Learning lexicographic orders

The purpose of this paper is to learn the order of criteria of lexicographic decision under various reasonable assumptions. We give a sample evaluation and an oracle based algorithm. In the worst case analysis we are dealing with the adversarial models. We show that if the distances of the samples are less than 4, then it is not learnable, but 4-distance samples are polynomial learnable.

[1]  Allan Borodin,et al.  Adversarial queueing theory , 1996, STOC '96.

[2]  Gerhard J. Woeginger,et al.  Competitive Odds and Ends , 1996, Online Algorithms.

[3]  R. Słowiński,et al.  Molp with an interactive assessment of a piecewise linear utility function , 1987 .

[4]  Allan Borodin,et al.  Online computation and competitive analysis , 1998 .

[5]  Theodor J. Stewart,et al.  Multiple Criteria Decision Analysis , 2001 .

[6]  Richard W. Hamming,et al.  Error detecting and error correcting codes , 1950 .

[7]  Yannis Siskos,et al.  Preference disaggregation: 20 years of MCDA experience , 2001, Eur. J. Oper. Res..

[8]  David L. Olson,et al.  Verbal Decision Analysis , 2005 .

[9]  J. Siskos.  Assessing a set of additive utility functions for multicriteria decision-making , 1982 .

[10]  M. Shakun,et al.  Decision support systems for semi-structured buying decisions , 1984 .

[11]  G. Dantzig,et al.  Notes on Linear Programming: Part 1. The Generalized Simplex Method for Minimizing a Linear Form under Linear Inequality Restraints , 1954 .

[12]  Scott A. Smolka,et al.  Interactive Computation: The New Paradigm , 2006 .

[13]  Peter C. Fishburn,et al.  LEXICOGRAPHIC ORDERS, UTILITIES AND DECISION RULES: A SURVEY , 1974 .

[14]  Eric Jacquet-Lagrèze,et al.  Interactive Assessment of Preferences Using Holistic Judgments the Prefcalc System , 1990 .

[15]  Allan Borodin,et al.  Adversarial queuing theory , 2001, JACM.

[16]  Donald E. Knuth,et al.  Sorting and Searching , 1973 .

[17]  John N. Tsitsiklis,et al.  Parallel and distributed computation , 1989 .

[18]  Eric Jacquet-Lagrèze,et al.  An Application of the UTA Discriminant Model for the Evaluation of R & D Projects , 1995 .

[19]  Eric Jacquet-Lagrèze,et al.  Binary preference indices: A new look on multicriteria aggregation procedures , 1982 .

[20]  Donald E. Knuth,et al.  The Art of Computer Programming: Volume 3: Sorting and Searching , 1998 .

[21]  Panos M. Pardalos,et al.  Advances in multicriteria analysis , 1995 .

[22]  Donald Ervin Knuth,et al.  The Art of Computer Programming , 1968 .