Bases and intersection generation groups of polytomous knowledge structures

In polytomous KST, each item can be assigned a different response scale, and the individual's answer to items reflects the individual's understanding level of knowledge. The polytomous knowledge space can be described by its basis, and the polytomous closure space can be represented by its minimal intersection generation group. The basis of a polytomous knowledge space based on different response scales is composed of its atoms, while the minimal intersection generation group of a polytomous closure space is composed of all intersection generators. Based on polytomous knowledge structures of different response scales of items, the polytomous knowledge state of an individual can be evaluated in the finite steps of item tests. Based on polytomous knowledge structures of different response scales of items, the polytomous knowledge state of an individual can be evaluated by testing some items so as to guide learning of individuals.