Polytomous knowledge structures constructed by L-fuzzy approximation operators

Rough set theory is more concerned with the character of the upper and lower approximations of a particular set than with the overall structure. Knowledge space theory can provide another new perspective on rough sets. In this paper, we establish a theoretical linkage between polytomous knowledge structures and L-fuzzy approximation operators. We generate polytomous knowledge structures constructed by L-fuzzy approximation operators and give the corresponding properties, and find that a polytomous knowledge space (polytomous closure space, respectively) and can be completely characterized by an upper (lower, respectively) L-fuzzy approximation. In particular, we discuss the dichotomous knowledge structure by the means of fuzzy approximation operators, which corresponds to the method of fuzzy skill maps. Finally, by L-fuzzy relation constructing two particular dichotomous knowledge structures, which are called backward-graded and forward-graded, is also discussed. This study proposes a framework to analyze L-fuzzy rough sets through knowledge space theory, bridging these mathematical disciplines.