**1. Introduction**

396 Fuzzy Inference System – Theory and Applications

Wang L. X. (1994). *Adaptative Fuzzy Systems and Control: Design and Stability Analysis*,

Yager R.R., Filev D.P. (1994). *Essentials of Fuzzy Modeling and Control,* Wiley, ISBN 978-

Prentice Hall, Inc., ISBN 978-0130996312, Upper Saddle River, NJ

0471017615, New York

When the Fuzzy Set Theory was proposed by Lotfi Zadeh in a seminal paper published in 1965, he noted that the technological resources available until then were not able to automate the activities related to industrial, biological or chemical problems. These activities use typically analog data which are inappropriate to be handled in a digital computer that works with well-defined numerical data, i.e. , discrete values.

Using this idea, Fuzzy Logic can be defined as a way to use data from typical analog processes that move through a continuous track in a digital computer that works with discrete values. The use of Fuzzy Logic for solving control problems has tremendously increased over the last few years. Recently the Fuzzy Logic has been used in industrial process control electronic equipment, entertainment devices, diagnose systems and even to control appliances. Thus, the teaching of fuzzy control in engineering courses is becoming a necessity. In a previous work, it has been presented a computational package for students' self-training on fuzzy control theory. The package contains all required instructions for the users to gain the understanding of fuzzy control principles. The training instructions are presented via a practical example.

Although this approach has proven to be convenient in giving to students an opportunity to appreciate real life like situations, it suffers a serious disadvantage: the type of learning. In fact, students often go through a "trial-and-error" method to select an appropriate control action, such as rule definitions or membership fitting. The problem of this type of learning is a tendency from students to get the erroneous concept that corrective actions are much a matter of guess. The purpose of this chapter is to present a strategy for an automatic membership function fitting using three different evolutionary algorithms, namely: modified genetic algorithms (MGA), particle swarm optimization (PSO) and hybrid particle swarm optimization (HPSO).

The proposed strategies are applied in a computational package for fuzzy logic learning. This computer program was developed for self-training in engineering students in the

An Evolutionary Fuzzy Hybrid System for Educational Purposes 399

With respect to logical limitations, they may vary according to the types of strategies

For the movement of the vehicle shall be laid down the following conditions: Acceleration equal to 1 (m/s2) and maximum speed 1 (m/s). These two values are used as reference for all movements. To reverse the direction of motion of the vehicle there are three possibilities,

a. shock against the wall: when the system verifies that the vehicle will collide against the

The user of this computational package can define a new system by creating the roles of relevance and control rules. Initially, the user sets the number of functions of relevance for each variable. When the functions are created, they are equally spaced on the surface of the control variable. The user can modify these functions of belongingness by Fuzzy Sets

To set the rules for the control, i.e., how the functions of relevance will be grouped, there is the Fuzzy Rules Edition window. In Figure 3, one can find two regions of interest. The first where there is the possibility of selecting the direction (forward or reverse) and coordinated corresponding to the angle of the car. The second region of interest contains the padding of the conclusion of the rule. This can be done by selecting one of the output values (or none for a rule does not set or reverse). For instance for *x* = LE (left), *y* = YT (small values), car angle = RB (right big angle) and direction = ahead (forward) values was selected as NB

(negative big angle) to wheel angle, which corresponds to rule:

b. rule that forces the inversion: when the reverse order is used as a result of a rule; or, c. lack of outputs: when no rule is used by the control, i.e., if the output is zero.

Edition window. Figure 2 presents an example of editing for the *x* input variable.


employed. Some examples of these strategies can be, among others:



which are:

wall in the next step;

Fig. 2. Fuzzy Sets Edition window

theory of fuzzy control. The program contains all necessary instructions for users to understand the principles of diffuse control. In this package the main goal is to park a vehicle in a garage, starting from any starting position. The user must first develop a set of fuzzy control rules and functions of relevance that will shape the trajectory of the vehicle. The processes of fuzzification and defuzzification variables are performed by the program without user interference.
