monoid

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monoid

[′mä‚nȯid]
(mathematics)
A semigroup which has an identity element.

monoid

An operator * and a value x form a monoid if * is associative and x is its left and right identity.
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A t-norm is a continuous mapping * : [0,1] x [0,1] [right arrow] [0,1] such that ([0,1], *) is abelian monoid with unit one and c * d [greater than or equal to] a * b if c [greater than or equal to] a and d [greater than or equal to] b for all a, b, c [member of] [0,1].
The last requirement comes from the fact that, given only the global transition function, we want to be able to isolate the influence of one cell; that is why we demand that + have an identity element, which makes now ([SIGMA], +) an abelian monoid.