Concept lattices defined from implication operators
Fuzzy Sets and Systems
Formal Concept Analysis: Mathematical Foundations
Formal Concept Analysis: Mathematical Foundations
Journal of Logic and Computation
Reduction and a Simple Proof of Characterization of Fuzzy Concept Lattices
Fundamenta Informaticae
Fundamenta Informaticae
Information Sciences: an International Journal
Formal concept analysis via multi-adjoint concept lattices
Fuzzy Sets and Systems
Overcoming Non-commutativity in Multi-adjoint Concept Lattices
IWANN '09 Proceedings of the 10th International Work-Conference on Artificial Neural Networks: Part I: Bio-Inspired Systems: Computational and Ambient Intelligence
Multi-adjoint t-concept lattices
Information Sciences: an International Journal
On multi-adjoint concept lattices: definition and representation theorem
ICFCA'07 Proceedings of the 5th international conference on Formal concept analysis
A new algebraic structure for formal concept analysis
Information Sciences: an International Journal
What is a fuzzy concept lattice? II
RSFDGrC'11 Proceedings of the 13th international conference on Rough sets, fuzzy sets, data mining and granular computing
Note on generating fuzzy concept lattices via Galois connections
Information Sciences: an International Journal
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A classical (crisp) concept is given by its extent (a set of objects) and its intent (a set of properties). In commutative fuzzy logic, the generalization comes naturally, considering fuzzy sets of objects and properties. In both cases (the first being actually a particular case of the second), the situation is perfectly symmetrical: a concept is given by a pair (A,B), where A is the largest set of objects sharing the attributes from B and B is the largest set of attributes shared by the objects from A (with the necessary nuance when fuzziness is concerned). Because of this symmetry, working with objects is the same as working with properties, so there is no need to make any choice. In this paper, we define concepts in a "non-commutative fuzzy world", where conjunction of sentences is not necessarily commutative, which leads to the following non-symmetrical situation: a concept has one extent (because, at the end of the day, concepts are meant to embrace, using certain descriptions, diverse sets of objects), but two intents, given by the two residua (implications) of the non-commutative conjunction.