Abstract
How to induce rules from data tables containing possibilistic information is described under using rough sets based on possible world semantics. A piece of possibilistic information is expressed in a normal and discrete possibility distribution. Under a degree of possibility, the incomplete data table is derived from a possibilistic data table. Rough sets and rules are derived from incomplete data tables. The rough sets and rules obtained under every degree of possibility are aggregated from the viewpoints of certainty and possibility. As a result, rough sets consist of objects with a degree expressed in an interval and an object also supports rules with a degree expressed in an interval value. Furthermore, a criterion is introduced to judge whether or not an object is regarded as validly supporting rules.
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Notes
- 1.
\(\mathcal{E}_{a_{i}}\) is formally \(\mathcal{E}_{a_{i}}(U)\). (U) is usually omitted.
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Nakata, M., Sakai, H. (2019). Rule Induction Based on Rough Sets from Possibilistic Data Tables. In: Seki, H., Nguyen, C., Huynh, VN., Inuiguchi, M. (eds) Integrated Uncertainty in Knowledge Modelling and Decision Making. IUKM 2019. Lecture Notes in Computer Science(), vol 11471. Springer, Cham. https://doi.org/10.1007/978-3-030-14815-7_8
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