Artificial Intelligence - Fuzzy Logic

Artificial Intelligence - Fuzzy Logic

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There are some situations where we cannot make a yes or no decision. This can be due to lack of information, unclear situation or dilemma. Similarly, there are conditions where computers face this kind of situation in decision-making. Fuzzy Logic is used to handle these uncertainties.

What is Fuzzy Logic?

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

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

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

Probabilities
CERTAINLY YES
POSSIBLY YES
CANNOT SAY
POSSIBLY NO
CERTAINLY NO

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

Characteristics of FLS's

Following are the characteristics of fuzzy logic systems −

• Versatile and simple method for applying machine learning technology.
• Allows to replicate the logical process of human reasoning.
• Can easily be modified to enhance or raise system performance.
• Fuzzy logic can control nonlinear systems that might be challenging to handle mathematically.

Architecture of FLS's

The fundamental architecture of fuzzy logic systems includes four components which include −

• Knowledge Base − It stores IF-THEN rules provided by experts.
• Inference Engine − It simulates the human reasoning process by making fuzzy inference on the inputs and IF-THEN rules.
• Defuzzification Module − It transforms the fuzzy set obtained by the inference engine into a crisp value.
• Fuzzification Module − It transforms the system inputs, which are crisp numbers, into fuzzy sets. It splits the input signal into five steps.

Following are the five steps of the Fuzzification Module −

Step	Description
LP	x is Large Positive
MP	x is Medium Positive
S	x is Small
MN	x is Medium Negative
LN	x is Large Negative

Membership Function

Membership functions allow 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 μ_A: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 applicable to fuzzify a numerical value. Simple membership functions are used 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 most 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. Hence the corresponding output also changes.

Example for FLS's

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

Algorithm of FLS's

The algorithm of fuzzy logic system is mentioned below −

• 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. (de-fuzzification)

Steps to Develop FLS's

Following is the detailed step by step description to develop a fuzzy logic system −

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 linguistic 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 −

Step 3: Construct knowledge base rules

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

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

Step 4: Obtain fuzzy value

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

Step 5: Perform de-fuzzification

De-fuzzification is then performed according to membership function for output variable.

Application Areas of FLS's

The key application areas of fuzzy logic are as given −

• Fuzzy logic has been used in Natural Language Processing and various artificial intelligence applications.
• It can be use in organization that handle large data to facilitate effective decision-making.
• It is been used for controlling fuel delivery and ignition depending on throttle position, cooling water temperature, RPM, and other factors.
• It can also be used for Pattern Recognition and Classification in handwriting detection. It also serves to search for blurry images.

Advantages of FLSs

The advantages of fuzzy logic are −

• Mathematical concepts within fuzzy reasoning are very simple.
• 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 understand.
• Fuzzy logic is a solution to complex problems in all fields of life, including medicine, as it resembles human reasoning and decision making.

Disadvantages of FLSs

While there are many advantages of fuzzy logic systems, there are certain challenges too which include −

• There is no systematic approach to fuzzy system designing.
• They are understandable only when simple.
• They are suitable for the problems which do not need high accuracy.