Tolerance relation
In mathematics, a tolerance relation is a relation that is reflexive and symmetric, but not necessarily transitive; a set X that possesses a tolerance relation can be described as a tolerance space.[1] Tolerance relations provide a convenient general tool for studying indiscernibility/indistinguishability phenomena. The importance of those for mathematics had been first recognized by Poincaré.[2]
See also
- Quasitransitive relation—a generalization to formalize indifference in social choice theory
- Rough set
References
- ^ Sossinsky, Alexey (1986-02-01). "Tolerance space theory and some applications". Acta Applicandae Mathematicae. 5 (2): 137–167. doi:10.1007/BF00046585.
- ^ Poincare, H. (1905). Science and Hypothesis (with a preface by J.Larmor ed.). New York: 3 East 14th Street: The Walter Scott Publishing Co., Ltd. pp. 22-23.
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Further reading
- 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:10.1007/s10559-008-9007-y
- Hryniewiecki, K. 1991, Relations of Tolerance, FORMALIZED MATHEMATICS, Vol. 2, No. 1, January–February 1991.
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