Fuzzy set operations

A fuzzy set operation is an operation on fuzzy sets. These operations are generalization of crisp set operations. There is more than one possible generalization. The most widely used operations are called "standard fuzzy set operations". There are three operations: fuzzy complements, fuzzy intersections, and fuzzy unions.
Standard fuzzy set operations.
Let A and B be fuzzy sets that A,B ⊆ U, u is any element (e.g. value) in the U universe: u ∈ U.
The complement is sometimes denoted by ∁A or A∁ instead of ¬A.
In general, the triple (i,u,n) is called De Morgan Triplet iff
so that for all "x","y" ∈ [0, 1] the following holds true: 
(generalized De Morgan relation). This implies the axioms provided below in detail.
Fuzzy complements.
"μA"("x") is defined as the degree to which "x" belongs to "A". Let "∁A" denote a fuzzy complement of "A" of type "c". Then "μ∁A"("x") is the degree to which "x" belongs to "∁A", and the degree to which "x" does not belong to "A". ("μA"("x") is therefore the degree to which "x" does not belong to "∁A".) Let a complement "∁A" be defined by a function
Axioms for fuzzy complements.
"c" is a "strong negator" (aka "fuzzy complement").
A function c satisfying axioms c1 and c2 has at least one fixpoint a* with c(a*) = a*,
and if axiom c3 is fulfilled as well there is exactly one such fixpoint. For the standard negator c(x) = 1-x the unique fixpoint is a* = 0.5 .
Fuzzy intersections.
The intersection of two fuzzy sets "A" and "B" is specified in general by a binary operation on the unit interval, a function of the form 
Axioms for fuzzy intersection.
Axioms i1 up to i4 define a t-norm (aka fuzzy intersection). The standard t-norm min is the only idempotent t-norm (that is, "i" ("a"1, "a"1) = "a" for all "a" ∈ [0,1]).
Fuzzy unions.
The union of two fuzzy sets "A" and "B" is specified in general by a binary operation on the unit interval function of the form
Axioms for fuzzy union.
Axioms u1 up to u4 define a t-conorm (aka s-norm or fuzzy intersection). The standard t-conorm max is the only idempotent t-conorm (i. e. u (a1, a1) = a for all a ∈ [0,1]).
Aggregation operations.
Aggregation operations on fuzzy sets are operations by which several fuzzy sets are combined in a desirable way to produce a single fuzzy set.
Aggregation operation on "n" fuzzy set (2 ≤ "n") is defined by a function