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.


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