AI - a Guide to Intelligent Systems.pdf - Member of EEPIS

102
FUZZY EXPERT SYSTEMS
Example:
tall men OR tall men ¼ tall men
tall men AND tall men ¼ tall men
Identity
A [ =O ¼ A
A \ X ¼ A
A \ =O ¼ =O
A [ X ¼ X
Example:
tall men OR undefined ¼ tall men
tall men AND unknown ¼ tall men
tall men AND undefined ¼ undefined
tall men OR unknown ¼ unknown
where undefined is an empty (null) set, the set having all degree of memberships
equal to 0, and unknown is a set having all degree of memberships equal
to 1.
Involution
:ð:AÞ ¼A
Example:
NOT (NOT tall men) ¼ tall men
Transitivity
If ðA BÞ\ðB CÞ then A C
Every set contains the subsets of its subsets.
Example:
IF (extremely tall men very tall men) AND (very tall men tall men)
THEN (extremely tall men tall men)
De Morgan’s Laws
:ðA \ BÞ ¼:A [:B
:ðA [ BÞ ¼:A \:B