The paper recalls the McNaughton theorem of fuzzy logic and the algorithms underlying its constructive proofs. It then shows how those algorithms can be combined with the algorithm underlying recent extension of the theorem to piecewise-linear functions with rational coefficients, and points out potential importance of the resulting combined algorithm for data mining. That result is immediately weakened through a complexity analysis of the algorithm that reveals that its worst-case complexity is doubly-exponential.
The paper addresses the problém of efficient and adequate representation of functions using two soft computing techniques: fuzzy logic and neural networks. The principle approach to the construction of approximating formulas is discussed. We suggest a generalized definition of the normál forms in predicate BL and ŁII logic and prove conditional equivalence between a formula and each of its normal forms. Some mutual relations between the normál forms will be also established.
We propose a generalization of simple coalition games in the context of games with fuzzy coalitions. Mimicking the correspondence of simple games with non-constant monotone formulas of classical logic, we introduce simple Łukasiewicz games using monotone formulas of Łukasiewicz logic, one of the most prominent fuzzy logics. We study the core solution on the class of simple Łukasiewicz games and show that cores of such games are determined by finitely-many linear constraints only. The non-emptiness of core is completely characterized in terms of balanced systems and by the presence of strong veto players.