# equivalence class

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## equivalence class

(mathematics)
An equivalence class is a subset whose elements are related to each other by an equivalence relation. The equivalence classes of a set under some relation form a partition of that set (i.e. any two are either equal or disjoint and every element of the set is in some class).
References in periodicals archive ?
(1994) paired an abstract picture, member of an equivalence class, with mild electric shock (US) that elicited a galvanic skin response (GSR).
Assuming that the first n facets intersect at a vertex, we can choose a representative [LAMBDA] = ([I.sub.n]|[[LAMBDA].sub.*]) for the D-J equivalence class of [lambda], where [I.sub.n] is the n x n identity matrix and [[LAMBDA].sub.*] is an n x(m - n) matrix.
If [alpha] = < a, [[mu].sub.[alpha]], [v.sub.[alpha]] > [epsilon] IF[[rho].sub.S](R), then we refer to the equivalence class of [mathematical expression not reproducible], and we refer to the family of all equivalence classes of a modulo [mathematical expression not reproducible].
If (u, v) [member of] R, it indicates that the objects u and v belong to the same equivalence class with the equivalence relation R; they are indiscernible.
In a similar way as before, [[alpha]] [conjunction] will denote the equivalence class with respect to ~[conjunction] that contains [alpha].
However, the product may contain functionally dependent components that have to be found and removed, which just means finding the simplest representative in the equivalence class for [alpha] x [beta].
The data, which is replaced by the equivalence class in the anonymization protection algorithm, is more likely to be found in its own laws, is usually used to reflect the development of the object, and is conducive to data mining for partners.
As an application of the main results, it is shown that if we identify every fuzzy number with the corresponding equivalence class, there would be more differentiable fuzzy functions than what is found in the literature.
Figure 3b is a partition with four equivalence classes, and each equivalence class has four points.
So the next level of privacy has been provided using the method called l-diversity  which contains l well represented distinct values within an equivalence class. Though privacy is improved in the l diversity method, it suffers from similarity attack and skewness attack.
Specifically, the sample can be two stimuli of the same equivalence class or two stimuli of distinct classes.

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