Introduction to fuzzy logic ME Sem II G.Anuradha

Syllabus Fuzzy Set Theory – Fuzzy set – Membership – operations – properties – Fuzzy relations

What is fuzzy? Do we require precision for all tasks? Name some tasks which do not require precision? Precision comes with high cost, so why cant we exploit the tolerance for imprecision. There comes in an optimized solution to the problem in hand.

Historical Perspective Till late nineteenth century, uncertainty represented undesirable state which had to be avoided But with statistical mechanics, probability theory became an quantifying factor for uncertainty. This was further supplement by Lofti Zadeh in 1965 which challenged not only probability theory as the sole representative of uncertainty but the foundation of probability.

Problems with little information are said to be ill-posed, complex or not sufficiently known. These problems are – Fuzzy – Vague – Ambiguous – Any form of ignorance – Due to natural variability

Difference between the key words I shall return soon-Vague (linguistic) I shall return in few minutes- Fuzzy I shall return within 2 minutes of 6 pm. – Uncertainty which has a quantifiable imprecision-can be handled by probability theory Vague proposition is fuzzy but the converse need not be true

Where can I use a fuzzy system? In situations involving highly complex systems whose behaviors are not well understood Situation where an approximate, but fast solution is warranted.

Limitations of fuzzy systems Fuzzy system are described for shallow models which are deductive in nature(tic-tac-toe) There are not suitable for deep models which are inductive in nature(Chess) The nature of uncertainty is very important that engineers should ponder prior to their selection of an appropriate method to express it. Here comes fuzzy sets which provides a mathematical way to represent vagueness

What is a classical set? Fuzzy sets are a generalization of classical sets.