What is Fuzzy Set ?

• 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 set 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.