Fuzzy Logic - A Practical Way Forward

- Debarshi Brahma

Electrical Engineering, PG-1

What if I asked you- “Are you going out to watch a movie today?” Your answer would probably be a simple 'yes' or a 'no'. Now, suppose you come back after watching the movie, and I ask you – “How was the movie?” What would be your answer? The answer this time cannot be a simple yes or a no. It might have been good, or very good, or even bad. Such questions which can have a plethora of variations of answers are common in our day-to-day lives. This gave rise to a new frontier, which was about to change a lot in the fields of applied maths, artificial intelligence, and many more. So, hold on to seatbelts and get ready to delve deeper.

It is amazing how binary systems (with a bivalued logic of 0 or 1), alone revolutionized the field of digital systems. Bivalent logic was first proposed by Aristotle, where he asserted that each event can be either true or false. In case of future events (or propositions as he called them), we have to wait for the outcome to be any of these two results. In other words, logic realizes itself afterward.

Einstein’s observations about maths and reality raise the question of just how well our maths and science is able to describe the world we live in. They try to fit all the phenomena in the logical framework through equations and rules. But the world we live in is uncertain, messy, and can be technically called stochastic (or probabilistic), which contains not only black and white but also the grey regions in between. As the great philosopher David Hume once noted, "just because the sun always rises, doesn’t mean it will necessarily do so tomorrow". This ‘’greyness’’ is the key thought behind fuzzy logic development.

The concept was first proposed by Lotfi A. Zadeh, a brilliant mathematician and electrical engineer at the University of California, Berkeley in 1965. He was the proponent of not only fuzzy mathematics but also Z-Transforms, a widely used technique in signal processing. In the 1960s, he was working on helping computers understand natural languages, which like the above questions, does not limit itself to 0 &1. To represent the various degrees of truths (or falses) involved, he proposed the use of Membership Grades. Let us see what these grades mean.

In classical set theory, any element can be either inside the set or outside it. So,

IA(x) = 1 , if x lies inside the set A, IA(x) = 0, if x lies outside set A.

But suppose x is 70 percent inside A, and 30 percent outside. Then we proceed to say that x is in A with a membership grade of 0.7. Now, this logic can be extended to practical questions too. For instance, “How tall is he?”. According to classical sets, suppose I assign the demarcation as 6 ft. If he is greater than 6 ft, he is tall (yes), otherwise, the answer is a ‘no’. But what about someone who is 5 ft 11 inches? Is the short according to this logic? Isn’t this bizarre and impractical? The tallness may vary from person to person and is easily assigned by fuzzy sets. I can say 6 ft is ‘tall’ with a degree of membership=0.9, whereas 5 ft 11 inches is ‘tall’ with a degree=0.85. The fuzzy set can be written as tall(height) = { 0.85/5’11’’, 0.9/6’ }. Thus, Fuzzy Logic is remarkable in the way it parallels the human thought system.

This is a brief diagram of a fuzzy system. We have an input that takes crisp values (yes and no). Then we fuzzify them (add membership grades to them). So, as a result, we get fuzzy sets. Then, comes the inference block. This is where the magic happens. Basically, we have a set of rules in the rule base, based on which we infer an output. Take a washing machine system, for instance, the rules can be designed as - IF clothes are dirty, THEN add more detergent. Or maybe, IF clothes very dirty, THEN spin very fast. Then comes the defuzzifier converts the result once again into crisp value, so that a decided action is performed based on the inference.

APPLICATIONS

Fuzzy Logic with its ability to handle uncertainties is widely used in the engineering and scientific worlds. Even simple daily objects like washing machines, air conditioners use them nowadays. Japan was the first country to make a subway out of fuzzy logic. The trains sense the weight onboard, how fast the train is going, the suspensions, all sorts of things to make sure that it maintains a smooth and error-free journey. It is reportedly 10 % more efficient than human-controlled trains. Tesla, Uber is relentlessly working towards bringing the fuzzy theory into their autonomous, driverless cars. Thus, fuzzy theory, which acts as a bridge between traditional maths and the ‘humanlike’ behaviors, is not only a theory but a new way to look at the world. It presents a practical way to solve real-life problems; sometimes it just takes some common sense and a bit of fuzzy thinking.