### 1. Introduction

*Fuzzy transform* and *normal forms* are the most often elaborated fuzzy approximation techniques at IRAFM. For many purposes (testing, demonstration, further usage in real applications, generating graphical outputs etc.) some software tools dealing with this issues had to be programmed.

### 2. Fuzzy transform - FTransf

For fuzzy transform of a function with one variable the FTrans software tool is published. It is multipurpose software whose algorithms were involved in real applications later on.

For a demonstration, a user can choose a function which is to be transformed as well as number and shapes of basic functions and other parameters including e.g. domain, shift of axes, displayed intervals etc. A regular noise as well as a random noise can be added to the chosen function and the inverse F-transform of the original function can be compared to the inverse F-transform of the function with added noise. Moreover, the software provides a user with a graph of errors to number of basic functions.

To see flash presentation of the software usage in EXE format - click here.

To see flash presentation of the software usage in SWF format - click here.

### 3. 3D F-transform

The F-transform of functions with two variables is implemented as well. This issue is utilized in the software *3D F-transform*.

This software provides us with algorithms more-dimensional and visual outputs for predefined set of functions with two variables. The software window is divided into four sub-windows, where one serves for its control and the three others for graphical outputs. Graph 2 displays the original function, Graph 3 an inverse F-transform of the chosen original function and Graph 1 is the difference graph which displays errors of the approximation given by the inverse F-tansform.

To see flash presentation of the software usage in EXE format - click here.

To see flash presentation of the software usage in SWF format - click here.

To download demonstration version of the 3D Ftransform software - click here.

### References:

[1] PERFILIEVA, I. Fuzzy Transforms: Theory and Applications. In Fuzzy Sets and Systems. FSTA 2006, 2006, 157, pp.993-1023, ISSN 0165-0114. Download Research report 58.

[2] PERFILIEVA, I.: VALÁŠEK, R. Fuzzy Transforms in Removing Noise. In: Reusch B. (Ed.) Computational Intelligence, Theory and Applications (Advances in Soft Computing). Berlin : Springer-Verlag, 2005. ISBN 3-540-22807-1. pp. 225-234.

[3] ŠTĚPNIČKA, M., VALÁŠEK, R. Fuzzy Transforms for Functions with Two Variables. In 6th Czech-Japan Seminar on Data Analysis and Decision Making under Uncertainty 2003. 2003-09-23-2003-09-23 Valtice, ČR. Ostrava : University of Ostrava, 2003. pp. 96-102.