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The paper presents results on factorization by similarity of fuzzy concept lattices with hedges. A fuzzy concept lattice is a hierarchically ordered collection of clusters extracted from tabular data. The basic idea of factorization by similarity is to have, instead of a possibly large original fuzzy concept lattice, its factor lattice. The factor lattice contains less clusters than the original concept lattice but, at the same time, represents a reasonable approximation of the original concept lattice and provides us with a granular view on the original concept lattice. The factor lattice results by factorization of the original fuzzy concept lattice by a similarity relation. The similarity relation is specified by a user by means of a single parameter, called a similarity threshold. Smaller similarity thresholds lead to smaller factor lattices, i.e. to more comprehensible but less accurate approximations of the original concept lattice. Therefore, factorization by similarity provides a trade-off between comprehensibility and precision.

We first describe the notion of factorization. Second, we present a way to compute the factor lattice directly from input data, i.e. without the need to compute the possibly large original concept lattice. Third, we provide an illustrative example to demonstrate our method.

We present an application of formal concept analysis aimed at representing a meaningful structure of knowledge communities in the form of a lattice-based taxonomy. The taxonomy groups together agents (community members) who develop a set of notions. If no constraints are imposed on how it is built, a knowledge community taxonomy may become extremely complex and difficult to analyze. We consider two approaches to building a concise representation, respecting the underlying structural relationships while hiding superfluous information: a pruning strategy based on the notion of concept stability and a representational improvement based on nested line diagrams and "zooming". We illustrate the methods on two examples: a community of embryologists and a community of researchers in complex systems.

This paper proposes a case-based classifier using a new approach that integrates rule-based and case-based reasoning approaches for enhanced accuracy. The rule-based reasoning component uses rules generated from a concept lattice of training data, binarized using fuzzy sets. These binarized data are stored as cases in the case-based classification component. The case-based component complements the rule-based component to enhance classification accuracy. Moreover, we designed the case-based component with an embedded similarity measure that uses a vector model for concept approximations. Thus, this design makes it possible to generate high quality rules and classify unseen new cases. In addition, the ability to build a knowledge base in lattice form is important for discovering hierarchical patterns, incrementing or updating the existing knowledge base, and inducing rules with our rule learning algorithm. The novel methodology was implemented and evaluated with benchmark datasets from the UCI repository and historic rubber prices in Thailand, demonstrating improvements in accuracy of classification calls. The results from the fact their several hierarchical datasets are very promising, with improved classification performance over prior reported methods.

We review a method of generating logical rules, or axioms, from empirical data. This method, using closed set properties of formal concept analysis, has been previously described and tested on rather large sets of deterministic data. In spite of the fact that formal concept techniques have been used to prune frequent set data mining results, frequency and/or statistical significance are totally irrelevant to this method. It is strictly logical and deterministic.

The contribution of this paper is a completely new extension of this method to create implications involving numeric inequalities. That is, numerical inequalities such as "age > 39" can be treated as logical predicates that have been extracted from the data itself and not postulated apriori.

Concept lattices are systems of conceptual clusters, called formal concepts, which are partially ordered by the subconcept/superconcept relationship. Concept lattices are basic structures used in formal concept analysis. In general, a concept lattice may contain overlapping clusters and need not be a tree. On the other hand, tree-like classification schemes are appealing and are produced by several clustering methods. In this paper, we present necessary and sufficient conditions on input data for the output concept lattice to form a tree after one removes its least element. We present these conditions for input data with yes/no attributes as well as for input data with fuzzy attributes. In addition, we show how Lindig's algorithm for computing concept lattices gets simplified when applied to input data for which the associated concept lattice is a tree after removing the least element. The paper also contains illustrative examples.

Microarray technologies, which can measure tens of thousands of gene expression values simultaneously in a single experiment, have become a common research method for biomedical researchers. Computational tools to analyze microarray data for biological discovery are needed. In this paper, we investigate the feasibility of using formal concept analysis (FCA) as a tool for microarray data analysis. The method of FCA builds a (concept) lattice from the experimental data together with additional biological information. For microarray data, each vertex of the lattice corresponds to a subset of genes that are grouped together according to their expression values and some biological information related to gene function. The lattice structure of these gene sets might reflect biological relationships in the dataset. Similarities and differences between experiments can then be investigated by comparing their corresponding lattices according to various graph measures. We apply our method to microarray data derived from influenza-infected mouse lung tissue and healthy controls. Our preliminary results show the promise of our method as a tool for microarray data analysis.

In real life, due to the complexity of objective things and the ambiguity of human thinking, people are often accustomed to expressing them with fuzzy linguistic values. To solve the decision-making problem with uncertain information of fuzzy linguistic values, this paper proposes a rule extraction method based on linguistic 3-tuple concept lattice. Introducing linguistic 3-tuple into formal context, the linguistic 3-tuple formal context and linguistic 3-tuple formal concept are proposed. Based on the linguistic 3-tuple formal context, we put forward the linguistic 3-tuple decision formal context and the algorithm of rule extraction based on linguistic 3-tuple concept lattice. Finally, the effectiveness and practicability of this model are illustrated by an example of student competition prediction system.