hierarchical Classification

数学科学：共识

• 批准号: 9012738
• 负责人: Stephen Boyce
• 金额: $ 6.59万
• 依托单位: Berea College
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1990
• 资助国家: 美国
• 起止时间: 1990-09-15 至 1993-02-28
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9012738&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Consensus; Programming; Hierarchical

The mathematical programming and consensus questions to be considered have interested the two principal investigators, during their previous research efforts. Since hierarchical classification can be viewed as a problem in mathematical programming, the possibility of linearizing in such a way as to admit use of Karamarkar's algorithm will be investigated. The consensus questions to be considered arise when one is confronted with several classifications for the same collection of objects and needs to determine the agreement among them. Much of the research which will be undertaken involves Stinebrickner's s- consensus method which simultaneously produces a consensus classification and an index measuring the degree of agreement. A revised s-consensus method has been shown to satisfy three minimal and reasonable axioms which describe consensus behavior. Efforts will focus on the discovery of new methods which produce a consensus classification and index simultaneously and the discovery of new axioms which consensus methods may satisfy. Undergraduate students will be trained and collaborate in this project.//

数学规划和共识问题 引起了两位主要研究者的兴趣， 在他们之前的研究工作中。 由于等级制度 分类可以被看作是数学问题 编程，以这种方式线性化的可能性， 承认使用Karamarkar的算法将被调查。 的 当一个人面临 对同一对象集合有几种分类 并需要确定它们之间的一致性。 大部分 将进行的研究涉及Stinebrickner的- 同时产生共识的共识方法 分类和衡量一致程度的指数。 一 修正的S-一致性方法已被证明满足三个 最小的和合理的公理描述共识行为。 努力将集中在发现新的方法， 一个共识分类和索引同时和 发现共识方法可能满足的新公理。 本科生将在这方面接受培训和合作 project.//