Definition of Formal Concept

A formal concept is a fundamental concept in formal concept analysis (FCA), which is a mathematical framework used for the classification and analysis of data. FCA is applied in various fields, including information retrieval, data mining, knowledge representation, and machine learning.

Attributes

In FCA, an attribute refers to a characteristic or property used to describe objects or entities. These attributes can be boolean (binary), meaning they have only two possible values (e.g., true or false), or they can be multi-valued, taking on more than two possible values.

Objects

In FCA, an object represents an individual item or entity that possess certain attribute values. Objects can be real-world entities, such as products, customers, or documents, or they can be abstract entities, such as concepts or ideas.

Formal Concept

A formal concept is a pair comprising of a set of objects and a set of attributes. These sets are defined in such a way that the objects within the set possess all the attributes in the attribute set. In other words, a formal concept represents a connection between objects and attributes, where all objects within the concept share common attribute values.

Concept lattice

In FCA, a concept lattice is a graphical representation of the set of all formal concepts that can be derived from a given set of objects and attributes. The concept lattice depicts the relationships and hierarchical structure between different formal concepts, showing which concepts are sub-concepts or super-concepts of others.

Generality and specificity

Formal concepts within a concept lattice can be ranked according to their generality or specificity. Generality refers to concepts that have a larger set of objects and a smaller set of attributes, while specificity refers to concepts with a smaller set of objects and a larger set of attributes. This ranking of concepts allows for the identification of general or specific patterns or relationships within the analyzed data.