Fuzzy sets allow for degrees of membership between 0 and 1, unlike conventional sets which have binary membership. A fuzzy set is a pair consisting of a universe of discourse and a membership function that assigns a value between 0 and 1 to each element in the universe. Fuzzy logic extends Boolean logic to handle imprecise and uncertain information using these fuzzy sets and degrees of membership. Fuzzy sets and logic have applications in areas like aerospace, automotive, business, electronics, and more to model imprecise concepts.

1. BY,
K.B.Snega,M.sc(cs).,

2.  Fuzzy sets are somewhat like a sets whose
element have degree of membership.
 Fuzzy sets were introduced by Lotfi A.
Zadeh and Dieter Klaua in 1965.

3.  In set theory many degree of membership
between 0 and 1 are allowed.
 A fuzzy set is a pair (U,m)
m:U→[0,1] Where,
U-universe of discourse.
x∈U,m(x) is grade of membership of x.
 The function m=µ(A) is the membership
function.

5. Fuzzy logic definition:
 A branch of logic that uses degrees of
membership in sets rather than strict true/false
membership.
 A tool to represent imprecise, ambiguous, and
vague information.
 Its power is the ability to perform meaningful
and reasonable operations.
 It extends conventional Boolean logic to
recognize partial truths and uncertainties.

9. Union:

10. INTERSECTION:

11. complement difference

14. Procedure for fuzzy controller

17.  Fuzzy set is flexible to use.
 Fuzzy set is conceptually easy to understand.
 Fuzzy set is tolerant of imprecise data.
 Fuzzy set is based on Natural language.

18. Fuzzy sets are used in the following areas,
 In Aerospace, To control the altitude of
Spacecraft.
 In Automotive, we use fuzzy for traffic control.
 In Business, used for decision making support
system.
 In electronics, used for Air Conditioning,
Washing machine timing and so on.
 In finance, used for fund management.
 Fuzzy is used in many areas such as defence,
Industries, Marine, Medical etc.