Abstract
We define the generalized fuzzy neighbourhood systems onthe set of fuzzy points in a nonempty setXand investigate their properties by using a new interior operator. With the help of these conceptswe introduce generalized fuzzy continuity, which include many of thevariations of fuzzy continuity already in the literature, as special cases
Highlights
A neighbourhood system assigns each object a family of nonempty subsets
This paper introduces generalized neighbourhood systems on the set of fuzzy points of a nonempty set
We focus our work to extend the notions of the generalized neighbourd system to the fuzzy settings
Summary
A neighbourhood system assigns each object a (possibly empty, ...nite or in...nite) family of nonempty subsets. Neighbourhoods play the most fundemantel role in mathematical analysis It is a common and intuitive notion. This paper introduces generalized neighbourhood systems on the set of fuzzy points of a nonempty set. We de...ne the generalized fuzzy neighbourhood systems on the set of fuzzy points in a nonempty set X and investigate their properties by using a new interior operator which corresponds to the notion of the interior operator in general form and gives us the way to show that every generalized fuzzy topology can be generated by a generalized fuzzy neighbourhood system. We introduce generalized fuzzy continuity with the help of generalized fuzzy neighbourhood systems These notions lead us to give a general form to various concepts discussed in the literature
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