Concept lattices defined from implication operators
Fuzzy Sets and Systems
Formal Concept Analysis: Mathematical Foundations
Formal Concept Analysis: Mathematical Foundations
Reduction and a Simple Proof of Characterization of Fuzzy Concept Lattices
Fundamenta Informaticae
Fundamenta Informaticae
On multi-adjoint concept lattices based on heterogeneous conjunctors
Fuzzy Sets and Systems
International Journal of Approximate Reasoning
Review: Formal Concept Analysis in knowledge processing: A survey on models and techniques
Expert Systems with Applications: An International Journal
On equivalence of conceptual scaling and generalized one-sided concept lattices
Information Sciences: an International Journal
Hi-index | 0.00 |
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.