Introduction: -The word "fuzzy" means "vagueness". Fuzziness occurs when the boundary of a piece of information is not clear-cut. Fuzzy sets have been introduced by Lotfi A. Zadeh (1965) as an extension of the classical notion of set. Classical set theory allows the membership of the elements in the se in binary terms, a bivalent condition - an element either belongs or does not belong to the set.
Fuzzy set theory permits the gradual assessment of the membership of elements in a set, described with the aid of a membership function valued in the real unit interval [0, 1].
Example:
Words like young, tall, good, or high are fuzzy.
− There is no single quantitative value which defines the term young.
− For some people, age 25 is young, and for others, age 35 is young.
− The concept young has no clean boundary.
− Age 1 is definitely young and age 100 is definitely not young.
− Age 35 has some possibility of being young and usually depends on the context in which it is being considered.
In real world, there exists much fuzzy knowledge; Knowledge that is vague, imprecise, uncertain, ambiguous, inexact, or probabilistic in nature. Human thinking and reasoning frequently involve fuzzy information, originating from inherently inexact human concepts. Humans, can give satisfactory answers, which are probably true. However, our systems are unable to answer many questions. The reason is, most systems are designed based upon classical set theory and two-valued logic which is unable to cope with unreliable and incomplete information and give expert opinions. our systems should also be able to cope with unreliable and incomplete information and give expert opinions. Fuzzy sets have been able provide solutions to many real world problems. Fuzzy Set theory is an extension of classical set theory where elements have degrees of membership.
Fuzzy Set Theory
Fuzzy set theory is an extension of classical set theory where elements have varying degrees of membership. A logic based on the two truth values, True and False, is sometimes inadequate when describing human reasoning. Fuzzy logic uses the whole interval between 0 (false) and 1 (true) to describe human reasoning.
− A Fuzzy Set is any set that allows its members to have different degree of membership, called membership function, in the interval [0 , 1].
- The degree of membership or truth is not same as probability; fuzzy truth is not likelihood of some event or condition. Fuzzy truth represents membership in vaguely defined sets.
− Fuzzy logic is derived from fuzzy set theory dealing with reasoning that is approximate rather than precisely deduced from classical predicate logic.
− Fuzzy logic is capable of handling inherently imprecise concepts.
− Fuzzy logic allows in linguistic form the set membership values to imprecise concepts like "slightly", "quite" and "very".
− Fuzzy set theory defines Fuzzy Operators on Fuzzy Sets.
