Galois Connections with Hedges
نویسندگان
چکیده
We introduce (fuzzy) Galois connections with hedges. Fuzzy Galois connections are basic structures behind so-called formal concept analysis of data with fuzzy attributes. Introducing hedges to Galois connections means introducing two parameters. The parameters influence the size of the set of all the fixpoints of a Galois connection. In the sense of formal concept analysis, the fixpoints, called formal concepts, are just the clusters extracted from data. The role of hedges is thus to control the number of extracted clusters. Stronger hedges lead to less clusters. We present definition, examples, and basic properties of Galois connections with hedges. In addition to that, we provide their axiomatization: Galois connections with hedges are exactly mappings induced by object-attribute data with fuzzy attributes. The effect of a parameterized reduction of the number of clusters from object-attribute data is demonstrated by examples.
منابع مشابه
Lagois Connections - a Counterpart to Galois Connections
In this paper we deene a Lagois connection, which is a generalization of a special type of Galois connection. We begin by introducing two examples of Lagois connections. We then recall the deenition of Galois connection and some of its properties; next we deene Lagois connection, establish some of its properties, and compare these with properties of Galois connections; and then we (further) dev...
متن کاملFuzzy Galois Connections
The concept of Galois connection between power sets is generalized from the point of view of fuzzy logic. Studied is the case where the structure of truth values forms a complete residuated lattice. It is proved that fuzzy Galois connections are in one-to-one correspondence with binary fuzzy relations. A representation of fuzzy Galois connections by (classical) Galois connections is provided. 1...
متن کاملOn closure axioms for a matroid using Galois connections∗
We present two systems of closure axioms for a matroid with the assistance of Galois connections. These axioms give a mathematical foundation for the connections between matroids, Galois connections and concept lattices. We deal with some relationship between matroids and geometric lattices by the above axioms. We also discuss some applications between matroids and concept lattices with the abo...
متن کاملGalois Connections: Mathematics, Art and Archives
Évariste Galois (1811–1832) has been increasingly recognised as an important mathematician who despite his short life developed mathematical ideas that today have led to applications in computer science (such as Galois connections) and elsewhere. Some of Galois’ mathematics can be visualised in interesting and even artistic ways, aided using software. In addition, a significant corpus of the hi...
متن کاملFuzzy Connections and Relations in Complete Residuated Lattices
In this paper, we investigate the properties of fuzzy Galois (dual Galois, residuated, and dual residuated) connections in a complete residuated lattice L. We give their examples. In particular, we study fuzzy Galois (dual Galois, residuated, dual residuated) connections induced by L-fuzzy relations.
متن کامل