Fuzzy Logic can be viewed as a super set of Boolean logic, as a multi-valued logic. It adds degrees between the absolute truth and absolute false to cover partial truth in between. In simple terms, fuzzy logic involves classifying objects and functions into fuzzy sets which could be given linguistic phrases. It is a form of reasoning that is neither exact, nor absolutely inexact. For example, too hot, little slow, phrases which do not give the idea of absolute, but a fuzzy estimate. While 33 degrees might be warm enough for a person from the equator, someone from the arctic might find the heat unbearable, or too hot. It is not possible to classify them into strict sets with defined boundaries which leads to the idea of fuzziness.
It has basically evolved from predicate logic, though many forms called t-norm fuzzy logics do exist in propositional logic too. It generally has an object and a predicate. For example: in the sentence, “Plato is a man”, ‘Plato’ is the object, and “is a man” is the predicate. But an important point about fuzzy logic is that it is deterministic and time-variant. A few salient points explained by Zader Lotfi on fuzzy logic are:
1. Exact reasoning or precise values is the extreme or limiting case of approximate reasoning.
2. Any system which works on logic can be fuzzified and everything would be a matter of degrees.
3. Knowledge is a collection of fuzzy constraints on a group of variables.
The bivalent sets being mutually exclusive it is not possible to have membership of more than one set. This leads to ambiguity in reasoning and perceptions as common sense fails to register the hard line rule. The same phenomenon when explained using fuzzy sets grants degrees of membership in the subsets through a membership function. It can help circumvent the rigorous mathematical modeling in system design.
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