Soft Computing

Course guarantor:

Lecturer:

Tutor:

Supervisor:

Department of Software Engineering

Synopsis:

Fuzzy systems and selected artificial neural networks are discused as special cases of Lipschitz continuous functions with constrained sensitivity and limited output. Both theories and application conventions are included.

Requirements:

Basic knowledge of algebra, calculus and programming techniques.

Syllabus of lectures:

1 Aims and methods of soft computing

2 Boolean algebra, its laws, applications and generalization

3 Lattice, residuated lattice and BL algebra

4 Theory of t-norms and derived operators

5 Fuzzy rules, similarity and data mining

6 Theory of Archimedean norms and their generators

7 Lipschitz continuity and constrained sensitivity of soft system

8 Fuzzy set, fuzzyfication and defuzzyfication

9 Fuzzy expert system, fuzzy decision and fuzzy control

10 Linear combination or distance and its fuzzification inside ANN

11 Softmax module inside ANN

12 Hierarchical structure of MLP, RBF, DNF, CNF, MPFN and other ANNs

13 Learning of soft systems as optimization task

14 Upper estimation of soft system sensitivity

Syllabus of tutorials:

1 Aims and methods of soft computing

2 Boolean algebra, its laws, applications and generalization

3 Lattice, residuated lattice and BL algebra

4 Theory of t-norms and derived operators

5 Fuzzy rules, similarity and data mining

6 Theory of Archimedean norms and their generators

7 Lipschitz continuity and constrained sensitivity of soft system

8 Fuzzy set, fuzzyfication and defuzzyfication

9 Fuzzy expert system, fuzzy decision and fuzzy control

10 Linear combination or distance and its fuzzification inside ANN

11 Softmax module inside ANN

12 Hierarchical structure of MLP, RBF, DNF, CNF, MPFN and other ANNs

13 Learning of soft systems as optimization task

14 Upper estimation of soft system sensitivity

Study Objective:

Knowledge:

The goal is to avoid the misunderstanding that soft system is a kind of weak one with unuseful properties. Fuzzy and ANN systems are putting together and then ivestigated as systems with many useful properties and application domains.

Abilities:

Orientation in given subject and ability to solve real tasks.

Study materials:

Key references:

Navara M., Olšák P.: Fundamentals of Fuzzy Sets (in Czech), Vydavatelsatví ČVUT, 2002.

Hakl F., Holeňa M.: Introduction to Theory of Neural Networks (in Czech), Vydavatelství ČVUT, Praha, 1998.

Recommended references:

Vysoký P.: Fuzzy řízení, Vydavatelství ČVUT, Praha, 1996.

Šíma J., Neruda R.: Teoretické otázky neuronových sítí, Matfyzpress, Praha, 1996.

Note:

Further information:

No time-table has been prepared for this course

The course is a part of the following study plans:

• Aplikace informatiky v přírodních vědách (compulsory course in the program)