Rule sets based bilevel decision model

Bilevel decision addresses the problem in which two levels of decision makers, each tries to optimize their individual objectives under constraints, act and react in an uncooperative, sequential manner. Such a bilevel optimization structure appears naturally in many aspects of planning, management and policy making. However, bilevel decision making may involve many uncertain factors in a real world problem. Therefore it is hard to determine the objective functions and constraints of the leader and the follower when build a bilevel decision model. To deal with this issue, this study explores the use of rule sets to format a bilevel decision problem by establishing a rule sets based model. After develop a method to construct a rule sets based bilevel model of a real-world problem, an example to illustrate the construction process is presented.

[1]  Art Lew,et al.  Decision table programming and reliability , 1976, ICSE '76.

[2]  Andrzej Skowron,et al.  A Rough Set Framework for Data Mining of Propositional Default Rules , 1996, ISMIS.

[3]  J. Bard,et al.  An algorithm for the discrete bilevel programming problem , 1992 .

[4]  Andrew Kusiak,et al.  Rough set theory: a data mining tool for semiconductor manufacturing , 2001 .

[5]  Roman Slowinski,et al.  Rough Classification of Patients After Highly Selective Vagotomy for Duodenal Ulcer , 1986, Int. J. Man Mach. Stud..

[6]  Udo W. Pooch,et al.  Translation of Decision Tables , 1974, ACM Comput. Surv..

[7]  Jonathan F. Bard,et al.  An explicit solution to the multi-level programming problem , 1982, Comput. Oper. Res..

[8]  Heinrich von Stackelberg,et al.  Stackelberg (Heinrich von) - The Theory of the Market Economy, translated from the German and with an introduction by Alan T. PEACOCK. , 1953 .

[9]  C Shi,et al.  AN EXTENDED KUHNTUCKER APPROACH FOR LINEAR BI-LEVEL PROGRAMMING , 2005 .

[10]  Marcin S. Szczuka,et al.  A New Version of Rough Set Exploration System , 2002, Rough Sets and Current Trends in Computing.

[11]  Xiaohua Hu,et al.  Rule Discovery from Databases with Decision Matrices , 1996, ISMIS.

[12]  Wayne F. Bialas,et al.  On two-level optimization , 1982 .

[13]  G. Anandalingam,et al.  A penalty function approach for solving bi-level linear programs , 1993, J. Glob. Optim..

[14]  Guangquan Zhang,et al.  On the definition of linear bilevel programming solution , 2005, Appl. Math. Comput..

[15]  Nick Cercone,et al.  Using Rough Sets as Tools for Knowledge Discovery , 1995, KDD.

[16]  Yi Zhang,et al.  RIDAS - a rough set based intelligent data analysis system , 2002, Proceedings. International Conference on Machine Learning and Cybernetics.

[17]  Stephan Dempe,et al.  Foundations of Bilevel Programming , 2002 .

[18]  Guoyin Wang,et al.  RRIA: A Rough Set and Rule Tree Based Incremental Knowledge Acquisition Algorithm , 2003, Fundam. Informaticae.

[19]  Jie Lu,et al.  An extended Kth-best approach for linear bilevel programming , 2005, Appl. Math. Comput..

[20]  Wayne F. Bialas,et al.  Two-Level Linear Programming , 1984 .

[21]  Jonathan F. Bard,et al.  Practical Bilevel Optimization: Algorithms and Applications , 1998 .

[22]  Petra Perner,et al.  Data Mining - Concepts and Techniques , 2002, Künstliche Intell..

[23]  Janusz Zalewski,et al.  Rough sets: Theoretical aspects of reasoning about data , 1996 .

[24]  Jie Lu,et al.  An extended Kuhn-Tucker approach for linear bilevel programming , 2005, Appl. Math. Comput..

[25]  Douglas H. Fisher,et al.  A Case Study of Incremental Concept Induction , 1986, AAAI.