Fuzzy Logic- Introduction and Implementation

FUZZY LOGIC

Founded by Lotfi A Zadeh in 1965, Fuzzy Logic was first implemented in steam engine speed control.

So what actually is Fuzzy Logic?

It is considered an extension of Boolean logic and a logic that handles the concept of partial truth. The range of truth value is between yes and no. It can be certainly yes, slightly yes, no, strictly no or anything and these are the terms under fuzzy set. It mimics the human reasoning about things. Like  if we ask someone, “hows the weather today?”, different people may have different answers. One may say “Its hot”, another may say “Its too hot” , some may say “Its normal” or someone living in Solukhumbu may say “Its too cold”.  The logic always represents vagueness.

Also according to Zadeh, the logic involves computing using words as linguistic variables. Any linguistic variable can be represented as <x,T(x),U,G,M> where
x=linguistic variable, T(x)=set of terms, U=universe of discourse, G=  syntax rules, M= semantic rules.

Linguistic Variables

Linguistic variables are those variables whose values are not number but words or sentences. Fuzzy logic bridges between these words and numbers.

e.g. temperature is a linguistic variable and set of terms=(too cold, cold, warm, hot, too hot). These terms are mapped to numerical values using membership functions.

Classic Logic Vs Fuzzy Logic

Fuzzifier

It involves fuzzification process where crisp numbers obtained from sensors are converted into fuzzy sets.

If we obtain speed of car from sensors to be a number like 3kmph, it is mapped to fuzzy function and words are collected like;

Car is moving to too slow.

Rules / Rule Base and Inference Engine

Rule Base contains all the rules and the if then conditions offered by the experts to control the decision making
system.
Inference Engine helps you to determines the degree of match between fuzzy input and the rules Based on the
match, it determines which rules we need to implement according to the given input field. After this, the applied rules
are combined to develop the control actions.

Defuzzifier

It involves defuzzification process where fuzzy sets are converted to crisp value for quantifiable result. Defuzzification is the interpretation of the membership degree for collected vague values in
first step of fuzzification.

Example: Very slow is indicated by 0.1 .
A bit faster is indicated by 0.9.

Different methods like center of sum, center of gravity are used.

Input: Aggregate output fuzzy set

Output: Single Number