C++ Neural Networks and Fuzzy Logic: Preface

the tank, and cold water flowing into the tank.

C++ Neural Networks and Fuzzy Logic:Preface

Section II: Fuzzy Control

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Step One: Defining Inputs and Outputs for the FLC

The range of values that inputs and outputs may take is called the universe of discourse. We need to define the

universe of discourse for all of the inputs and outputs of the FLC, which are all crisp values. Table 16.11

shows the ranges:

Table 16.11 Universe of Discourse for Inputs and Outputs for FLC

NameInput/OutputMinimum valueMaximum value

LevelSenseI010

HeatKnobO010

TempSenseI0125

Step Two: Fuzzify the Inputs

The inputs to the FLC are the LevelSense and the TempSense. We can use triangular membership functions to

fuzzify the inputs, just as we did in Chapter 3, when we constructed the fuzzifier program. There are some

general guidelines you can keep in mind when you determine the range of the fuzzy variables as related to the

crisp inputs (adapted from Yan, et al.):

1.  Symmetrically distribute the fuzzified values across the universe of discourse.

2.  Use an odd number of fuzzy sets for each variable so that some set is assured to be in the middle.

The use of 5 to 7 sets is fairly typical.

3.  Overlap adjacent sets (by 15% to 25% typically) .

Both the input variables LevelSense and TempSense are restricted to positive values. We use the following

fuzzy sets to describe them:

XSmall, Small, Medium, Large, XLarge

In Table 16.12 and Figure 16.3, we show the assignment of ranges and triangular fuzzy membership functions

for LevelSense. Similarly, we assign ranges and triangular fuzzy membership functions for TempSense in

Table 16.13 and Figure 16.4. The optimization of these assignments is often done through trial and error for

achieving optimum performance of the FLC.

Table 16.12 Fuzzy Variable Ranges for LevelSense