Evaluation of the conclusion part of fuzzu system

Use strength of fuzzy rule for Shaping Output Fuzzy Set, fuzzy set for output is allocated by the conclusions part in the rule, this set is represented by functions of membership and which refers to the Qualities of results and this process is called Implication.

Implication are done by cutting membership functions for output at the point where its coordinate y equal to the strength of the rule and figure follows illustrates this. It is clear from this figure that the strength of the rule is 0.75, so the output function (quality) cut off at the point where its coordinate y equal to strength of the rule (0.75). There are cases where conclusions part is free of fuzzy variables resulting in the emergence of two types of fuzzy systems, namely:

1) Mamdani Systems:

Is the most common and complexity type, and the Mamdani method was one of the first control systems built by fuzzy set theory, these systems have emerged in the world in 1975 by Abraham Mamdani in an attempt to control the collection Heater (Boiler) and a Steam Engine by building linguistic control rules set obtained from experienced workers. Mamdani efforts built on the search by Lotfi A. Zadeh in 1973 and the search was focused on fuzzy algorithms to complex systems and decision-making processes.

2) Sugeno Systems:
In some cases, it is more efficient to be the expression of functions of membership of output using constants and linear equations instead of fuzzy sets and this type of output called Singleton Output Membership Functions , it can be considered as these functions a preparatory step to the stage of removing the fuzzification described in the next paragraph,