1. MUNICIPALITIES CLASSIFICATION BASED ON FUZZY RULES
Miroslav Hudec
INFOSTAT – Bratislava
Mirko Vujošević
FON – Beograd
Lenka Priehradníková

2. Classification Purpose: estimating of road maintenance needs in winter
The data of municipalities are in the Information system MOŠ/MIS
(2891 municialities
803 indicators)
The tool for classification – fuzzy inference system and his improvement: neuro-fuzzy system

3. Fuzzy systems These systems are categorised into two families:
Mamdani:
Takagi-Sugeno-Kang:
Ri (i=1,..,l) denotes the i-th fuzzy rule, xj (j=1,...,n), is the input, yi is the output of the fuzzy rule Ri , Aki - is the k-th fuzzy membership function in i-th rule and Bi denotes the output fuzzy membership functions , aji - are the i-th coefficient of the j-th output and i-th rule

4. Fuzzy systems The basic elements of the fuzzy systems are:
Fuzzification
Knowledge base
Processing of the rules
Defuzzification

5. Fuzzification
- length of roads
number of days
with snow

6. Fuzzification total yearly rainfalls (precipitation) needs for winter
maintenance

7. Knowledge base IF – THEN rules
1. If length of roads is Very Small and number of days with snow is Very Small and precipitation is Very Small Then maintenance is Very Small.
2. If length of roads is Medium and number of days with snow is Very Small and precipitation is Small Then maintenance is Small.
3. If length of roads is Medium and number of days with snow is Medium and precipitation is Medium Then maintenance is Medium.
4. If length of roads is Medium and number of days with snow is Very High and precipitation is High Then maintenance is High.
5. If length of roads is Very High Then maintenance is Very High.

8. Processing of the rules and defuzzification
The MatLab software and the Sugeno model of the FIS was used in this paper.
Processing of the rules:
Aggregation, implication and accumulation. Operator min is used as
t-norm.
Defuzzification is not part of this model.

9. Results for some selected municipalities

10. Geographical interpretation

11. Discussion of Fuzzy systems
The classification results were reasonable and expected for selected region.
The results may slightly vary with the definition of the particular parameters of the used fuzzy inference system and with the selected method of defuzzification but not so much as with the choices of parameters of membership functions and set of inference rules.
No constraints in number of fuzzy sets, rules and ranked municipalities

12. Neuro-fuzzy system - ANFIS

13. Advantages of ANFIS
ANFIS can improve the process of determining membership functions. Membership functions obtained in fuzzification process depend on parameters and changing the parameters will change the shape of the membership function and ranking results. Because of sensitivity to expert choices of the membership function parameters, these membership function parameters can be modified using ANFIS.

14. Constraints of ANFIS
Neuro-fuzzy systems need sets for training and checking his parameters.
Obtained ANFIS structure has 153 parameters.
For well trained ANFIS there are needed more than 300 municipalities in training and checking data sets.

15. Thank you for your attention