In a real-life problem with some ambiguity, the ‘fuzzy entropy’ measures the total amount of ambiguity associated with the fuzzy set. Analogous to this, a fuzzy knowledge measure may be considered for the total amount of precision present in a fuzzy set. Cognitively, fuzzy entropy and fuzzy knowledge measure seem to be dual concepts. We establish the duality of weighted fuzzy knowledge measure and weighted fuzzy entropy through characterization theorems. In many situations, every element of the universe of discourse may not be equally important for the expert. Therefore, a certain weight may be assigned to a particular member of the universe of discourse. In this work, we introduce a weighted fuzzy knowledge measure and demonstrate the effectiveness of the weighted fuzzy knowledge measure through a comparative study. We also discuss the application of the proposed weighted fuzzy knowledge measure in multi-attribute decision-making (MADM).
