When the fuzzy rule base is not sufficient to provide the performance that meets the requirement of the fuzzy control system, the fuzzy rule base contains some unsatisfactory fuzzy rules and needs to be adjusted.
It is a requirement of the fuzzy logic system that the inputs of the fuzzy controller should lie within the input fuzzy set, i.e., in between 0 and 1.
In addition, the genetic algorithm has been added to the control structure in order to optimize the proposed control system to meet the requirement of realizing fuzzy-based control approach.
The fuzzy requirements of the problem (3.1) can be quantified by electing a membership function μ ( f ( x ) ) (Figure 2) which is differentiable in the open interval f ( x 1 ) < f ( x ) < f ( x 0 ) where μ ( f ( x ) ) is defined by μ ( f ( x ) ) = { 1, f ( x ) ≤ f ( x 1 ), f ( x ) − f ( x 1 ) f ( x ¯ 0 ) − f ( x ¯ 1 ), f ( x 1 ) ≤ f ( x ) ≤ f ( x 0 ), 0, f ( x ) ≥ f ( x 0 ), (4.6).
To meet these requirements, we develop an evolving version of fuzzy pattern tree learning, in which model adaptation is realized by anticipating possible local changes of the current model, and confirming these changes through statistical hypothesis testing.
Stability and performance requirements in fuzzy control of Takagi Sugeno systems are usually stated as fuzzy summations, i.e., sums of terms, related to Lyapunov functions, which are weighted by membership functions or products of them.
Tuning of fuzzy design variables eliminate the requirement of expertise needed for setting these variables.
The approach first eliminates solutions that are not technically feasible, with reasons, and then ranks the remaining solutions on the basis of the degree of agreement with the set of design requirements (using a fuzzy logic algorithm).
The main advantages are the simple design, no requirement of system model, and release of fixed universal range of fuzzy output.
When the relative weights of customer requirements and the relationship measures between customer requirements and technical attributes are expressed as fuzzy numbers, calculating the importance of each technical attribute falls into the category of fuzzy weighted average, in which the derived membership function of the fuzzy importance of each technical attribute is not explicitly known.
