Hybrid Rough Sets and Applications in Uncertain Decision-MakingBy Lirong Jian

Reference: M00002024

Condition: New product

ISBN 9781138372757

Published September 10, 2018 by Auerbach Publications

284 Pages 43 B/W Illustrations

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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
     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

Author(s)

Biography

Lirong Jian received her PhD in management science and engineering from Southeast University, Nanjing, China, in 2004. She then had two years of postdoctoral 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 the International Institute for General Systems Studies, Inc. Among his other professional endeavors, Professor Lin has had the honor of mobilizing scholars from over 80 countries representing more than 50 different scientific disciplines. Over the years, he has served on the editorial boards of 11 professional journals, including Kybernetes: The International Journal of Cybernetics, Systems and Management Science; the Journal of Systems Science and Complexity; the International Journal of General Systems, and Advances in Systems Science and Applications. He is also a coeditor of the book series entitled Systems Evaluation, Prediction and Decision-Making, published by Taylor & Francis (2008).

Some of Lin’s research was funded by the United Nations, the State of Pennsylvania, the National Science Foundation of China, and the German National Research Center for Information Architecture and Software Technology. By the end of 2009, he had published nearly 300 research papers and over 30 monographs, and edited volumes on special topics. His works were published by such prestigious publishers as Springer, Wiley, World Scientific, Kluwer Academic (now part of Springer), Academic Press (now part of Springer), and others. Throughout his career, Lin’s scientific achievements have been recognized by various professional organizations and academic publishers. In 2001, he was inducted into the honorary fellowship of the World Organization of Systems and Cybernetics. Lin’s professional career started in 1984 when his first paper was published. His research interests are mainly in the area of systems research and applications in a wide range of disciplines of traditional science, such as mathematical modeling, foundations of mathematics, data analysis, theory and methods of predictions of disastrous natural events, economics and finance, management science, and philosophy of science.

Reviews

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

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