Consider a heap of sand. Remove a grain from it. Is it still a heap? Keep on removing grains from it, till what point it is a heap and exactly at what point it ceases to be a heap? Exactly which grain changes it from heap to non-heap? This is known as Sorites Paradox.
If a person starts plucking hair from his head, the person is not bald after plucking first hair, nor after plucking second hair. Then exactly when we can say that person is starting to get bald?
Aristotelian logic ie the binary logic defines everything in TRUE or FALSE, BLACK or WHITE manner. An element either belongs to the set A or it does not belong to set A, ie A or not-A, it can not be both. A statement can only be true or false, there is nothing in between.
If we observe the world around us, there is vagueness, there is ambiguity. Things can not always be classified as Black or White but most of the times they have shades.Most of the times human beings think and communicate in gradation and not in crisp manner. In our thought process or the natural languages, meaning of the words is often vague and even when it is well defined, while using the word as a label for a set, the boundaries within which objects belong to or do not belong to a set are vague. A person X does not totally dislike strawberry ice cream, but is not very fond of it either, so she likes it to some degree. Some kids like school very much, some kids completely dislike it, but there are many kids who like some aspects of it and dislike some. Person with age 90 years, is old and person with age 20 years is young, but what about the person with age 35? Is he young or old?
Aristotelian logic falters in the scenario, when terms are not strictly defined. This is where Fuzzy Logic comes into picture.Fuzzy logic defines the terms in more-or-less manner instead of yes-or-no manner.
If we wish to define the set A of tall persons, then we would set a criterion to decide if a person is tall or not. Suppose we decide a person with height 5 feet 9 inches or more belongs to this set then a person with height 5 feet 8 inches does not belong to this set although person does with height 4 feet 1 inch. So, both these people belong to set not-A.
But does that mean the person having height 5 feet 9 inches is tall and person with height 5 feet 8 inch is not tall? Instead of this crisp definition of sets, Fuzzy logic defines the concept of membership. Every element has a membership in the set, taking value between 0 and 1. The person having height 6 feet may have membership value 1, where as the person having height 5 feet 8 inches, may have 0.8 as membership value to this set and so on. So every element belongs to set A and set not-A as well, to some degree. A piece of cloth can not always be either dry or wet, it can be dry to some amount and wet to some extent, weather can be cold to some degree and hot to some degree.
In 1964, Professor Lotfi Zadeh developed the theory of Fuzzy sets. He was the first one to give this theory a definite form, though many thinkers in the past had pondered on this question of non-crisp sets. Buddha, founder of Buddhism, who lived in India around 500 BC, says that world is full of contradictions and almost everything contains some of its opposition, ie things can be A or not-A at the same time. Bertrand Russell had encountered this idea of fuzziness when he stated his paradox.
Today, Fuzzy logic is used in many day-to-day appliances, since it allows more human-like interpretation and reasoning in machines by considering intermediate values between True / False, hot / cold, bright / dark, clean / dirty etc.
Fuzzy washing machines decide the washing cycle required to wash the laundry depending upon its degree of dirtiness. If it is 100% dirty, then say 2 minutes will be added to the basic washing cycle and 1 minute if it is 50% dirty and so on. It can also decide the amount of detergent to be added depending on the above degree of dirtiness of the laundry.
Smart Air-conditioners use fuzzy logic to adjust flow of air according to degree of hotness or coldness. Smart TVs adjust the color and contrast modes. Japan is the leader when it comes to making use of Fuzzy Logic in order to make systems more intelligent.
In future, more and more systems can be built using Fuzzy Logic which incorporates human thinking, experience and reasoning instead of limiting it to only true / false values.