Lotusland of Mathematical Dreams

This was one subject which kept haunting me through out the engineering curriculum. Not only was that my ma’am, teaching the subject, make any sense; but also, the text book, reminded me more of heiroglyphics.

Life went on smoothly, after some how I managed to pass the paper. Finally a job demanded me to shift to a far off place, requiring me to take care of myself. Its all easy I thought. All except a single job, washing. I hated washing. So I decided to buy one of the best washing machines around (all that my pocket could afford, though).

Seeing me, the shop keeper greeted me so well. I threw at him all my requirements. So he showed me a beautiful washing machine (which I hope works). It had a lot of features, gratifying the needs of the lazy soul inside me. He said it had an additional feature, it can automatically decide on the amount of water, detergent and all such inputs required, which is supported by fuzzy logic. Think of the devil, and here comes the devil himself. This theory, has decided with whatever mind it had, not to leave me alone, till my grave may be.

Even my shopkeeper keeps talking about fuzzy logic and its uses. The engineer inside me got hurt a lot. So a decision came to browse through a couple of pages on the web till I can spell the word fuzzy logic in a proper way.

I am now in my office. Is this sentance true. It is true if I am inside the office. It is false if I am outside the office. So what will happen if I am at the gate. It is partly true and partly false. Just like a half full glass is half empty too.

In normal, classic logic, every statement, proposition, has a value of 0 or 1, depending on it is true or false. So in a situation like the one mentioned previously, we cant assign a proper value like this. The value is 0.5 in that case.

Now, think of a statement P. Its truth value assignment is p. p=1 means the statement is true. p=0 means the statement is false. Here comes fun, think of those paradox that your friends used to bombard you with. Think, of a statement like, “this statement is false”.

Let’s call that statement P. Its truth value is p. The truth value for the converse of P (i.e. Not-P) is (1-p). The statement says, in words, that the truth value of P is (1-p). This means if p=0, p becomes (1-0) =1 and if p=1, (1-p) gives 0. So the value of p keeps oscillating. The only case where this becomes true is when p=0.5. That is permissible with fuzzy logic.