Recently, fuzzy FCA becomes popular in researchers for representing the knowledge precisely. In this study we present a method for decomposition of given fuzzy formal context into several crisp formal contexts with help of distinct granules of fuzzy relation. The presented method reduces the lattice of given fuzzy formal context into several lattices for refining the interested patterns. From the obtained crisp formal contexts, we can generate the formal concepts in order to visualize them in lattice structure for describing the knowledge of given research field. Proposed method can be helpful for the researchers for reducing number of concepts, visualization of concepts for distinct fuzzy relations, and reduction of fuzzy lattice into several lattices in fuzzy context related fields. © 2012 Published by Elsevier Ltd.

Aswani Kumar Cherukuri

Department of Information Technology

School of Information Technology and Engineering

Vellore Campus

Singh P.K

Fulltext

Vellore Institute of Technology (VIT) is a private university located in&nbsp;Tamil Nadu, India. Founded in 1984, as Vellore Engineering College, the institution offers 20 undergraduate, 34 postgraduate, four integrated and four research programs. It has campuses in Vellore, Amravati, Bhopal and Chennai.

VIT is one of the top ranked private universities in India according to NIRF, THE and QS Rankings.&nbsp;Govt. of India has recognized&nbsp;VIT, Vellore as an&nbsp;Institution of Eminence. This has allowed VIT to take independent quality initiatives and move up in world ranking.

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VIT University

Procedia Engineering

Granular Computing

Concept lattice reduction using different subset of attributes as information granules

In this paper we propose a method for reducing the number of formal concepts in formal concept analysis of data with fuzzy attributes. We compute the weight of fuzzy formal concepts based on Shannon entropy. Further, the number of fuzzy formal concepts is reduced at chosen granulation of their computed weight. We show that the results obtained from the proposed method are in good agreement with Levenshtein distance method and interval–valued fuzzy formal concepts method but with less computational complexity. © 2014, Springer-Verlag Berlin Heidelberg.

International Journal of Machine Learning and Cybernetics

Concepts reduction in formal concept analysis with fuzzy setting using Shannon entropy

Abstract In recent years, FCA has received significant attention from research communities of various fields. Further, the theory of FCA is being extended into different frontiers and augmented with other knowledge representation frameworks. In this backdrop, this paper aims to provide an understanding of the necessary mathematical background for each extension of FCA like FCA with granular computing, a fuzzy setting, interval-valued, possibility theory, triadic, factor concepts and handling incomplete data. Subsequently, the paper illustrates emerging trends for each extension with applications. To this end, we summarize more than 350 recent (published after 2011) research papers indexed in Google Scholar, IEEE Xplore, ScienceDirect, Scopus, SpringerLink, and a few authoritative fundamental papers.

International Journal of Applied Mathematics and Computer Science

A comprehensive survey on formal concept analysis, its research trends and applications

Formal concept analysis (FCA) is a mathematical framework for data analysis and processing tasks. Based on the lattice and order theory, FCA derives the conceptual hierarchies from the relational information systems. From the crisp setting, FCA has been extended to fuzzy environment. This extension is aimed at handling the uncertain and vague information represented in the form of a formal context whose entries are the degrees from the scale [0, 1]. The present study analyzes the fuzziness in a given many-valued context which is transformed into a fuzzy formal context, to provide an insight into generating the fuzzy formal concepts from the fuzzy formal context. Furthermore, considering that a major problem in FCA with fuzzy setting is to reduce the number of fuzzy formal concepts thereby simplifying the corresponding fuzzy concept lattice structure, the current paper solves the problem by linking an interval-valued fuzzy graph to the fuzzy concept lattice. For this purpose, we propose an algorithm for generating the interval-valued fuzzy formal concepts. To measure the weight of fuzzy formal concepts, an algorithm is proposed using Shannon entropy. The knowledge represented by formal concepts using interval-valued fuzzy graph is compared with entropy-based-weighted fuzzy concepts at chosen threshold. © 2015, Springer-Verlag Berlin Heidelberg.

Soft Computing

Knowledge representation using interval-valued fuzzy formal concept lattice

Formal Concept Analysis (FCA) is a mathematical framework for knowledge processing tasks. FCA has been successfully incorporated into fuzzy setting and its extension (interval- valued fuzzy set) for handling vagueness and impreciseness in data. However, the analysis in such settings is restricted to unipolar space. Recently, some applications of bipolar information are shown in bipolar fuzzy graph, lattice theory as well as in FCA. The adequate analysis of bipolar information using FCA requires incorporation of bipolar fuzzy set and an appropriate lattice structure. For this purpose, we propose an algorithm for generating the bipolar fuzzy formal concepts, a method for (α β)-cut of bipolar fuzzy formal context and its implications with illustrative examples. © 2014 Elsevier Inc. All rights reserved.

Journal	Data powered by TypesetProcedia Engineering
Publisher	Data powered by TypesetElsevier BV
ISSN	1877-7058
Open Access	Yes