Granule 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]  A. Talman,et al.  The Theory of Markets , 1999 .

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

[3]  Jonathan F. Bard,et al.  Practical Bilevel Optimization: Algorithms and Applications (Nonconvex Optimization and Its Applications) , 2006 .

[4]  S. Tsumoto,et al.  Rough Set Theory and Granular Computing , 2003 .

[5]  Qing He,et al.  Rule sets based bilevel decision model , 2006, ACSC.

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

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

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

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

[10]  Zhongzhi Shi,et al.  Tolerance granular space and its applications , 2005, 2005 IEEE International Conference on Granular Computing.

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

[12]  Andrzej Skowron,et al.  Approximation Spaces in Rough Neurocomputing , 2003 .

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

[14]  Witold Pedrycz,et al.  Granular Computing - The Emerging Paradigm , 2007 .

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

[16]  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 .

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

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

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

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

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

[22]  Zhongzhi Shi,et al.  Tolerance Relation Based Granular Space , 2005, RSFDGrC.

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

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

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

[26]  Lech Polkowski,et al.  Rough Sets in Knowledge Discovery 2 , 1998 .

[27]  C. Chen,et al.  Stackelburg solution for two-person games with biased information patterns , 1972 .

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

[29]  XIAOHUA Hu,et al.  LEARNING IN RELATIONAL DATABASES: A ROUGH SET APPROACH , 1995, Comput. Intell..

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

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

[32]  Yiyu Yao,et al.  Granular computing for data mining , 2006, SPIE Defense + Commercial Sensing.

[33]  Jonathan F. Bard,et al.  Practical Bilevel Optimization , 1998 .

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

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

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

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

[38]  Jiawei Han,et al.  Data Mining: Concepts and Techniques , 2000 .