Tolerance relation
Encyclopedia
In mathematics, a tolerance relation is a relation
that is reflexive
and symmetric
. It does not need to be
transitive
.
http://mizar.org/fm/1991-2/pdf2-1/toler_1.pdf FORMALIZED MATHEMATICS, Vol. 2, No. 1, January–February 1991.
Binary relation
In mathematics, a binary relation on a set A is a collection of ordered pairs of elements of A. In other words, it is a subset of the Cartesian product A2 = . More generally, a binary relation between two sets A and B is a subset of...
that is reflexive
Reflexive relation
In mathematics, a reflexive relation is a binary relation on a set for which every element is related to itself, i.e., a relation ~ on S where x~x holds true for every x in S. For example, ~ could be "is equal to".-Related terms:...
and symmetric
Symmetric relation
In mathematics, a binary relation R over a set X is symmetric if it holds for all a and b in X that if a is related to b then b is related to a.In mathematical notation, this is:...
. It does not need to be
transitive
Transitive relation
In mathematics, a binary relation R over a set X is transitive if whenever an element a is related to an element b, and b is in turn related to an element c, then a is also related to c....
.
External links
- Gerasin, S. N., Shlyakhov, V. V., and Yakovlev, S. V. 2008. Set coverings and tolerance relations. Cybernetics and Sys. Anal. 44, 3 (May 2008), 333–340. DOI= http://dx.doi.org/10.1007/s10559-008-9007-y
- Hryniewiecki, K. 1991, Relations of Tolerance
http://mizar.org/fm/1991-2/pdf2-1/toler_1.pdf FORMALIZED MATHEMATICS, Vol. 2, No. 1, January–February 1991.