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**1 - 1**of**1**### FUZZY METHODS FOR SIMPLIFYING A BOOLEAN FORMULA INFERRED FROM EXAMPLES

"... In order to state a symbolic description of observed data we learn a minimal monotone DNF (Disjunctive Normal Form) formula consistent with them. Then, in the idea that a short formula – i.e. made up of few monomials, each represented by the product of few literals – is better understandable by the ..."

Abstract
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In order to state a symbolic description of observed data we learn a minimal monotone DNF (Disjunctive Normal Form) formula consistent with them. Then, in the idea that a short formula – i.e. made up of few monomials, each represented by the product of few literals – is better understandable by the user than a longer one, we propose here an algorithm to simplify in this direction the formula learnt from examples. We obtain concise formulas by violating their consistency on a part of the observed examples in some regions of the sample space that we consider as fuzzy borders of the formulas. Special membership functions to these regions allow us to manage the balance between conciseness and description power of the final formula as an optimisation problem that is solved via a simulated annealing procedure on a set of artificially constructed benchmarks.