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 (1972). 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. The concept of semisets opens the way for a formulation of an alternative set theory. Semisets can be used to represent sets with imprecise boundaries.
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- 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 (1972). 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. The concept of semisets opens the way for a formulation of an alternative set theory. Semisets can be used to represent sets with imprecise boundaries. Vilém Novák (1984) studied approximation of semisets by fuzzy sets, which are often more suitable for practical applications of the modeling of imprecision.
- 在集合論中，一個真類稱為半集合，當且僅當它包含在一個集合中。 半集合的理論最早由捷克數學家Petr Vopěnka和Petr Hájek於1972年提出的，在馮諾伊曼-博內斯-哥德爾集合論（NBG）的基礎上作出了變化；日在標準NBG中，分離公理是不允許半集合存在的。半集合的概念開闢了一種作為替代的集合論。 半集合用於表示那些 邊界不明確 的集合。Vilém Novák (1984) 研究了怎樣用模糊集對半集合進行逼近，而這通常也是為不明確性建立數學模型的實際手段。
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- 在集合論中，一個真類稱為半集合，當且僅當它包含在一個集合中。 半集合的理論最早由捷克數學家Petr Vopěnka和Petr Hájek於1972年提出的，在馮諾伊曼-博內斯-哥德爾集合論（NBG）的基礎上作出了變化；日在標準NBG中，分離公理是不允許半集合存在的。半集合的概念開闢了一種作為替代的集合論。 半集合用於表示那些 邊界不明確 的集合。Vilém Novák (1984) 研究了怎樣用模糊集對半集合進行逼近，而這通常也是為不明確性建立數學模型的實際手段。
- 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 (1972). 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. The concept of semisets opens the way for a formulation of an alternative set theory. Semisets can be used to represent sets with imprecise boundaries.
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