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Extra resources for Advanced Machine Learning Technologies and Applications: First International Conference, AMLTA 2012, Cairo, Egypt, December 8-10, 2012. Proceedings
Certainty). If a formula α holds in every ψ ∈ DD(Φ), α also holds in ψ actual . In this case, we say α certainly holds in ψ actual . (Possibility). If a formula α holds in some ψ ∈ DD(Φ), there exists such a possibility that α holds in ψ actual . In this case, we say α possibly holds in ψ actual . Fig. 1. An basic chart for Φ and a set DD(Φ) of derived DISs Even if there exists the information incompleteness in Φ, we have the following decision making. (1) If a formula α certainly holds, we think α holds under the uncertainty.
This issue in RNIA slightly seems analogous to backpropagation in Neural Networks. Keywords: Estimation of actual information, Constraint, Rough sets, Data dependency, Rules. 1 Introduction Rough set theory oﬀers a mathematical approach to vagueness . It has many applications related to the areas of classiﬁcation, feature reduction, rule generation, machine learning, data mining, knowledge discovery and others [8, 9]. Rough set theory is usually employed to deal with data tables with deterministic information, which we call Deterministic Information Systems (DISs).
We assume that if a truth value of a statement attached to a given place is equal to 0 then the token does not exist in the place. The number β(t) is placed in a net picture over a transition t. Usually, this number is interpreted as a truth degree of an implication corresponding to a given transition t ,. The meaning of the threshold function γ is explained below. The operator binding function δ connects transitions with triples of operators (opIn , opOut1 , opOut2 ). The ﬁrst operator appearing in this triple is called the input operator, and two remaining ones are called the output operators.