Skills and fuzzy knowledge structures

In knowledge space theory (KST), knowledge structure is an effective feature to evaluate individuals’ knowledge and guide future learning. How to construct knowledge structures is one of the key research problems in KST. At present, the knowledge structure has been generalized to the polytomous knowledge structure. This article mainly focuses on the special polytomous knowledge structures delineated by Skills, which are called fuzzy knowledge structures. We consider how to construct fuzzy knowledge structures based on the relationship between items and skills, and how to find the learning paths for specific knowledge domains. First, we construct knowledge structures in four models, which are the conjunctive model of skill maps, the disjunctive and conjunctive models of fuzzy skill maps, and the competency model of fuzzy skill multimaps. Second, we assess individuals’ skills and find the learning paths for the specific knowledge domains in the first three models. Finding the learning paths for a specific knowledge domain can guide learning and improve the learning efficiency of individuals. Finally, we analyze some data sets to show that the algorithms proposed are effective and applicable. These works can be applied to adaptive learning systems, which bring great convenience for assessing individuals’ knowledge and guiding future learning.

On the Solvability and Number of Solutions of Production-Logical Equations in a Fuzzy LP-Structure

For the construction and study of formal models of intelligent information systems, algebraic methods are useful. One of the topical directions here is the production-type logical systems, which are widespread in computer science. In recent years, the author and his followers have been developing the algebraic theory of LP-structures (lattice production structures). It is designed to formalize and solve a number of knowledge management problems in production systems. The method of relevant backward inference (LP-inference) was also introduced and investigated, which significantly reduces the number of calls to external information sources in comparison with classical inference. Subsequently, the theory was generalized to speed up inference in distributed production systems. At the same time, modern intelligent systems are characterized by fuzzy knowledge and fuzzy reasoning. There­fore, there is a need to extend the theory of LP-structures to fuzzy production systems. This research was initiated in previous articles by the author. Some concepts are introduced that impart fuzziness to LP-structures, and certain properties of fuzzy LP-inference are established. In recent works, research results are presented that systematically generalize the theory of LP-structures to the case of fuzzy knowledge bases. The terminology of FLP-structures with fuzzy logical relation (Fuzzy LP-structures) is introduced, the main standard properties are proved. The present work complements the FLP-structure model by investigating a class of production-logical equations. Relevant inference ideas are based on it, reducing the number of calls to external sources of information. Methods for solving these equations are formulated. For the first time, questions about the existence and number of solutions have been resolved. Finding a solution to a production-logical equation corresponds to the backward fuzzy inference in a production system. The proved theorems can be used for software implementation of fuzzy LP-structures and corresponding optimization of fuzzy inference. Some ideas for this implementation are discussed.