Hybrid Rough Sets and Applications in Uncertain Decision-Making

As a powerful approach to data reasoning, rough set theory has proven to be invaluable in knowledge acquisition, decision analysis and forecasting, and knowledge discovery. With the ability to enhance the advantages of other soft technology theories, hybrid rough set theory is quickly emerging as a method of choice for decision making under uncertain conditions. Keeping the complicated mathematics to a minimum, Hybrid Rough Sets and Applications in Uncertain Decision-Making provides a systematic introduction to the methods and application of the hybridization for rough set theory with other related soft technology theories, including probability, grey systems, fuzzy sets, and artificial neural networks. It also: Addresses the variety of uncertainties that can arise in the practical application of knowledge representation systems Unveils a novel hybrid model of probability and rough sets Introduces grey variable precision rough set models Analyzes the advantages and disadvantages of various practical applications The authors examine the scope of application of the rough set theory and discuss how the combination of variable precision rough sets and dominance relations can produce probabilistic preference rules out of preference attribute decision tables of preference actions. Complete with numerous cases that illustrate the specific application of hybrid methods, the text adopts the latest achievements in the theory, method, and application of rough sets.

IntroductionBackground and Significance of Soft Computing Technology Analytical Method of Data Mining Automatic Prediction of Trends and Behavior Association Analysis Cluster Analysis Concept Description Deviation Detection Knowledge Discovered by Data MiningCharacteristics of Rough Set Theory and Current Status of Rough Set Theory Research Characteristics of the Rough Set Theory Current Status of Rough Set Theory Research Analysis with Decision-Making Non-Decision-Making AnalysisHybrid of Rough Set Theory and Other Soft Technologies Hybrid of Rough Sets and Probability Statistics Hybrid of Rough Sets and Dominance Relation Hybrid of Rough Sets and Fuzzy Sets Hybrid of Rough Set and Grey System Theory Hybrid of Rough Sets and Neural Networks Rough Set TheoryInformation Systems and Classification Information Systems and Indiscernibility Relation Set and Approximations of Set Attributes Dependence and Approximation Accuracy Quality of Approximation and Reduct Calculation of the Reduct and Core of Information System Based on Discernable Matrix Decision Table and Rule Acquisition The Attribute Dependence, Attribute Reduct, and Core Decision Rules Use the Discernibility Matrix to Work Out Reducts, Core, and Decision Rules of Decision Table Data Discretization Expert Discrete Method Equal Width Interval Method and Equal Frequency Interval Method The Most Subdivision Entropy Method Chimerge MethodCommon Algorithms of Attribute Reduct Quick Reduct Algorithm Heuristic Algorithm of Attribute Reduct Genetic AlgorithmApplication Case Data Collecting and Variable Selection Data Discretization Attribute Reduct Rule Generation Simulation of the Decision Rules Hybrid of Rough Set Theory and ProbabilityRough Membership FunctionVariable Precision Rough Set Model ß-Rough Approximation Classification Quality and ß-Reduct Discussion about ß Value Construction of Hierarchical Knowledge Granularity Based on VPRS Knowledge Granularity Relationship between VPRS and Knowledge Granularity Approximation and Knowledge GranularityClassification Quality and Granularity Knowledge Granularity Construction of Hierarchical Knowledge Granularity Methods of Construction of Hierarchical Knowledge Granularity Algorithm DescriptionMethods of Rule Acquisition Based on the Inconsistent Information System in Rough Set Bayes’ Probability Consistent Degree, Coverage, and SupportProbability RulesApproach to Obtain Probabilistic Rules Hybrid of Rough Set and Dominance Relation Hybrid of Rough Set and Dominance RelationDominance-Based Rough Set The Classification of the Decision Tables with Preference Attribute Dominating Sets and Dominated Sets Rough Approximation by Means of Dominance Relations Classification Quality and Reduct Preferential Decision Rules Dominance-Based Variable Precision Rough Set Inconsistency and Indiscernibility Based on Dominance Relation ß-Rough Approximation Based on Dominance Relations Classification Quality and Approximate Reduct Preferential Probabilistic Decision Rules Algorithm DesignAn Application Case Post Evaluation of Construction Projects Based on Dominance-Based Rough Set Construction of Preferential Evaluation Decision Table Search of Reduct and Establishment of Preferential Rules Performance Evaluation of Discipline Construction in Teaching-Research Universities Based on Dominance-Based Rough Set The Basic Principles of the Construction of Evaluation Index System The Establishment of Index System and Determination of Weight and Equivalent Data Collection and Pretreatment Data Discretization Search of Reducts and Generation of Preferential Rules Analysis of Evaluation Results Hybrid of Rough Set Theory and Fuzzy Set TheoryThe Basic Concepts of the Fuzzy Set Theory Fuzzy Set and Fuzzy Membership Function Operation of Fuzzy SubsetsFuzzy Relation and Operation Synthesis of Fuzzy Relations?-Cut Set and the Decomposition Proposition The Fuzziness of Fuzzy Sets and Measure of FuzzinessRough Fuzzy Set and Fuzzy Rough Set Rough Fuzzy Set Fuzzy Rough SetVariable Precision Rough Fuzzy Sets Rough Membership Function Based on ?-Cut Set The Rough Approximation of Variable Precision Rough Fuzzy Set The Approximate Quality and Approximate Reduct of variable Precision The Probabilistic Decision Rules Acquisition of Rough Fuzzy Decision Table Algorithm DesignVariable Precision Fuzzy Rough Set Fuzzy Equivalence Relation Precision Fuzzy Rough Model Acquisition of Probabilistic Decision Rules in Fuzzy Rough Decision Table Measure Methods of the Fuzzy Roughness for Output Classification Distance Measurement Entropy Measurement Hybrid of Rough Set and Grey SystemThe Basic Concepts and Methods of the Grey System Theory Grey Number, Whitening of Grey Number, and Grey DegreeTypes of Grey Numbers Whitenization of Grey Numbers and Grey Degree Grey Sequence Generation GM(1, 1) Model Grey Correlation Analysis Grey Correlation Order Grey Clustering Evaluation Clusters of Grey Correlation Cluster with Variable Weights Grey Cluster with Fixed WeightsEstablishment of Decision Table Based on Grey ClusteringThe Grade of Grey Degree of Grey Numbers and Grey Membership Function Based on Rough Membership Function Grey Rough ApproximationsReduced Attributes Dominance Analysis Based on Grey Correlation AnalysisA Hybrid Approach of Variable Precision Rough Set, Fuzzy Set, and Neural NetworkNeural Network IntroductionBackground and Significance of Soft Computing Technology Analytical Method of Data Mining Automatic Prediction of Trends and Behavior Association Analysis Cluster Analysis Concept Description Deviation Detection Knowledge Discovered by Data MiningCharacteristics of Rough Set Theory and Current Status of Rough Set Theory Research Characteristics of the Rough Set Theory Current Status of Rough Set Theory Research Analysis with Decision-Making Non-Decision-Making AnalysisHybrid of Rough Set Theory and Other Soft Technologies Hybrid of Rough Sets and Probability Statistics Hybrid of Rough Sets and Dominance Relation Hybrid of Rough Sets and Fuzzy Sets Hybrid of Rough Set and Grey System Theory Hybrid of Rough Sets and Neural Networks Rough Set TheoryInformation Systems and Classification Information Systems and Indiscernibility Relation Set and Approximations of Set Attributes Dependence and Approximation Accuracy Quality of Approximation and Reduct Calculation of the Reduct and Core of Information System Based on Discernable Matrix Decision Table and Rule Acquisition The Attribute Dependence, Attribute Reduct, and Core Decision Rules Use the Discernibility Matrix to Work Out Reducts, Core, and Decision Rules of Decision Table Data Discretization Expert Discrete Method Equal Width Interval Method and Equal Frequency Interval Method The Most Subdivision Entropy Method Chimerge MethodCommon Algorithms of Attribute Reduct Quick Reduct Algorithm Heuristic Algorithm of Attribute Reduct Genetic AlgorithmApplication Case Data Collecting and Variable Selection Data Discretization Attribute Reduct Rule Generation Simulation of the Decision Rules Hybrid of Rough Set Theory and ProbabilityRough Membership FunctionVariable Precision Rough Set Model ß-Rough Approximation Classification Quality and ß-Reduct Discussion about ß Value Construction of Hierarchical Knowledge Granularity Based on VPRS Knowledge Granularity Relationship between VPRS and Knowledge Granularity Approximation and Knowledge GranularityClassification Quality and Granularity Knowledge Granularity Construction of Hierarchical Knowledge Granularity Methods of Construction of Hierarchical Knowledge Granularity Algorithm DescriptionMethods of Rule Acquisition Based on the Inconsistent Information System in Rough Set Bayes’ Probability Consistent Degree, Coverage, and SupportProbability RulesApproach to Obtain Probabilistic Rules Hybrid of Rough Set and Dominance Relation Hybrid of Rough Set and Dominance RelationDominance-Based Rough Set The Classification of the Decision Tables with Preference Attribute Dominating Sets and Dominated Set

Lirong Jian received her PhD in management science and engineering from Southeast University, Nanjing, China, in 2004. She then had two years ofpostdoctoral experience specializing in management science and engineering at Nanjing University of Aeronautics and Astronautics, China. At present, she is serving as a professor at the College of Economics and Management of Nanjing University of Aeronautics and Astronautics; she is also working as a guide for doctoral students in management science and systems engineering. Dr. Jian is principally engaged in forecasting and decision-making methods, soft computing, and project management and system modeling. She has also directed and/or participated in nearly 20 projects at the national, provincial, and ministerial levels, for which she received four provincial awards in scientific research and applications. Over the years, she has published over 40 research papers and 6 books. Sifeng Liu received his bachelor’s degree in mathematics from Henan University, Kaifeng, China in 1981, and his MS in economics and his PhD in systems engineering from Huazhong University of Science and Technology, Wuhan, China, in 1986 and 1998, respectively. He has been to Slippery Rock University, Pennsylvania, and to Sydney University, Australia, as a visiting professor. At present, Professor Liu is the director of the Institute for Grey Systems Studies and the dean of the College of Economics and Management of Nanjing University of Aeronautics and Astronautics. He is also a distinguished professor and guide for doctoral students in management science and systems engineering. Dr. Liu’s main research activities are in grey systems theory and in regional technical innovation management. He has directed more than 50 projects at the national, provincial, and ministerial levels, has participated in international collaboration projects, and has published over 200 research papers and 16 books. Over the years, he has received 18 provincial and national awards for his outstanding achievements in scientific research and applications. In 2002, one of his papers was recognized by the World Organization of Systems and Cybernetics as one of the best papers of its 12th International Congress. Dr. Liu is a member of the evaluation committee of the Natural Science Foundation of China (NSFC) and a member of the standing committee for teaching guide in management science and engineering of the Ministry of Education, China. He also serves as an expert on soft science at the Ministry of Science and Technology, China. Professor Liu currently serves as the chair of the technical committee of the IEEE SMC on Grey Systems; the president of the Grey Systems Society of China (GSSC); a vice president of the Chinese Society for Optimization, Overall Planning and Economic Mathematics (CSOOPEM); a cochair of the Beijing Chapter and the Nanjing Chapter of IEEE SMC; a vice president of the Econometrics and Management Science Society of Jiangsu Province (EMSSJS); a vice president of the Systems Engineering Society of Jiangsu Province (SESJS); and a member of the Nanjing Decision Consultancy Committee. He serves as the editor in chief of Grey Systems: Theory and Application, and as a member of the editorial boards of over 10 professional journals, including The Journal of Grey System (United Kingdom); Scientific Inquiry (United States); The Journal of Grey System (Taiwan, China); Chinese Journal of Management Science; Systems Theory and Applications; Systems Science and Comprehensive Studies in Agriculture; and the Journal of Nanjing University of Aeronautics and Astronautics. Dr. Liu has won several accolades, such as the National Excellent Teacher in 1995, Excellent Expert of Henan Province in 1998, National Expert with Prominent Contribution in 1998, Expert Enjoying Government’s Special Allowance in 2000, xcellent Science and Technology Staff in Jiangsu Province in 2002, National Advanced Individual for Returnee and Achievement Award for Returnee in 2003, and Outstanding Managerial Personnel of China in 2005. Yi Lin holds all his educational degrees (BS, MS, and PhD) in pure mathematics from Northwestern University, Xi’an, China and Auburn University, Alabama, and has had one year of postdoctoral experience in statistics at Carnegie Mellon University, Pittsburgh, Pennsylvania. Currently, he serves as a guest or specially appointed professor in economics, finance, systems science, and mathematics at several major universities in China, including Huazhong University of Science and Technology, Changsha National University of Defence Technology, and Nanjing University of Aeronautics and Astronautics, and as a professor of mathematics at the Pennsylvania State System of Higher Education (Slippery Rock campus). Since 1993, he has been serving as the president of theInternational Institute for General Systems Studies, Inc. Among his other professional endeavors, Professor Lin has had the honor of mobilizing scholars from over 8