Computing the Mixed Concept Lattice
Abstract
The classical approach on Formal Concept Analysis (FCA) extracts knowledge from a binary table K = (G, M, I) taking into account the existing relationships (given by the binary relation I) between objects G and attributes M. Thus, this classical setting accounts only for positive information. Particularly, FCA allows to define and compute the concept lattice B(K) from this positive information. As an extension of this framework, some works consider not only this positive information, but also the negative information that is explicit when objects have no relation to specific attributes (denoted by K). These works, therefore, use the apposition of positive and negative information to compute the mixed concept lattice B^{\#}(K). In this paper, we propose to establish the relationships between extents and intents of concepts in B(K), B(\overline{K}) and B^{\#}(K) and how to address an incremental algorithm to compute B^{\#}(K) merging the knowledge on B(K), B(\overline{K}) previously obtained with classical methods.
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Please, cite this work as:
[Pér+22] F. Pérez-Gámez, P. Cordero, M. Enciso, et al. “Computing the Mixed Concept Lattice”. In: Information Processing and Management of Uncertainty in Knowledge-Based Systems - 19th International Conference, IPMU 2022, Milan, Italy, July 11-15, 2022, Proceedings, Part I. Ed. by D. Ciucci, I. Couso, J. Medina, D. Slezak, D. Petturiti, B. Bouchon-Meunier and R. R. Yager. Vol. 1601. Communications in Computer and Information Science. Springer, 2022, pp. 87-99. DOI: 10.1007/978-3-031-08971-8_8. URL: https://doi.org/10.1007/978-3-031-08971-8_8.