How Fuzzy FCA and Pattern Structures are connected?

International audienceFCA is a mathematical formalism having many applicationsin data mining and knowledge discovery. Originally it deals with binarydata tables. However, there is a number of extensions that enrich standard FCA. In this paper we consider two important extensions: fuzzyFCA and pattern structures, and discuss the relation between them. Inparticular we introduce a scaling procedure that enables representing afuzzy context as a pattern structure

Galois Connection with Truth Stressers: Foundation for Formal Concept Analysis of Object-Attribute Data with Fuzzy Stressers

Galois connections appear in several areas of mathematics and computer science, and their applications. A Galois connection between sets X and Y is a pair ↑ , ↓ of mappings ↑ assigning subcollections of Y to subcollections of X, and ↓ assigning subcollections of X to subcollections of Y . By definition, Galois connections have to satisfy certain conditions. Galois connections can be interpreted in the following manner: For subcollections A and B of X and Y , respectively, A ↑ is the collection of all elements of Y which are in a certain relationship to all elements from A, and B ↓ is the collection of all elements of X which are in the relationship to all elements in B. From the very many examples of Galois connections in mathematics, let us recall the following. Let X be the set of all logical formulas of a given language, Y be the set of all structures (interpretations) of the same language. For A ⊆ X and B ⊆ Y , let A ↑ consist of all structures in which each formula from A is true, let B ↓ denote the set of all formulas which are true in each structure from B. Then, ↑ and ↓ is a Galois connection. As an example of applications of Galois connections, consider the following example which is the main source of inspiration for the present paper. Let X and Y denote a set of objects and attributes, respectively, Let I denote the relationship "to have" between objects and attributes. Then X, Y , and I can be seen as representing an object-attribute data table (for instance, organisms as objects, and their properties as attributes). If, for subcollections A of X and B of Y , A ↑ denotes the collection of all attributes shared by all objects from A, and B ↓ denotes the collection of all objects sharing all attributes from B, then ↑ and ↓ form a Galois connection. These connections form the core of socalled formal concept analysis (FCA) of object-attribute data, se

Heterogeneous environment on examples

We propose a running example for heterogeneous approach based on new type of fuzzification that diversifies fuzziness of every object, fuzziness of every attribute and fuzziness of every table value in a formal context. Moreover we suggest another working examples on heterogeneous environment and provide additional utilization and illustration of this new model that allows to use Formal Concept Analysis also for heterogenenous data. An interpretation of heterogeneous formal concepts and the resulting concept lattice is included

Heterogeneous environment on examples

We propose a running example for heterogeneous approach based on new type of fuzzification that diversifies fuzziness of every object, fuzziness of every attribute and fuzziness of every table value in a formal context. Moreover we suggest another working examples on heterogeneous environment and provide additional utilization and illustration of this new model that allows to use Formal Concept Analysis also for heterogenenous data. An interpretation of heterogeneous formal concepts and the resulting concept lattice is included

Concept coupling learning for improving concept lattice-based document retrieval

© 2017 Elsevier Ltd The semantic information in any document collection is critical for query understanding in information retrieval. Existing concept lattice-based retrieval systems mainly rely on the partial order relation of formal concepts to index documents. However, the methods used by these systems often ignore the explicit semantic information between the formal concepts extracted from the collection. In this paper, a concept coupling relationship analysis model is proposed to learn and aggregate the intra- and inter-concept coupling relationships. The intra-concept coupling relationship employs the common terms of formal concepts to describe the explicit semantics of formal concepts. The inter-concept coupling relationship adopts the partial order relation of formal concepts to capture the implicit dependency of formal concepts. Based on the concept coupling relationship analysis model, we propose a concept lattice-based retrieval framework. This framework represents user queries and documents in a concept space based on fuzzy formal concept analysis, utilizes a concept lattice as a semantic index to organize documents, and ranks documents with respect to the learned concept coupling relationships. Experiments are performed on the text collections acquired from the SMART information retrieval system. Compared with classic concept lattice-based retrieval methods, our proposed method achieves at least 9%, 8% and 15% improvement in terms of average MAP, IAP@11 and P@10 respectively on all the collections

On Scaling of Fuzzy FCA to Pattern Structures

International audienceFCA is a mathematical formalism having many applications in data mining and knowledge discovery. Originally it deals with binary data tables. However, there is a number of extensions that enrich standard FCA. In this paper we consider two important extensions: fuzzy FCA and pattern structures, and discuss the relation between them. In particular we introduce a scaling procedure that enables representing a fuzzy context as a pattern structure. Studying the relation between different extensions of FCA is of high importance, since it allows migrating methods from one extension to another. Moreover, it allows for more simple implementation of different extensions within a software

Attribute Extended Algorithm of Lattice-Valued Concept Lattice Based on Congener Formal Context

This paper is the continuation of our research work about lattice-valued concept lattice based on lattice implication algebra. For a better application of lattice-valued concept lattice into data distributed storage and parallel processing, it is necessary to research attribute extended algorithm based on congener formal context. The definitions of attribute extended formal context and congener formal context are proposed. On condition that the extent set stays invariable when the new attribute is increased, the necessary and sufficient conditions of forming attribute values are researched. Based on these conditions, the algorithms of generating lattice-valued congener formal context and establishing concept lattice are given, by which we can provide a useful basis for union algorithm and constructing algorithm of lattice-valued concept lattices in distributed and parallel system