Two experiments investigated possible interactions between existing equivalence relations among stimuli and the acquisition of simple discriminations involving the same stimuli. During the first phase of Experiment 1, two adult humans learned two sets of six conditional relations among arbitrary visual stimuli designed to produce two independent sets of three, three-member equivalence classes (...

In this paper, the notions of $(T,S)$-composition matrix and$(T,S)$-interval-valued intuitionistic fuzzy equivalence matrix areintroduced where $(T,S)$ is a dual pair of triangular module. Theyare the generalization of composition matrix and interval-valuedintuitionistic fuzzy equivalence matrix. Furthermore, theirproperties and characterizations are presented. Then a new methodbased on $tilde{...

Let X be a proper scheme over a field K. There are two ways of organizing the points of X into equivalence classes using rational curves. One is the notion of R-equivalence introduced by [Manin72]. Two points x1, x2 ∈ X(K) are called directly R-equivalent if there is a morphism p : P → X with p(0:1) = x1 and p(1:0) = x2. This generates an equivalence relation called R-equivalence. The set of R-...

A Borel equivalence relation on a Polish space is countable if all of its equivalence classes are countable. Standard examples of countable Borel equivalence relations (on the space of subsets of the integers) that occur in recursion theory are: recursive isomorphism, Turing equivalence, arithmetic equivalence, etc. There is a canonical hierarchy of complexity of countable Borel equivalence rel...

In this article we deal with the notion of equivalence relation. The main properties of equivalence relations are proved. Then we define the classes of abstraction determined by an equivalence relation. Finally, the connections between a partition of a set and an equivalence relation are presented. We introduce the following notation of modes: Equivalence Relation, a partition. [4] provide the ...