Wireless Sensor and Actuator Networks for Lighting Energy ...

A is empty f A
(x) = 0, x X (3.1)
Equality:
Two fuzzy sets A and B are equal if and only if the membership functions are
identical for all x in X.
Complement:
Containment:
A = B f A
(x) = f B
(x), x X (3.2)
The complement of the fuzzy set A is denoted as A´ and is defined by
f A
(x) = 1 f A
(x), x X (3.3)
The fuzzy set A is contained in fuzzy set B or is a subset of B, if and only if f A (x)
f B (x) for all x in X.
Union:
A B f A
(x) f B
(x), x X (3.4)
The union of two fuzzy sets A and B with the membership functions f A (x) and
f B (x) respectively is a fuzzy set C ( C = A B ) with corresponding membership
function:
Intersection:
f C
(x) = max{ f A
(x), f B
(x)}, x X (3.5)
The intersection of two fuzzy sets A and B with the membership functions f A (x)
and f B (x) respectively is a fuzzy set C ( C = A B ) with corresponding membership
function :
De Morgan’s laws:
f C
(x) = min{ f A
(x), f B
(x)}, x X (3.6)
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