<s>
Fuzzy	B-General_Concept
set	I-General_Concept
operations	I-General_Concept
are	O
a	O
generalization	O
of	O
crisp	O
set	O
operations	O
for	O
fuzzy	O
sets	O
.	O
</s>
<s>
The	O
most	O
widely	O
used	O
operations	O
are	O
called	O
standard	O
fuzzy	B-General_Concept
set	I-General_Concept
operations	I-General_Concept
;	O
they	O
comprise	O
:	O
fuzzy	O
complements	O
,	O
fuzzy	O
intersections	O
,	O
and	O
fuzzy	O
unions	O
.	O
</s>
<s>
i	O
is	O
a	O
t-norm	B-General_Concept
,	O
</s>
<s>
u	O
is	O
a	O
t-conorm	B-General_Concept
(	O
aka	O
s-norm	O
)	O
,	O
</s>
<s>
Axioms	O
i1	O
up	O
to	O
i4	O
define	O
a	O
t-norm	B-General_Concept
(	O
aka	O
fuzzy	O
intersection	O
)	O
.	O
</s>
<s>
The	O
standard	O
t-norm	B-General_Concept
min	O
is	O
the	O
only	O
idempotent	O
t-norm	B-General_Concept
(	O
that	O
is	O
,	O
i	O
(	O
a1	O
,	O
a1	O
)	O
=	O
a	O
for	O
all	O
a	O
∈	O
 [ 0 , 1 ] 	O
)	O
.	O
</s>
<s>
Axioms	O
u1	O
up	O
to	O
u4	O
define	O
a	O
t-conorm	B-General_Concept
(	O
aka	O
s-norm	O
or	O
fuzzy	O
union	O
)	O
.	O
</s>
<s>
The	O
standard	O
t-conorm	B-General_Concept
max	O
is	O
the	O
only	O
idempotent	O
t-conorm	B-General_Concept
(	O
i	O
.	O
e	O
.	O
u	O
(	O
a1	O
,	O
a1	O
)	O
=	O
a	O
for	O
all	O
a	O
∈	O
 [ 0 , 1 ] 	O
)	O
.	O
</s>
<s>
Aggregation	O
operations	B-General_Concept
on	I-General_Concept
fuzzy	I-General_Concept
sets	I-General_Concept
are	O
operations	O
by	O
which	O
several	O
fuzzy	O
sets	O
are	O
combined	O
in	O
a	O
desirable	O
way	O
to	O
produce	O
a	O
single	O
fuzzy	O
set	O
.	O
</s>
