Semantics of quotient operators in fuzzy relational databases
Fuzzy Sets and Systems
Efficient mining of association rules using closed itemset lattices
Information Systems
Rough Sets: Theoretical Aspects of Reasoning about Data
Rough Sets: Theoretical Aspects of Reasoning about Data
Formal Concept Analysis: Mathematical Foundations
Formal Concept Analysis: Mathematical Foundations
Fuzzy Relational Systems: Foundations and Principles
Fuzzy Relational Systems: Foundations and Principles
Modal-style operators in qualitative data analysis
ICDM '02 Proceedings of the 2002 IEEE International Conference on Data Mining
A Possibility-Theoretic View of Formal Concept Analysis
Fundamenta Informaticae - New Frontiers in Scientific Discovery - Commemorating the Life and Work of Zdzislaw Pawlak
Optimal triangular decompositions of matrices with entries from residuated lattices
International Journal of Approximate Reasoning
Discovery of optimal factors in binary data via a novel method of matrix decomposition
Journal of Computer and System Sciences
Similarity relations and fuzzy orderings
Information Sciences: an International Journal
Possibility theory and formal concept analysis: context decomposition and uncertainty handling
IPMU'10 Proceedings of the Computational intelligence for knowledge-based systems design, and 13th international conference on Information processing and management of uncertainty
A parallel between extended formal concept analysis and bipartite graphs analysis
IPMU'10 Proceedings of the Computational intelligence for knowledge-based systems design, and 13th international conference on Information processing and management of uncertainty
On multi-adjoint concept lattices based on heterogeneous conjunctors
Fuzzy Sets and Systems
A completeness analysis of frequent weighted concept lattices and their algebraic properties
Data & Knowledge Engineering
Clustering sets of objects using concepts-objects bipartite graphs
SUM'12 Proceedings of the 6th international conference on Scalable Uncertainty Management
A formal concept view of abstract argumentation
ECSQARU'13 Proceedings of the 12th European conference on Symbolic and Quantitative Approaches to Reasoning with Uncertainty
Using concept lattice theory to obtain the set of solutions of multi-adjoint relation equations
Information Sciences: an International Journal
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Formal concept analysis is a lattice-theoretic framework devised for the extraction of knowledge from Boolean data tables. A possibility-theoretic view of formal concept analysis has been recently introduced, and in particular set-valued counterparts of the four set-functions, respectively, evaluating potential or actual, possibility or necessity, that underlie bipolar possibility theory. It enables us to retrieve an enlarged perspective for formal concept analysis, already laid bare by some researchers like Dunsch and Gediga, or Georgescu and Popescu. The usual (Galois) connection that defines the notion of a formal concept as the pair of its extent and its intent is based on the actual (or guaranteed) possibility function, where each object in a concept has all properties of its intent, and each property is possessed by all objects of its extent. Noticing the formal similarity between the operator underlying classical formal concept analysis and the notion of division in relational algebra, we briefly indicate how to define approximate concepts by relaxing the universal quantifier in the definition of intent and extent as already done for relational divisions. The main thrust of the paper is the detailed study of another connection based on the counterpart to necessity measures. We show that it leads to partition a formal context into disjoint subsets of objects having distinct properties, and to split a data table into independent sub-tables.