Formal Concept Analysis is a well established mathematical model for data analysis and processing tasks. Computing all the fuzzy formal concepts and their visualization is an important concern for its practical applications. In this process a major problem is how to control the size of concept lattice. For this purpose current study focus on constructing a fuzzy homomorphism map h:F = ðOi; Pj; ~RÞ ! D ¼ ðXm; Yn; ~uÞ for the given fuzzy formal context F where, m B i and n B j. We show that reduced fuzzy concept lattice preserves the generalization and specialization with an illustrative example. © Springer India 2014.

Aswani Kumar Cherukuri

Department of Information Technology

School of Information Technology and Engineering

Vellore Campus

Singh P.K

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

A Note on Constructing Fuzzy Homomorphism Map for a Given Fuzzy Formal Context

Advances in Intelligent Systems and Computing Proceedings of the Third International Conference on Soft Computing for Problem Solving

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 model based on lattice theory. FCA is successfully extended from crisp setting to fuzzy setting as well as interval-valued fuzzy setting. These extensions of fuzzy set define the data in the unipolar space and lack in representing bipolarity. However, bipolar fuzzy set represents the positive and negative information simultaneously. This extension has been applied recently in lattice theory, graph theory and in FCA as well. In this paper, we focus on introducing the link between bipolar fuzzy graph and concept lattice. Copyright © 2014 Inderscience Enterprises Ltd.

Journal	Data powered by TypesetAdvances in Intelligent Systems and Computing Proceedings of the Third International Conference on Soft Computing for Problem Solving
Publisher	Data powered by TypesetSpringer India
ISSN	2194-5357
Open Access	0