The aim of this paper is to introduce and study new classes of FP-multifunctions, called FP-lower (upper) irresolute and semi-irresolute, FP-presemi-open and FP-weak semi-open multifunctions, where the domain of these functions is a classical bitopological space with their values as arbitrary L-fuzzy sets in L-fuzzy bitopological space in view of Šostak’s sense. Also, we prove several characterizing theorems for these functions from different angles and we establish various properties of these multifunctions along with their mutual relationships.
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