Conditions that the quotient of $L$-fuzzy up-sets forms a complete lattice

Peng He; Xue-ping Wang

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arXiv · 1610.09305

Conditions that the quotient of $L$-fuzzy up-sets forms a complete lattice

Peng He·Xue-ping Wang

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Abstract

This paper deals with conditions under which the quotient of $L$-fuzzy up-sets forms a complete lattice by using terminologies of closure operators. It first gives a condition that a family of some subsets of a nonempty set can be represented by $L$-fuzzy up-sets, which is then used to formulate a necessary and sufficient condition under which the quotient of $L$-fuzzy up-sets forms a complete lattice. This paper finally shows that the quotient of a kind of $L$-fuzzy up-sets is isomorphic to an interval generated by an $L$-fuzzy up-set.

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BibTeX RIS

Peng He, Xue-ping Wang. 2016-10-25. Conditions that the quotient of $L$-fuzzy up-sets forms a complete lattice. https://arxiv.org/abs/1610.09305

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