Description:

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.

Contents:

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

Seminar contents:

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

Recommended literature:

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.

Keywords:

Soft computing, fuzzy system, artificial neural network, constrained sensitivity.

Abbreviations used:

Semester:

• W ... winter semester (usually October - February)
• S ... spring semester (usually March - June)
• W,S ... both semesters

Mode of completion of the course:

• A ... Assessment (no grade is given to this course but credits are awarded. You will receive only P (Passed) of F (Failed) and number of credits)
• GA ... Graded Assessment (a grade is awarded for this course)
• EX ... Examination (a grade is awarded for this course)
• A, EX ... Examination (the award of Assessment is a precondition for taking the Examination in the given subject, a grade is awarded for this course)

Weekly load (hours per week):

• P ... lecture
• C ... seminar
• L ... laboratory
• R ... proseminar
• S ... seminar