Reduction of the size ofL-fuzzy contexts. A tool for differential diagnoses of diseases

Abstract

Information extraction from an L-fuzzy context becomes a hard problem when we work with a large set of objects and/or attributes. The goal of this paper is to present two different and complementary techniques to reduce the size of the context. First, using overlap indexes, we will establish rankings among the elements of the context that will allow us to determine those that do not provide relevant information and eliminate them. Second, by means of Choquet integrals, we will aggregate some objects or attributes of the context in order to jointly use the provided information. One interesting application of the developed theory consists on helping in the differential diagnoses of diseases that share a large number of symptoms and, therefore, that are difficult of distinguish.

Identifying Non-Sublattice Equivalence Classes Induced by an Attribute Reduction in FCA

“…The most common redundant data consist of repeated entries, which can be removed without cost, or dependent variables, which can be derived from the independent variables, whose detection is an appealing research topic in many areas dealing with data analysis, such as Formal Concept Analysis (FCA). This mathematical theory was original developed in the 1980s by R. Wille and B. Ganter [1], and it has intensively been studied from a theoretical and applied point of view [2][3][4][5][6][7][8][9][10][11][12]. Two important features of FCA, in which the notion of Galois connection is fundamental [13][14][15][16], is that the information contained in a relational dataset can be described in a hierarchic manner by means of a complete lattice [17] and that dependencies between attributes can be determined [18][19][20][21], which is fundamental to applications.…”

“…The detection of (ir)relevant attributes or objects of a given formal context in FCA has been studied from different points of view, for example: in order to obtain a concept lattice isomorphic to the original one [22][23][24][25][26], to efficiently reduce the size of the concept lattice [8,[27][28][29][30][31][32], to extensional stability [33], to consider contexts with positive and negative attributes [34], to apply the rough set philosophy [35][36][37], etc. Notice that the different mechanisms focused on attribute reduction can dually be adapted to object reduction.…”

Knowledge extraction from L-fuzzy contexts associated with criteria evolving over time

“…In [9,10] an L-fuzzy context was determined as a tuple (L, X, Y, R), where L is a complete lattice, X and Y the sets of objects and attributes and R ∈ L X×Y a fuzzy relation defined among them. This is an exten-sion of the formal context of Wille in which the relation among objects and attributes is not binary and belongs to a complete lattice L. The L-fuzzy concept analysis has been developed as a tool for knowledge extraction using L-fuzzy concepts ( [4,7,5]).…”