Wireless Sensor and Actuator Networks for Lighting Energy ...

De Morgan’s laws in the traditional set theory also hold in fuzzy set theory with
the operations of complement, union, and intersection.
(A B) = A
B
(A B) = A
B
(3.7)
Distributive laws:
theory.
The distributive laws in the traditional set theory also apply to the fuzzy set
C (A B) = (C A) (C B)
C (A B) = (C A) (C B)
(3.8)
Algebraic product:
The algebraic product of two fuzzy sets A and B with the membership functions
f A (x) and f B (x) is denoted by AB whose membership function is
f AB
(x) = f A
(x) f B
(x), x X (3.9)
Algebraic sum:
The algebraic sum of two fuzzy sets A and B with the membership functions
f A (x) and f B (x) is denoted by A+B whose membership function is
f A+ B
(x) = f A
(x) + f B
(x), x X (3.10)
The algebraic sum is only meaningful if f A+B (x) is less than or equal to unity for all x in
X.
Absolute difference:
The absolute difference of two fuzzy sets A and B with the membership
functions f A (x) and f B (x) is denoted by |A-B| whose membership function is
f A B
(x) = f A
(x) f B
(x) , x X (3.11)
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