:: FUZZY_3 semantic presentation
definition
let C1 be non
empty set ,
C2 be non
empty set ;
func Zmf c1,
c2 -> RMembership_Func of
a1,
a2 equals :: FUZZY_3:def 1
chi {} ,
[:C1,C2:];
correctness
coherence
chi {} ,[:C1,C2:] is RMembership_Func of C1,C2;
by FUZZY_1:13;
func Umf c1,
c2 -> RMembership_Func of
a1,
a2 equals :: FUZZY_3:def 2
chi [:C1,C2:],
[:C1,C2:];
correctness
coherence
chi [:C1,C2:],[:C1,C2:] is RMembership_Func of C1,C2;
by FUZZY_1:2;
end;
:: deftheorem Def1 defines Zmf FUZZY_3:def 1 :
:: deftheorem Def2 defines Umf FUZZY_3:def 2 :
theorem Th1: :: FUZZY_3:1
theorem Th2: :: FUZZY_3:2
theorem Th3: :: FUZZY_3:3
theorem Th4: :: FUZZY_3:4
for
C1,
C2 being non
empty set for
f being
RMembership_Func of
C1,
C2 holds
(
max f,
(Umf C1,C2) = Umf C1,
C2 &
min f,
(Umf C1,C2) = f &
max f,
(Zmf C1,C2) = f &
min f,
(Zmf C1,C2) = Zmf C1,
C2 )
theorem Th5: :: FUZZY_3:5
theorem Th6: :: FUZZY_3:6
theorem Th7: :: FUZZY_3:7