Tel: +86.10.6278.7724   liu@tsinghua.edu.cn    http://orsc.edu.cn/liu

Here are text book, lecture slides, matlab uncertainty toolbox, C++ source files of algorithms related to uncertainty theory. Feel free to download and use them. If you have any questions or comments, please contact me at liu@tsinghua.edu.cn.

Text Book

B. Liu, Uncertainty Theory, 4th edition, http://orsc.edu.cn/liu/ut.pdf.

When the sample size is too small (even no-sample) to estimate a probability distribution, we have to invite some domain experts to evaluate their belief degree that each event will occur. Since human beings usually overweight unlikely events, the belief degree may have much larger variance than the real frequency. Perhaps some people think that the belief degree is subjective probability. However, it is inappropriate because probability theory may lead to counterintuitive results in this case. In order to distinguish from probability, this phenomenon was named "uncertainty". How do we understand uncertainty? How do we model uncertainty? In order to answer those questions, an uncertainty theory was founded in 2007 and then became a branch of mathematics for modeling human uncertainty. This book provides a self-contained, comprehensive and up-to-date presentation of uncertainty theory, uncertain statistics, uncertain programming, uncertain risk analysis, uncertain logic, uncertain inference, uncertain process, uncertain calculus, and uncertain differential equation. This book also shows applications of uncertainty theory to scheduling, logistics, data mining, control, and finance.


Lecture Slides

Download All Lecture Slides (Lecture.zip) (Main.pdf is the main file. Latex source files are included)

First Page
Uncertainty Theory
Uncertain Statistics
Uncertain Programming
Uncertain Risk Analysis
Uncertain Reliability Analysis
Uncertain Set
Uncertain Logic
Uncertain Inference
Uncertain Process
Uncertain Calculus
Uncertain Differential Equation

Matlab Uncertainty Toolbox

Matlab Uncertainty Toolbox is a collection of functions built on Matlab for many methods of uncertainty theory, including arithmetic operations, uncertain programming, risk analysis, uncertain logic, uncertain inference, uncertain control, uncertain differential equation and uncertain finance.

Download Matlab Uncertainty Toolbox (Uncertainty.Toolbox.zip)

boolean_system_calculator.m     expected_value.m     variance.m     entropy.m     distance.m    

uncertain_statistics_1.m     uncertain_statistics_2.m     uncertain_statistics_3.m    

uncertain_programming_1.m     uncertain_programming_2.m    

uncertain_logic_truth_value_1.m     uncertain_logic_truth_value_2.m     uncertain_logic_entailment_1.m     uncertain_logic_entailment_2.m    

C++ Source Files

UTLab.h   (Head File)

Boolean System Calculator
Boolean-System-Calculator.cpp    Boolean-System-Calculator.exe   

Principle of Least Squares
Principle-Least-Squares.cpp

Machine-Scheduling-Problem
Machine-Scheduling-Problem.cpp   

Vehicle Routing Problem
Vehicle-Routing-Problem.cpp   

Project Scheduling Problem
Project-Scheduling-Problem.cpp   

Uncertain Differential Equation
Uncertain-Differential-Equation.cpp

Genetic Algorithms
GA-1.cpp    GA-1.pdf    (Nonlinear Programming)
GA-2.cpp    GA-2.pdf    (Goal Programming)
GA-3.cpp    GA-3.pdf    (Multilevel Programming)