Fall 2015.  Types of Uncertainty 1. Randomness : Probability Knowledge about the relative frequency of each event in some domain Lack of knowledge which.

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Presentation transcript:

Fall 2015

 Types of Uncertainty 1. Randomness : Probability Knowledge about the relative frequency of each event in some domain Lack of knowledge which event will occur in next time 2. Incompleteness : Imputation by EM Lack of knowledge or insufficient data 3. Ambiguity : Dempster-Shafer’s Belief Theory for Evidential Reasoning Uncertainty due to the lack of evidence ex) “The criminal is left-handed or not”

 Types of Uncertainty (continued) 4. Imprecision : Ambiguity due to the lack of accuracy of observed data ex) Character Recognition 5. Fuzziness (vagueness) : Uncertainty due to the vagueness of boundary ex) Beautiful woman, Tall man

 Powerful tool for vagueness  Description of vague linguistic terms and algorithms  Operation on vague linguistic terms  Reasoning with vague linguistic rules  Representation of clusters with vague boundaries

History of Fuzzy Sets and Applications 1965 Zadeh Fuzzy Sets 1965 Zadeh Fuzzy Sets 1972 Sugeno Fuzzy Integrals 1972 Sugeno Fuzzy Integrals 1975 Zadeh 1975 Zadeh Fuzzy Algorithm & Approximate Reasoning Fuzzy Algorithm & Approximate Reasoning 1974 Mamdani Fuzzy Control 1974 Mamdani Fuzzy Control 1978 North Holland Fuzzy Sets and Systems 1978 North Holland Fuzzy Sets and Systems 1982 Bezdek Fuzzy C-Mean 1982 Bezdek Fuzzy C-Mean

Fuzzy Sets Applications Methods Fuzzy Measure Fuzzy Logic Fuzzy Integrals Fuzzy Measure Fuzzy Relation Fuzzy Numbers Extension Principle Fuzzy Optimization Linguistic Variable Fuzzy Algorithm Approximate Reasoning Foundation Clustering Pattern Recognition Data Processing Decision Making Evaluation Estimation Expert Systems Fuzzy Computer Fuzzy Control

Theory on fuzzy sets 1) fuzzy set 2) fuzzy number 3) fuzzy logic 4) fuzzy relation Applications 1) fuzzy database 2) fuzzy control and expert system 3) robotics 4) fuzzy computer 5) pattern recognition Rough Sets & Applications

 Examination 40% (1 exam)  Term Project40% (2-3 projects)  Presentation 20%

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