Hybrid Rough Sets and Applications in Uncertain Decision-Making: 1st Edition (Paperback) book cover

Hybrid Rough Sets and Applications in Uncertain Decision-Making

1st Edition

By Lirong Jian, Sifeng Liu, Yi Lin

Auerbach Publications

284 pages | 43 B/W Illus.

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Description

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.

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

Table of Contents

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

About the Authors

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.

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Systems Evaluation, Prediction, and Decision-Making

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Subject Categories

BISAC Subject Codes/Headings:
BUS049000
BUSINESS & ECONOMICS / Operations Research
MAT003000
MATHEMATICS / Applied
TEC009000
TECHNOLOGY & ENGINEERING / Engineering (General)