FUZZY TRANSFORMACE A JEJÍ APLIKACE NA PROBLÉMY V INŽENÝRSKÉ PRAXI

Mgr. Martin ŠTĚPNIČKA

Doctoral thesis

FUZZY TRANSFORM AND ITS APPLICATIONS TO PROBLEMS IN ENGINEERING PRACTICE

Abstract:

Teorie fuzzy mnoˇzin iniciov´ana L.A. Zadehem poskytla matematik°um vhodn´y n´astroj k modelov´an´? fenom´enu v´agnosti a inˇzn´yr°um vnesla nov´e svˇetlo do teorie ˇr´?zen´? (regulace). Pozdˇeji, v roce 1985, T. Takagi a M. Sugeno navrhli fuzzy model, kter´y se stal obl´?ben´y d´?ky sv´ym aproximaˇcn´?m moˇznostem. Koneˇcnˇe v 90-t´ych letech se nˇekolik prac´? zab´yvalo aproximaˇcn´?mi moˇznostmi dalˇs´?ch obecnˇe pouˇz´?van´ych fuzzy model°u. Na z´akladˇe tohoto historick´eho v´yvoje byly poloˇzeny z´aklady nov´eho oboru zvan´eho fuzzy aproximace, kter´y se zab´yv´a aproximaˇcn´?mi vlastnostmi fuzzy model°u a jejich rozvojem. Fuzzy transformace (F-transformace) jakoˇzto konkr´etn´? z´astupce metod tohoto oboru je hlavn´?m objektem studia t´eto pr´ace.

Abstract:

The fuzzy set theory initiated by L.A. Zadeh provided mathematicians with an appropriate tool for modelling the vagueness phenomenon and shed new light into the control theory for engineers. Later, in 1985, T. Takagi and M. Sugeno invented a particular fuzzy model which became very popular due to its approximation ability. Finally, in the 1990?s, several studies aimed at approximation properties of the other widely used fuzzy models. Based on the historical development briefly recapitulated above, a new field called fuzzy approximation focusing on approximation properties of fuzzy models and development of new methods using fragments of the fuzzy set theory has been established. Fuzzy transform (F-transform), a particular method belonging to this field, is the main object of the study in this thesis.

Keywords

Fuzzy transformace, Aproximace, Numerick´e metody, Parcil´aln´?

Language used: Czech

Date on which the thesis was submitted / produced: 20. 6. 2007

Accessible from:: 20. 6. 2007

Thesis defence

• Date of defence: 26. 2. 2008
• Supervisor: prof. Irina Perfiljeva, CSc.

University of Ostrava

Faculty of Science

Doctoral programme / field:
Applied Mathematics / Fuzzy Modelling