Problems in the real world turn out to be quite complex, due to uncertainty in the parameters that define the problem and due to uncertainty in the situations in which that particular problem occurs.
Probability theory is an age old theory, which excellently handles this uncertainty. But this probability theory can be applied only to situations whose occurrence of events is greatly determined by random process.Fuzzy Set Theory exhibits immense potential for effective solving of the uncertainty in the problem. The fuzzyness means “vagueness” or “ambiguity” or “uncertainty”. Fuzzy Set Theory is an excellent mathematical tool to handle uncertainty occurred due to vagueness.
Professor Lotfi A. Zadeh of the University of California introduced this fuzzy set theory in 1965.
Unlike crisp situations, fuzzy situations cannot be well-defined as there is always some uncertainty involved in them. Here are some of the examples of crisp situations and fuzzy situations:
Examples of Crisp situations:
- Is water colorless?
- Sun always rises in the East and sets in the West.
- Is milk white in color?
- Is honey sweet?
Examples of Fuzzy situations.
- Is ramaraobobby reliable?
- Is Google Chrome the best web browser?
- Is Wonderful Tech Stuff the best tech blog in India?
First, in all the example of crisp situations above the answer is well-defined which means, it can be either be Yes or No but can never be both to anyone anywhere. Whereas in the case of fuzzy situations, there is some ambiguity involved in them as the answer depends on various factors that will change with time. Thus fuzzy situations are said to be vague and uncertain in their definition.