ABSTRACT A DEA-BASED APPROACH TO RANKING MULTI-CRITERIA ALTERNATIVES Tuncer, Ceren M.Sc., Department of Industrial Engineering Supervisor: Prof. Dr. Murat K&ouml / ksalan August 2006, 88 pages This thesis addresses the problem of ranking multi-criteria alternatives. A Data Envelopment Analysis (DEA)-based approach, the Method of the Area of the Efficiency Score Graph (AES) is proposed. Rather than assessing the alternatives with respect to the fixed original alternative set as done in the existing DEA-based ranking methods, AES considers the change in the efficiency scores of the alternatives while reducing the size of the alternative set. Producing a final score for each alternative that accounts for the progress of its efficiency score, AES favors alternatives that manage to improve quickly and maintain high levels of efficiency. The preferences of the Decision Maker (DM) are incorporated into the analysis in the form of weight restrictions. The utilization of the AES scores of the alternatives in an incremental clustering algorithm is also proposed. The AES Method is applied to rank MBA programs worldwide, sorting of the programs is also performed using their AES scores. Results are compared to another DEA-based ranking method. Keywords: Ranking, data envelopment analysis, weight restrictions.

A term weighting scheme measures the importance of a term in a collection. A document ranking model uses these term weights to find the rank or score of a document in a collection. We present a series of cluster-based term weighting and document ranking models based on the TF-IDF and Okapi BM25 models. These term weighting and document ranking models update the inter-cluster and intra-cluster frequency components based on the generated clusters. These inter-cluster and intra-cluster frequency components are used for weighting the importance of a term in addition to the term and document frequency components. In this thesis, we will show how these models outperform the TF-IDF and Okapi BM25 models in document clustering and ranking.

Empirical Bayes methods have been around for a long time and have a wide range of applications. These methods provide a way in which historical data can be aggregated to provide estimates of the posterior mean. This thesis revisits some of the empirical Bayesian methods and develops new applications. We first look at a linear empirical Bayes estimator and apply it on ranking and symbolic data. Next, we consider Tweedie’s formula and show how it can be applied to analyze a microarray dataset. The application of the formula is simplified with the Pearson system of distributions. Saddlepoint approximations enable us to generalize several results in this direction. The results show that the proposed methods perform well in applications to real data sets.