Degree of F-irresolute function in (L, M)-fuzzy topological spaces

In this paper, we present a new vision for studying ${F}$-open, ${F}$-continuous, and ${F}$-irresolute function in $(L,M)$-fuzzy topological spaces based on the implication operation and $(L,M)$-fuzzy ${F}$-open operator cite{2}. These kinds of functions are generalized with their elementary properties to $(L,M)$-fuzzy topological spaces setting based on graded concepts. Moreover, a systematic discussion of their relationship with the degree of $mathbf{F}$-compactness, ${F}$-connectedness, ${F}T_1$, and ${F}T_2$ is carried out.}