1st Edition

Hybrid Rough Sets and Applications in Uncertain Decision-Making

By Lirong Jian, Sifeng Liu, Yi Lin Copyright 2011
    284 Pages 43 B/W Illustrations
    by Auerbach Publications

    284 Pages 43 B/W Illustrations
    by Auerbach Publications

    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.

    Introduction
    Background 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 Mining
    Characteristics 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 Analysis
    Hybrid 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 Theory
    Information 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 Method
    Common Algorithms of Attribute Reduct
         Quick Reduct Algorithm
         Heuristic Algorithm of Attribute Reduct
         Genetic Algorithm
    Application Case
         Data Collecting and Variable Selection
         Data Discretization
         Attribute Reduct
         Rule Generation
         Simulation of the Decision Rules

    Hybrid of Rough Set Theory and Probability
    Rough Membership Function
    Variable Precision Rough Set Model
         β-Rough Approximation
         Classification Quality and β-Reduct
         Discussion about β Value
         Construction of Hierarchical Knowledge Granularity Based on VPRS 
         Knowledge Granularity
         Relationship between VPRS and Knowledge Granularity
              Approximation and Knowledge Granularity
              Classification Quality and Granularity Knowledge Granularity 
              Construction of Hierarchical Knowledge Granularity
              Methods of Construction of Hierarchical Knowledge Granularity 
              Algorithm Description
    Methods of Rule Acquisition Based on the Inconsistent Information System in Rough Set 
         Bayes’ Probability
         Consistent Degree, Coverage, and Support
         Probability Rules
         Approach to Obtain Probabilistic Rules Hybrid of Rough Set and Dominance Relation

    Hybrid of Rough Set and Dominance Relation
    Dominance-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 
         β-Rough Approximation Based on Dominance Relations
         Classification Quality and Approximate Reduct
         Preferential Probabilistic Decision Rules
         Algorithm Design
    An 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 Theory
    The Basic Concepts of the Fuzzy Set Theory
         Fuzzy Set and Fuzzy Membership Function
         Operation of Fuzzy Subsets
         Fuzzy Relation and Operation
         Synthesis of Fuzzy Relations
         λ-Cut Set and the Decomposition Proposition
         The Fuzziness of Fuzzy Sets and Measure of Fuzziness
    Rough Fuzzy Set and Fuzzy Rough Set
         Rough Fuzzy Set
         Fuzzy Rough Set
    Variable Precision Rough Fuzzy Sets
         Rough Membership Function Based on λ-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 Design
    Variable 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 System
    The Basic Concepts and Methods of the Grey System Theory
         Grey Number, Whitening of Grey Number, and Grey Degree
              Types 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 Weights
    Establishment of Decision Table Based on Grey Clustering
    The Grade of Grey Degree of Grey Numbers and Grey Membership Function Based on Rough Membership Function
    Grey Rough Approximations
    Reduced Attributes Dominance Analysis Based on Grey Correlation Analysis

    A Hybrid Approach of Variable Precision Rough Set, Fuzzy Set, and Neural Network
    Neural Network

    Introduction
    Background 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 Mining
    Characteristics 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 Analysis
    Hybrid 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 Theory
    Information 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 Method
    Common Algorithms of Attribute Reduct
         Quick Reduct Algorithm
         Heuristic Algorithm of Attribute Reduct
         Genetic Algorithm
    Application Case
         Data Collecting and Variable Selection
         Data Discretization
         Attribute Reduct
         Rule Generation
         Simulation of the Decision Rules

    Hybrid of Rough Set Theory and Probability
    Rough Membership Function
    Variable Precision Rough Set Model
         β-Rough Approximation
         Classification Quality and β-Reduct
         Discussion about β Value
         Construction of Hierarchical Knowledge Granularity Based on VPRS 
         Knowledge Granularity
         Relationship between VPRS and Knowledge Granularity
              Approximation and Knowledge Granularity
              Classification Quality and Granularity Knowledge Granularity 
              Construction of Hierarchical Knowledge Granularity
              Methods of Construction of Hierarchical Knowledge Granularity 
              Algorithm Description
    Methods of Rule Acquisition Based on the Inconsistent Information System in Rough Set 
         Bayes’ Probability
         Consistent Degree, Coverage, and Support
         Probability Rules
         Approach to Obtain Probabilistic Rules Hybrid of Rough Set and Dominance Relation

    Hybrid of Rough Set and Dominance Relation
    Dominance-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 
         β-Rough Approximation Based on Dominance Relations
         Classification Quality and Approximate Reduct
         Preferential Probabilistic Decision Rules
         Algorithm Design
    An 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 Theory
    The Basic Concepts of the Fuzzy Set Theory
         Fuzzy Set and Fuzzy Membership Function
         Operation of Fuzzy Subsets
         Fuzzy Relation and Operation
         Synthesis of Fuzzy Relations
         λ-Cut Set and the Decomposition Proposition
         The Fuzziness of Fuzzy Sets and Measure of Fuzziness
    Rough Fuzzy Set and Fuzzy Rough Set
         Rough Fuzzy Set
         Fuzzy Rough Set
    Variable Precision Rough Fuzzy Sets
         Rough Membership Function Based on λ-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 Design
    Variable 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 System
    The Basic Concepts and Methods of the Grey System Theory
         Grey Number, Whitening of Grey Number, and Grey Degree
              Types 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 Weights
    Establishment of Decision Table Based on Grey Clustering
    The Grade of Grey Degree of Grey Numbers and Grey Membership Function Based on Rough Membership Function
    Grey Rough Approximations
    Reduced Attributes Dominance Analysis Based on Grey Correlation Analysis

    A Hybrid Approach of Variable Precision Rough Set, Fuzzy Set, and Neural Network

    Introduction
    Background 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 Mining
    Characteristics 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 Analysis
    Hybrid 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 Theory
    Information 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 Method
    Common Algorithms of Attribute Reduct
         Quick Reduct Algorithm
         Heuristic Algorithm of Attribute Reduct
         Genetic Algorithm
    Application Case
         Data Collecting and Variable Selection
         Data Discretization
         Attribute Reduct
         Rule Generation
         Simulation of the Decision Rules

    Hybrid of Rough Set Theory and Probability
    Rough Membership Function
    Variable Precision Rough Set Model
         β-Rough Approximation
         Classification Quality and β-Reduct
         Discussion about β Value
         Construction of Hierarchical Knowledge Granularity Based on VPRS 
         Knowledge Granularity
         Relationship between VPRS and Knowledge Granularity
              Approximation and Knowledge Granularity
              Classification Quality and Granularity Knowledge Granularity 
              Construction of Hierarchical Knowledge Granularity
              Methods of Construction of Hierarchical Knowledge Granularity 
              Algorithm Description
    Methods of Rule Acquisition Based on the Inconsistent Information System in Rough Set 
         Bayes’ Probability
         Consistent Degree, Coverage, and Support
         Probability Rules
         Approach to Obtain Probabilistic Rules Hybrid of Rough Set and Dominance Relation

    Hybrid of Rough Set and Dominance Relation
    Dominance-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 
         β-Rough Approximation Based on Dominance Relations
         Classification Quality and Approximate Reduct
         Preferential Probabilistic Decision Rules
         Algorithm Design
    An 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 Theory
    The Basic Concepts of the Fuzzy Set Theory
         Fuzzy Set and Fuzzy Membership Function
         Operation of Fuzzy Subsets
         Fuzzy Relation and Operation
         Synthesis of Fuzzy Relations
         λ-Cut Set and the Decomposition Proposition
         The Fuzziness of Fuzzy Sets and Measure of Fuzziness
    Rough Fuzzy Set and Fuzzy Rough Set
         Rough Fuzzy Set
         Fuzzy Rough Set
    Variable Precision Rough Fuzzy Sets
         Rough Membership Function Based on λ-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 Design
    Variable 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 System
    The Basic Concepts and Methods of the Grey System Theory
         Grey Number, Whitening of Grey Number, and Grey Degree
              Types 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 Weights
    Establishment of Decision Table Based on Grey Clustering
    The Grade of Grey Degree of Grey Numbers and Grey Membership Function Based on Rough Membership Function
    Grey Rough Approximations
    Reduced Attributes Dominance Analysis Based on Grey Correlation Analysis

    A Hybrid Approach of Variable Precision Rough Set, Fuzzy Set, and Neural Network
    Neural Network
         An Overview of the Development of Neural Network
         Structure and Types of Neural Network
         Perceptron
              Perceptron Neuron Model
              Network Structure of Perceptron Neutral Network
              Learning Rules of Perceptron Neutral Network
         Back Propagation Network
              BP Neuron Model
              Network Structure of BP Neutral Network
              BP Algorithm
         Radial Basis Networks
              Radial Basis Neurons Model
              The Network Structure of the RBF
         Realization of the Algorithm of RBF Neural Network
         Probabilistic Neural Network
              PNN Structure
              Realization of PNN Algorithm
    Knowledge Discovery in Databases Based on the Hybrid of VPRS and Neural Network 
         Collection, Selection, and Pretreatment of the Data 
         Construction of Decision Table
         Searching of β-Reduct and Generation of Probability Decision Rules 
         Searching of β-Reduct
              Learning and Simulation of the Neural Network
    System Design Methods of the Hybrid of Variable Precision Rough Fuzzy and Neutral Network 
         Construction of Variable Precision Rough Fuzzy Neutral Network
         Training Algorithm of the Variable Precision Rough Fuzzy Neutral Network

    Application Analysis of Hybrid Rough Set
    A Survey of Transport Scheme Choice
    Transport Scheme Choice Decision Undertaking No Consideration into Preference Information
         Choice Decision Based on Rough Set
         Probability Choice Decision Based on VPRS
         Choice Decision Based on Grey Rough Set
         Probability Choice Decision Based on the Hybrid of VPRS and Probabilistic Neural Network
    Transport Scheme Choice Decision Undertaking Consideration into Preference Information
         Choice Decision Based on the Dominance Rough Set
         Choice Decision Based on the Dominance-Based VPRS

    Bibliography
    Index

    Biography

    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 bo

    The book presents the mathematical theory of rough sets: its interpretation, properties and applications for data and reasoning, especially for decision analysis and forecasting. Also, the relation between rough set theory (RST) and other soft computing theories, such as fuzzy set theory, grey systems, neural networks and probability and statistics, is considered as a tool to manage uncertainty and incomplete information. … This book especially targets postgraduates interested in activities such as economic management, information sciences, social sciences or applied mathematics, and aims to draw their attention to the soft computing approach.
    Maria-Teresa Lamata, in Mathematical Reviews, Issue 2012D