# Artificial Intelligence - Fuzzy Logic Systems

Fuzzy Logic Systems (FLS) produce satisfactory but definite output in response to incomplete, ambiguous, distorted, or inaccurate (fuzzy) input.

## What is Fuzzy Logic?

Fuzzy Logic (FL) is a method of thinking that resembles human reasoning. The methodology of FL imitates the method of decision making in humans that includes all intermediate possibilities between digital values YES and NO.

The conventional logic block that a computer can comprehend takes precise input and produces a definite output as TRUE or FALSE, which is identical to human’s YES or NO.

The inventor of fuzzy logic, Lotfi Zadeh, saw that unlike computers, the human decision making incorporates a range of possibilities between YES and NO, such as −

 CERTAINLY YES POSSIBLY YES CANNOT SAY POSSIBLY NO CERTAINLY NO

The fuzzy logic works on the levels of possibilities of contribution to achieve the definite output.

### Implementation

• It can be implemented in systems with different sizes and capabilities ranging from small micro-controllers to large, networked, workstation-based control systems.

• It can be implemented in hardware, software, or a mix of both.

## Why Fuzzy Logic?

Fuzzy logic is valuable for commercial and practical purposes.

• It can control machines and consumer products.
• It may not give exact reasoning, but acceptable reasoning.
• Fuzzy logic assists to deal with the uncertainty in engineering.

## Fuzzy Logic Systems Architecture

It has four primary parts as shown −

• Fuzzification Module − It changes the system inputs, which are crisp numbers, into fuzzy sets. It splits the input signal into five steps such as −

 LP x is Large Positive MP x is Medium Positive S x is Small MN x is Medium Negative LN x is Large Negative
• Knowledge Base − It stores IF-THEN rules provided by specialists.

• Inference Engine − It reproduces the human reasoning process by making fuzzy inference on the inputs and IF-THEN rules.

• Defuzzification Module − It changes the fuzzy set obtained by the inference engine into a crisp value.

The membership functions work on fuzzy sets of variables.

### Membership Function

Membership functions permit you to quantify linguistic term and represent a fuzzy set graphically. A membership function for a fuzzy set A on the universe of discourse X is defined as μA:X → [0,1].

Here, each element of X is mapped to a value between 0 and 1. It is called membership value or degree of membership. It quantifies the degree of membership of the element in X to the fuzzy set A.

• x axis represents the universe of discourse.
• y axis represents the degrees of membership in the [0, 1] interval.

There can be multiple membership functions relevant to fuzzify a numerical value. Straightforward membership functions are utilized as use of complex functions does not add more precision in the output.

All membership functions for LP, MP, S, MN, and LN are shown as below −

The triangular membership function shapes are generally common among various other membership function shapes such as trapezoidal, singleton, and Gaussian.

Here, the input to 5-level fuzzifier varies from -10 volts to +10 volts. Subsequently the corresponding output additionally changes.

## Example of a Fuzzy Logic System

Let us consider an air conditioning system with 5-level fuzzy logic system. This system changes the temperature of air conditioner by looking at the room temperature and the target temperature value.

### Algorithm

• Define linguistic Variables and terms (start)
• Construct membership functions for them. (start)
• Construct knowledge base of rules (start)
• Convert crisp data into fuzzy data sets using membership functions. (fuzzification)
• Evaluate rules in the rule base. (Inference Engine)
• Combine results from each rule. (Inference Engine)
• Convert output data into non-fuzzy values. (defuzzification)

### Development

Step 1 − Define linguistic variables and terms

Linguistic variables are input and output variables in the form of simple words or sentences. For room temperature, cold, warm, hot, etc., are semantic terms.

Temperature (t) = {very-cold, cold, warm, very-warm, hot}

Every member of this set is a linguistic term and it can cover some portion of overall temperature values.

Step 2 − Construct membership functions for them

The membership functions of temperature variable are as shown −

Step3 − Construct knowledge base rules

Create a matrix of room temperature values versus target temperature values that an air conditioning system is required to provide.

RoomTemp. /Target Very_Cold Cold Warm Hot Very_Hot
Very_Cold No_Change Heat Heat Heat Heat
Cold Cool No_Change Heat Heat Heat
Warm Cool Cool No_Change Heat Heat
Hot Cool Cool Cool No_Change Heat
Very_Hot Cool Cool Cool Cool No_Change

Build a set of rules into the knowledge base in the form of IF-THEN-ELSE structures.

Sr. No. Condition Action
1 IF temperature=(Cold OR Very_Cold) AND target=Warm THEN Heat
2 IF temperature=(Hot OR Very_Hot) AND target=Warm THEN Cool
3 IF (temperature=Warm) AND (target=Warm) THEN No_Change

Step 4 − Obtain fuzzy value

Fuzzy set tasks perform evaluation of rules. The operations utilized for OR and AND are Max and Min respectively. Combine all results of evaluation to form a final outcome. This outcome is a fuzzy value.

Step 5 − Perform defuzzification

Defuzzification is then performed according to participation work for yield variable.

## Application Areas of Fuzzy Logic

The key application areas of fuzzy logic are as given −

Automotive Systems

• Automatic Gearboxes
• Four-Wheel Steering
• Vehicle environment control

Consumer Electronic Goods

• Hi-Fi Systems
• Photocopiers
• Still and Video Cameras
• Television

Domestic Goods

• Microwave Ovens
• Refrigerators
• Toasters
• Vacuum Cleaners
• Washing Machines

Environment Control

• Air Conditioners/Dryers/Heaters
• Humidifiers

• Mathematical concepts within fuzzy reasoning are straightforward.

• You can modify a FLS by just adding or deleting rules due to flexibility of fuzzy logic.

• Fuzzy logic Systems can take imprecise, distorted, noisy input information.

• FLSs are easy to construct and comprehend.

• Fuzzy logic is a solution to complex problems in all fields of life, including medicine, as it resembles human reasoning and decision making.