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Information 2018, 9(11), 266;

ImplicPBDD: A New Approach to Extract Proper Implications Set from High-Dimension Formal Contexts Using a Binary Decision Diagram

Department of Computer Science, Pontifical Catholic University of Minas Gerais (PUC Minas), Belo Horizonte 31980-110, Brazil
Laboratory of Artificial Intelligence and Decision Support (LIAAD), INESC TEC, Porto 4200-465, Portugal
Federal Service of Data Processing (SERPRO), Belo Horizonte 31035-536, Brazil
Author to whom correspondence should be addressed.
This paper is an extended version of our paper published in Santos, P., Neves, J., Silva, P., Dias, S. M., Zárate, L., and Song, M. (2018). An Approach to Extract Proper Implications Set from High-dimension Formal Contexts using Binary Decision Diagram. In Proceedings of the 20th International Conference on Enterprise Information Systems (Vol. 1, pp. 50–57). Science and Technology Publications.
These authors contributed equally to this work.
Received: 20 September 2018 / Revised: 12 October 2018 / Accepted: 22 October 2018 / Published: 25 October 2018
PDF [1026 KB, uploaded 25 October 2018]


Formal concept analysis (FCA) is largely applied in different areas. However, in some FCA applications the volume of information that needs to be processed can become unfeasible. Thus, the demand for new approaches and algorithms that enable processing large amounts of information is increasing substantially. This article presents a new algorithm for extracting proper implications from high-dimensional contexts. The proposed algorithm, called ImplicPBDD, was based on the PropIm algorithm, and uses a data structure called binary decision diagram (BDD) to simplify the representation of the formal context and enhance the extraction of proper implications. In order to analyze the performance of the ImplicPBDD algorithm, we performed tests using synthetic contexts varying the number of objects, attributes and context density. The experiments show that ImplicPBDD has a better performance—up to 80% faster—than its original algorithm, regardless of the number of attributes, objects and densities. View Full-Text
Keywords: formal concept analysis; proper implication; binary decision diagram formal concept analysis; proper implication; binary decision diagram

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Santos, P.G.; Ruas, P.H.B.; Neves, J.C.V.; Silva, P.R.; Dias, S.M.; Zárate, L.E.; Song, M.A.J. ImplicPBDD: A New Approach to Extract Proper Implications Set from High-Dimension Formal Contexts Using a Binary Decision Diagram . Information 2018, 9, 266.

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