On the irredundant generation of knowledge spaces
Journal of Mathematical Psychology
A generalization of knowledge space theory to problems with more than two answer alternatives
Journal of Mathematical Psychology
A note on the correspondence among entail relations, rough set dependencies, and logical consequence
Journal of Mathematical Psychology
Knowledge Spaces
Fuzzy Relational Systems: Foundations and Principles
Fuzzy Relational Systems: Foundations and Principles
Knowledge Spaces with Graded Knowledge States
KAM '08 Proceedings of the 2008 International Symposium on Knowledge Acquisition and Modeling
Isotone fuzzy Galois connections with hedges
Information Sciences: an International Journal
Evaluation of IPAQ questionnaires supported by formal concept analysis
Information Sciences: an International Journal
Attribute implications in a fuzzy setting
ICFCA'06 Proceedings of the 4th international conference on Formal Concept Analysis
Information Sciences: an International Journal
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Knowledge spaces represent a framework for assessment of knowledge with solid theoretical foundations, methodology, software tools, and practical applications. The underlying assumption in knowledge spaces is that a knowledge state of an individual is represented by a set of items which the individual has mastered. In this paper, we propose an extension of the theory of knowledge spaces which accounts for gradedness of knowledge states. Namely, we assume that a knowledge state is represented by a fuzzy (graded) set with degrees representing levels to which an individual has mastered the items. If 0 and 1 are the only degrees, our approach coincides with that of ordinary knowledge spaces. We develop basic concepts and results in the graded setting including bases of graded knowledge states and their computation and a logic of partial failure with its completeness theorem. We also present an illustrative example. The main aim of this paper is to demonstrate mathematical and computational feasibility of knowledge spaces with graded knowledge states.