## Introduction

This article is about a fuzzy logic controller based on mamdani Inference Engine. Fuzzy logic is an approximation process, in which crisp inputs are turned to fuzzy values based on linguistic variables, set of rules and the inference engine provided. For example:

I have a train, I considered the Linguistic Variable "Speed" of the train has 2 membership functions Low and High, in which "Low" has range from 0 mph - 10 mph and "High" from 10 mph - 20 mph.

So If I got a Crisp input of 5 -> its fuzzy value is Low.

Imagine more if the range from 0-10 is not constant but a triangular graph with the max height of 1 and for Low a triangle graph with 3 distinct points 0,5,10.

Now for a singleton input of 4, the fuzzy value = y = (4-0)/(5-0) = 0.8, therefore our fuzzy input = 0.8 Low, imagine that the linguistic variables are intersecting so that a single input can be defined as (0.8 Low 0.4 High).

This process is called fuzzification...

After we get the fuzzy inputs, we compare it against a rule base. A rule base is a set of rules that is responsible for final output.

For example, if I said my rules are:

Rule 1: If Speed is High, Then Brake is Pushed

Rule 2: If Speed is Low, Then Brake is Released

So now using our Inference Engine, the Engine that would compare and deduct our fuzzy output, with fuzzy input ( 0.8 Low , 0.4 High) we can say based upon the rules mentioned above that the brakes will be down by (0.4 Pushed 0.8 Released) --> Fuzzy output.

This is the Rule Base and Inference Engine Process using mamdani concept...

Then the fuzzy output enters the defuzzification method, which is a method to weigh the fuzzy outputs and return a crisp output force which will be applied to the brakes.

Fig. 1-1

## Using the Code

In the project attached with this article, 3 sub projects exist:

- A C# class library contains the engine that implements the steps talked about in the above example.
- A Window Forms Project
`FuzzyLogicUI`

which is a User Interface built for this fuzzy logic controller, you can add linguistic variables and membership functions, rules and a result panel to show you the different steps of the system.
- A console based test to the Fuzzy Logic Controller for better understanding of the system.

### The Fuzzy Library (DLL)

#### The Class Diagram

### Steps

#### 1- Configure Your Fuzzy Controller

The allowed configuration for this system, is the (And Logic Connection) and Implication.

For a Rule: IF X1 is Low And X2 is High -> Y1 is Low.

How to calculate the final firing strength, if X1-> 0.8 X2-> 0.4 so Y1-> ?

If we use an (AND Connection) in this system you can define the AND Method between product or minimum , so for Y1 = min(0.8,0.4) = 0.4 due to an "AND" connection between X1 & X2.

Config configure = new Config(ImpMethod.Prod,ConnMethod.Min);

#### 2- Create Your Linguistic Variables and its Membership Functions

Using above Train example: we define the Train to have speed for input. For speed: High, Med, Low for the result (output) Brake: Release, Push.

LingVariable speed = new LingVariable("Speed", VarType.Input);
speed.setRange(0, 35);
speed.addMF(new Trapmf("Low", -10, 0, 10, 15));
speed.addMF(new Trimf("Medium", 10, 20, 30));
speed.addMF(new Trapmf("High", 25, 30, 35, 40));
LingVariable brake = new LingVariable("Brake", VarType.Output);
brake.setRange(0, 65);
brake.addMF(new Trapmf("Released", -10, 0, 20, 41));
brake.addMF(new Trapmf("Pushed", 41, 60, 65, 70));

#### 3- Crisp Inputs and Fuzzification Process

Fuzzification is the process of evaluating the crisp input against the membership functions of the lingstic variable Speed, `membershipfunction `

is an abstract class, with an abstract method "`getOutput`

", any object inheriting this class needs to define their `getOutput(double)`

function, such as in `Trimf `

and `Trapmf`

. Based upon this feature, more `membershipfunction`

s can be implemented to extend the fuzzy controller capabilities.

`Fuzzification `

method then returns a list of fuzzy numbers, each fuzzy number consists of a function name and firing strength from `getOutput(double)`

.

Example: fuzzynumber(0.8,"Low") FuzzyNumber(0.4,"High")

The list of fuzzy numbers is then added to a fuzzy Set with list of Fuzzy numbers and linguistic Variable name for further processing.

FLC c = new FLC(conf);
double speedCrispVal = 30;
FuzzySet fuzzy_speed = new FuzzySet(c.Fuzzification(speedCrispVal,speed), speed.Name);

After we fuzzify all our inputs, add it to a list of fuzzysets:

List<FuzzySet> input_sets = new List<FuzzySet>();
input_sets.Add(fuzzy_speed);

#### 4- Make the rules !

Define the rulebase, the rules that our system uses to approximate.

For Rule 1, from the above example:

"IF Speed is High, Then Brake is pushed."

List<ruleitem> rule1in = new List<ruleitem>();
List<ruleitem> rule1out = new List<ruleitem>();
rule1in.AddRange(new RuleItem[1] { new RuleItem("Speed", "High") } );
rule1out.AddRange(new RuleItem[1] { new RuleItem("Brake", "Pushed") } );
List<rule> rules = new List<rule>();
rules.Add(new Rule(rule1in, rule1out, Connector.And));

#### 5- Evaluate the Rule

During the rules evaluation at the Inference system, the firing strength of the output is determined as in this example:

Fuzzy input: X1 = 0.8 Low X2 = 0.5 High.

Rule: "IF X1 Low and X2 High Then Y1 is Low."

Configuration: And connection evaluated by min(X1,X2).

Evaluation: min(X1,X2) => min(0.8,0.5) = Y1 = 0.5 Low.

Fuzzy out: Y1 = 0.5 Low.

If more rules are overlapping, such as "IF X1 is High, THEN Y1 is Low" where the Y1 is 0.7 Low, the maximum of Y1 firing strengths is taken, in this case ( 0.7 ).

InferEngine engine = new InferEngine(configure, rules, input_sets);
List<FuzzySet> fuzzy_out = engine.evaluateRules();

#### 6- DeFuzzification and Crisp Output

The `Defuzzification `

method is a method to calculate the fuzzy out to convert to a crisp value. In this system, two methods of defuzzification are used, you can choose between them in Configuration.

Centroid `Defuzzification`

, Modified High `Defuzzification`

.

double crisp_brake_force = c.DeFuzzification(fuzzy_out, brake);

## Points of Interest

This project has been made very flexible and extendable for future development and upgrading. The GUI is made to realise the Fuzzy Logic controller and to try it out, it is made mainly for educational purposes. The `FuzzySet`

s and `FuzzyNumber `

classes are provided for more depth in fuzzy process.

For more tests and examples, try GUI Project Predefined Tests, or the console based test project "`FuzzyTest`

".