Formal concept analysis offers a powerful framework for studying knowledge space theory. This paper makes three key constructions. First, theoretical advancement: We establish a novel connection between skill maps and formal contexts by introducing fuzzy skill context. Our primary theoretical innovation is the development of fuzzy disjunctive formal concepts, which create new linkages between KST and FCA. Second, framework construction: We propose a new fuzzy skill mapping with rigorous mathematical justification. Integrate this mapping with fuzzy formal contexts to build fuzzy skill contexts and fuzzy disjunctive formal concepts. Develop methods for constructing knowledge states and assessing competence states. Third, practical applications: We present two learning path generation algorithms based on the master fringe of current knowledge states and competence states, respectively. Experimental results demonstrate their effectiveness in real-world applications.