equivalence classes

equivalence classes

[i′kwiv·ə·ləns ‚klas·əs]
(mathematics)
The collection of pairwise disjoint subsets determined by an equivalence relation on a set; two elements are in the same equivalence class if and only if they are equivalent under the given relation.
McGraw-Hill Dictionary of Scientific & Technical Terms, 6E, Copyright © 2003 by The McGraw-Hill Companies, Inc.
References in periodicals archive ?
Mizael, Santos, & de Rose, 2016) may transfer across members of equivalence classes, so that humans may exhibit attitudes toward objects with which they have no direct experience.
in [2], Choi constructs a bijection between the set of Davis-Januszkiewicz equivalence classes of small covers over an n-cube and the set of acyclic digraphs with n-labeled nodes.
Also, their equivalence classes are given and studied.
The accuracy of equivalent partitions in knowledge characteristics is studied and the difference in equivalence classes is analyzed.
Because of Corollary 5.8, we know that [[gamma].sub.nk](A) will be a singleton whenever D is invertible, so in that case, these boosting functions are well-defined on the equivalence classes. Note that it might also not necessarily be true that a [[gamma].sub.nk]([[A].sub.k]), by which we mean the set
The main object in functions' algebra is the set of vector functions, divided into equivalence classes, which form a lattice.
Ellis avowedly follows Paul Churchland's thesis that higher levels of hierarchical organization, including mental phenomena, are Platonic entities that can best be viewed as "equivalence classes." Complex systems are typically multiply realizable; that is, many lower level states instantiate the "same" abstract category--a wide array of amino acid, cellular, or neurological configurations can instantiate the same biological function, meaning, idea, or intention, for example.
Input: RTST([t.sub.th]) and [mathematical expression not reproducible]; Output: Substgrp; % the set of equivalent class BEGIN (1) Substgrp = 0; (2) FOR each r in R' (3) [t.sub.s] = r; (4) if [t.sub.s] < [t.sub.th] then (5) [mathematical expression not reproducible] % The set of equivalence classes with sampling interval of [t.sub.s] is obtained.
We start this section by recalling some pertinent concepts and key lemmas from the function of bounded variation, fuzzy numbers, and fuzzy number equivalence classes which will be used later.
Figure 3b is a partition with four equivalence classes, and each equivalence class has four points.