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Knowledge representation using interval-valued fuzzy formal concept lattice

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Abstract

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.

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Acknowledgments

Authors sincerely acknowledge the financial support from National Board of Higher Mathematics, Dept. of Atomic Energy, Govt. of India under the grant number 2/48(11)/2010-R&D II/10806. Authors thank the anonymous reviewer for their useful suggestions and remarks to improve the quality of the paper.

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Authors and Affiliations

  1. School of Information Technology and Engineering, VIT University, Vellore, 632014, Tamilnadu, India

    Prem Kumar Singh & C. Aswani Kumar

  2. Faculty of Science, Kunming University of Science and Technology, Kunming, 650500, People’s Republic of China

    Jinhai Li

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  1. Prem Kumar Singh
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  2. C. Aswani Kumar
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  3. Jinhai Li
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Correspondence to Prem Kumar Singh or C. Aswani Kumar.

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Communicated by V. Loia.

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Singh, P.K., Aswani Kumar, C. & Li, J. Knowledge representation using interval-valued fuzzy formal concept lattice. Soft Comput 20, 1485–1502 (2016). https://doi.org/10.1007/s00500-015-1600-1

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