In the present paper, we first introduced the notion of
k-fuzzy
-open (
k-
-
-open) sets as a generalized novel class of fuzzy open (
-open) sets on fuzzy topological spaces (
) in
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In the present paper, we first introduced the notion of
k-fuzzy
-open (
k-
-
-open) sets as a generalized novel class of fuzzy open (
-open) sets on fuzzy topological spaces (
) in the sense of Šostak. The class of
k-
-
-open sets is contained in the class of
k-
-
-open sets and contains all
k-
-semi-open and
k-
-pre-open sets. Also, we introduced the closure and interior operators with respect to the classes of
k-
-
-closed and
k-
-
-open sets and discussed some of their properties. After that, we defined and studied the notions of
-
-continuous (resp.
-
-irresolute) functions between
and
. However, we displayed and investigated the notions of
-almost (resp.
-weakly)
-continuous functions, which are weaker forms of
-
-continuous functions. Next, we presented and characterized some new
-functions via
k-
-
-open and
k-
-
-closed sets, called
-
-open (resp.
-
-irresolute open,
-
-closed,
-
-irresolute closed, and
-
-irresolute homeomorphism) functions. The relationships between these classes of functions were investigated with the help of some examples. We also introduced some new types of
-separation axioms called
k-
-
-regular (resp.
k-
-
-normal) spaces via
k-
-
-closed sets and discussed some properties of them. Lastly, we explored and studied some new types of
-compactness called
k-
-almost (resp.
k-
-nearly)
-compact sets.
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