Abstract
The objective of this article is to investigate the problem of generating both positive and negative exact association rules when a formal context K of (positive) attributes is provided. A straightforward solution to this problem consists of conducting an apposition of the initial context K with its complementary context \(\Tilde{K}\), construct the concept lattice \(\mathfrak{B}(K|\Tilde{K})\) of apposed contexts and then extract rules. A more challenging problem consists of exploiting rules generated from each one of the contexts K and \(\Tilde{K}\) to get the whole set of rules for the context \(K|\Tilde{K}\).
In this paper, we analyze a set of identified situations based on distinct types of input, and come out with a set of properties. Obviously, the global set of (positive and negative) rules is a superset of purely positive rules (i.e., rules with positive attributes only) and purely negative ones since it generally contains mixed rules (i.e., rules in which at least a positive attribute and a negative attribute coexist).
The paper presents also a set of inference rules to generate a subset of all mixed rules from positive, negative and mixed ones. Finally, two key conclusions can be drawn from our analysis: (i) the generic basis containing negative rules, \(\Sigma_{\Tilde{K}}\), cannot be completely and directly inferred from the set Σ K of positive rules or from the concept lattice \(\mathfrak{B}(K)\), and (ii) the whole set of mixed rules may not be completely generated from Σ K alone, \(\Sigma_K \cup \Sigma_{\Tilde{K}}\) alone, or \(\mathfrak{B}(K)\) alone.
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Missaoui, R., Nourine, L., Renaud, Y. (2008). Generating Positive and Negative Exact Rules Using Formal Concept Analysis: Problems and Solutions. In: Medina, R., Obiedkov, S. (eds) Formal Concept Analysis. ICFCA 2008. Lecture Notes in Computer Science(), vol 4933. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-78137-0_13
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DOI: https://doi.org/10.1007/978-3-540-78137-0_13
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