In this paper, we will introduce the notions of semiopenness, semicontinuity, preopenness, precontinuity, irresolutness and preirresolutness degree of functions in (L, M)-fuzzy topological spaces based on the implication operation. Their elementary properties in topology will be extended to the setting of (L, M)-fuzzy topology through graded concepts. Further we characterize and discuss their relationships with the degree of semi(pre)-compactness, semi(pre)-connectedness, Semi - T1, Pre - T1, Semi - T2, and Pre - T2.
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