idempotent

(redirected from Idempotency)
Also found in: Dictionary, Thesaurus, Wikipedia.

idempotent

[¦i‚dem¦pōt·ənt]
(mathematics)
An element x of an algebraic system satisfying the equation x 2= x.
An algebraic system in which every element x satisfies x 2= x.

idempotent

(1)
A function f : D -> D is idempotent if

f (f x) = f x for all x in D.

I.e. repeated applications have the same effect as one. This can be extended to functions of more than one argument, e.g. Boolean & has x & x = x. Any value in the image of an idempotent function is a fixed point of the function.

idempotent

(2)
This term can be used to describe C header files, which contain common definitions and declarations to be included by several source files. If a header file is ever included twice during the same compilation (perhaps due to nested #include files), compilation errors can result unless the header file has protected itself against multiple inclusion; a header file so protected is said to be idempotent.

idempotent

(3)
The term can also be used to describe an initialisation subroutine that is arranged to perform some critical action exactly once, even if the routine is called several times.

idempotent

An operation that produces the same results no matter how many times it is performed. For example, a database query that does not change any data in the database is idempotent.

Functions can be designed as idempotent if all that is desired is to ensure a certain operation has been completed. For example, with an idempotent delete function, if a request to delete a file is successfully completed for one program, all subsequent requests to delete that file from other programs would return the same success confirmation message. In a non-idempotent delete function, an error would be returned for the second and subsequent requests indicating that the file was not there.
References in periodicals archive ?
We have studied some desirable properties of the IFNIFCOA and IFNIFCOG operators, such as commutativity, idempotency and monotonicity, and applied the IFNIFCOA and IFNIFCOGM operators to multiple attribute decision making with fuzzy number intuitionistic fuzzy information.
D] [Eta]([Eta](f(z))) by idempotency of [Eta]: [Eta](f([Rho](z))) [[is less than or equal to].
Sometimes it denotes binary choice, written [x[U]y, but usually its argument is a set -- either because the profile of [U] in [Sigma] declares it so, or because the appropriate axioms of commutativity, associativity, and idempotency are given.
It can be shown that these definitions of fuzzy union and intersection are the only ones that naturally extend the corresponding standard set theory notions by satisfying all the usual requirements of associativity, commutativity, idempotency, and distributivity (Lemaire, 1990).
Similar to the OWA and the GOWA operators [1, 46], the GITOWD operator has many desirable properties, such as commutativity, monotonicity, boundedness, and idempotency.