Credibility Theory Baoding Liu Uncertainty Theory Laboratory Department of Mathematical Sciences Tsinghua University It is a new branch of mathematics that studies the behavior of fuzzy phenomena.

Uncertainty Theory & Uncertain Programming U T L A B Baoding Liu Tsinghua University Fashion of Mathematics 2300 Years Ago: Euclid: “Elements”, First Axiomatic System 1899: Hilbert: Independence, Consistency, Completeness 1931: K. Godel: Incompleteness Theorem 1933: Kolmogoroff: Probability Theory 2004: B. Liu: Credibility Theory

Uncertainty Theory & Uncertain Programming U T L A B Baoding Liu Tsinghua University Why I do not possibility measure?

Uncertainty Theory & Uncertain Programming U T L A B Baoding Liu Tsinghua University Five Axioms

Uncertainty Theory & Uncertain Programming U T L A B Baoding Liu Tsinghua University Credibility Subadditivity Theorem

Uncertainty Theory & Uncertain Programming U T L A B Baoding Liu Tsinghua University Credibility Semicontinuity Laws

Uncertainty Theory & Uncertain Programming U T L A B Baoding Liu Tsinghua University Credibility Extension Theorem

Uncertainty Theory & Uncertain Programming U T L A B Baoding Liu Tsinghua University Fuzzy Variable

Uncertainty Theory & Uncertain Programming U T L A B Baoding Liu Tsinghua University Credibility Measure by Membership Function Liu and Liu (IEEE TFS, 2002)

Uncertainty Theory & Uncertain Programming U T L A B Baoding Liu Tsinghua University Independent Fuzzy Variables

Uncertainty Theory & Uncertain Programming U T L A B Baoding Liu Tsinghua University Theorem: Extension Principle of Zadeh

Uncertainty Theory & Uncertain Programming U T L A B Baoding Liu Tsinghua University Expected Value

Uncertainty Theory & Uncertain Programming U T L A B Baoding Liu Tsinghua University Why the Definition Reasonable?

Uncertainty Theory & Uncertain Programming U T L A B Baoding Liu Tsinghua University Credibility Distribution

Uncertainty Theory & Uncertain Programming U T L A B Baoding Liu Tsinghua University A Sufficient and Necessary Condition

Uncertainty Theory & Uncertain Programming U T L A B Baoding Liu Tsinghua University Entropy (Li and Liu, 2005)

Uncertainty Theory & Uncertain Programming U T L A B Baoding Liu Tsinghua University

Uncertainty Theory & Uncertain Programming U T L A B Baoding Liu Tsinghua University Essential of Uncertainty Theory

Uncertainty Theory & Uncertain Programming U T L A B Baoding Liu Tsinghua University What Mathematics Made?

Uncertainty Theory & Uncertain Programming U T L A B Baoding Liu Tsinghua University Fuzzy Programming

Uncertainty Theory & Uncertain Programming U T L A B Baoding Liu Tsinghua University The Simplest The Most Fundamental Problem

Uncertainty Theory & Uncertain Programming U T L A B Baoding Liu Tsinghua University Expected Value Criterion

Uncertainty Theory & Uncertain Programming U T L A B Baoding Liu Tsinghua University Liu and Liu (IEEE TFS, 2002) Find the decision with maximum expected return subject to some expected constraints. Fuzzy Expected Value Model

Uncertainty Theory & Uncertain Programming U T L A B Baoding Liu Tsinghua University Optimistic Value Criterion

Uncertainty Theory & Uncertain Programming U T L A B Baoding Liu Tsinghua University (Maximax) Chance-Constrained Programming Liu and Iwamura (FSS, 1998) Maximize the optimistic value subject to chance constraints.

Uncertainty Theory & Uncertain Programming U T L A B Baoding Liu Tsinghua University Pessimistic Value Criterion

Uncertainty Theory & Uncertain Programming U T L A B Baoding Liu Tsinghua University (Minimax) Chance-Constrained Programming Liu (IS, 1998) Maximize the pessimistic value subject to chance constraints.

Uncertainty Theory & Uncertain Programming U T L A B Baoding Liu Tsinghua University Credibility Criterion

Uncertainty Theory & Uncertain Programming U T L A B Baoding Liu Tsinghua University Fuzzy Dependent-Chance Programming Liu (IEEE TFS, 1999) Find the decision with maximum chance to meet the event in an uncertain environment.

Uncertainty Theory & Uncertain Programming U T L A B Baoding Liu Tsinghua University Classify Uncertain Programming via Graph Information Philosophy Single-Objective P MOP GP DP MLP Structure EVMCCPDCP Random Fuzzy Fuzzy random Fuzzy Stochastic

Uncertainty Theory & Uncertain Programming U T L A B Baoding Liu Tsinghua University Last Words [1] Liu B., Foundation of Uncertainty Theory. [2] Liu B., Introduction to Uncertain Programming. If you want an electronic copy of my book, or source files of hybrid intelligent algorithms, please download them from