Click here to recommend this site to a friend. It wont take more than a minute.

  Introduction to Fuzzy Logic

1.1 Concepts in Fuzzy Logic

Fuzzy logic is a relatively newly concept. As with other revolutionary ideas it was not accepted until only recently due to the overwhelming evidence in its favour. One reason is that fuzzy logic considers systems as imprecise while classical systems consider impreciseness as a fault. Normal logic considers statements as having a truth-value of either 0 or 1 i.e. false or true. Normally accepted sets in mathematics consist of well-defined objects which are either in the set (truth-value 1) or not in the set (truth-value 0).

Now consider the statements:

The engine has become hot.

The engine has become very hot.

The engine temperature is about 200 C.

What does one consider hot? Of course it depends on the object, in this case the engine. But even when the object is known, can we actually set limits for hotness, say something like 200 C or 250 C. Classical theories attempt to do so. But this is impossible. If we consider that the cut off is 200 C does it mean that a temperature of 199 C is not hot? Thus there is a certain fuzziness involved. Now this can be taken care of by fuzzy logic. According to fuzzy logic, a temperature of 199 C is neither totally hot nor totally warm (considering that warm is the subdivision beneath hot). Thus some persons may call a temperature of 199 C as warm but others may call it hot. As the temperature increases the probability that a person classifies the engine as hot increases. Along with this the truth-value of the temperature as a member of the set 'hot' also increases. Thus in fuzzy logic truth-values (also known as confidence in fuzzy logic) can vary from 0 to 1. Truth-values can also be represented as percentages or as points out of 1000. A temperature of 199 C may have truth-value of hot as 0.5 and as the temperature increases to 250 C the truth-value increases to 1 so that the engine at 250 C is well and truly hot. The temperatures thus are fuzzy variables while 'hot' constitutes a fuzzy set for temperatures of engines.

Fuzzy logic sets can have certain sub-sets (also sometimes called hedges). Consider the second statement. The statement gives more information than the first. The word 'very' indicates that the temperature is more than just hot. Which means that for 'very hot' 199 C will have a far lower truth-value for the fuzzy sub-set 'very hot'. There can be various other sub-sets like 'not very hot' and 'somewhat hot'.

The third statement gives an example of a fuzzy number. 'About 12:30' is not the exact time. It is only approximate. The confidence of 'about 12:30' is maximum for 12:30 and it tapers towards either side. Thus 'about 12:30' is an example of a fuzzy number.

1.2 Advantages of fuzzy logic

The main advantage of fuzzy logic is that it can account for overlap between two adjacent states. This it does by acknowledging the intrinsic fuzziness associated with the system. The role model for fuzzy logic is the human brain. It attempts to make machines think on similar lines as humans. This immensely reduces the computational power required to solve a problem and also renders complex, non-linear systems solvable. It accounts for semantics which is considered useless by the classical theories. Consider the statement:

If the profits of a company are high and sales are increasing then credit rating is fairly safe.

An expert knows what this statement means though he does not know the exact number above which profits can be considered high. Input the same to a computer and the first question it will ask is the cutoff point for 'high profits'. However by assigning confidence (truth-value) equations to the variable profits, the computer may be programmed to think in a more human way. Segregation of data can be most effectively carried out by fuzzy logic. Most of the natural systems are inherently fuzzy.

Fuzzy logic is very useful in areas where a large number of factors have to be considered to arrive at a conclusion The different weightages of these factors and their overall contribution to the final result can be effectively summed up through fuzzy equations.

Get introduced to this very interesting concept

Fuzzy logic and SURVEYS?? Is it possible to relate these diverse fields? Read and find out.

Some of the best books on this subject that I've come across

A few interesting links on fuzzy logic

.