Semiset

Semiset

In set theory, a semiset is a proper class which is contained in a set.The theory of semisets was proposed and developed by Czech mathematicians Petr Vopěnka and Petr Hájek. It is based on a modification of the von Neumann-Bernays-Gödel set theory; in standard NBG, the existence of semisets is precluded by the axiom of separation. Semisets can be used to represent sets with imprecise boundaries.

The theory of semisets is more general than fuzzy set theory. Vilém Novák studied the relationship between semisets and fuzzy sets. The concept of semisets leads into a formulation of an alternative set theory. It is a complicated theory, so it has to be approximated by fuzzy sets in many practical applications.

References

*Vopěnka, P., and Hájek, P. The Theory of Semisets. Amsterdam: North-Holland, 1972.
*Novák, V. "Fuzzy sets - the approximation of semisets." Fuzzy Sets and Systems 14 (1984): 259-272.


Wikimedia Foundation. 2010.

Игры ⚽ Нужно сделать НИР?

Look at other dictionaries:

  • Alternative set theory — Generically, an alternative set theory is an alternative mathematical approach to the concept of set. It is a proposed alternative to the standard set theory. Some of the alternative set theories are: *the theory of semisets; *rough set theory;… …   Wikipedia

  • List of mathematics articles (S) — NOTOC S S duality S matrix S plane S transform S unit S.O.S. Mathematics SA subgroup Saccheri quadrilateral Sacks spiral Sacred geometry Saddle node bifurcation Saddle point Saddle surface Sadleirian Professor of Pure Mathematics Safe prime Safe… …   Wikipedia

  • List of set theory topics — Logic portal Set theory portal …   Wikipedia

  • Petr Hájek — (* 6 February 1940, Prague) is a Czech scientist in the area of mathematical logic [http://www.radio.cz/cz/clanek/91701 Český rozhlas in Czech] and a professor of mathematics. He worked in the Department of Computer Science at the Academy of… …   Wikipedia

Share the article and excerpts

Direct link
… Do a right-click on the link above
and select “Copy Link”