Wyniki wyszukiwania - BazTech

Ograniczanie wyników

Znaleziono wyników: 3

Liczba wyników na stronie

Wyniki wyszukiwania

Wyszukiwano:
w słowach kluczowych: interpolation property

Sortuj według:

Ogranicz wyniki do:

Generalized Interpolation in First Order Logic

Borzyszkowski T.

Fundamenta Informaticae

2005

Vol. 66, nr 3

199--219

We consider the Craig Interpolation Property for many sorted first-order logic. The Craig Interpolation Property explored in this paper is inspired by the institution independent generalization of this property presented in [21]. In [3] the author presents the interpolation result for the institution of many sorted first-order logic, with both morphisms in the pushout square being injective on sort names. The author also shows that the Craig Interpolation Property does not hold when both morphisms are certain morphisms which are noninjective on sort names. An open question in that paper was whether the interpolation property holds with only one morphism being injective on sort names. In this paper we give answer to this question. Following the overall structure of the classical proof presented in [7] for single sorted first-order logic, but with new technicalities concerning the many sorted case, we show that many sorted first-order logic has the interpolation property when just one (left or right) morphism is injective on sort names.

Beta Fuzzy Logic Systems: Approximation Properties in the mimo Case

Alimi A. M., Hassine R., Selmi M.

International Journal of Applied Mathematics and Computer Science

2003

Vol. 13, no 2

225-238

Many researches have been interested in the approximation properties of Fuzzy Logic Systems (FLS), which, like neural networks, can be seen as approximation schemes. Almost all of them tackled the Mamdani fuzzy model, which was shown to have many interesting approximation features. However, only in few cases the Sugeno fuzzy model was considered. In this paper, we are interested in the zero-order Multi-Input-Multi-Output (MIMO) Sugeno fuzzy model with Beta membership functions. This leads to Beta Fuzzy Logic Systems (BFLS). We show that BFLSs are universal approximators. We also prove that they possess the best approximation property and the interpolation characteristic.

Beta Fuzzy Logic Systems: Approximation Properties in the Siso Case

Alimi A. M., Hassine R., Selmi M.

International Journal of Applied Mathematics and Computer Science

2000

Vol. 10, no 4

857-875

In this paper, a Single-Input Single-Output (SISO) Sugeno fuzzy model of the zeroth order with Beta membership functions for input variables is adopted. After the introduction of Beta Fuzzy Logic Systems (BFLS) a constructive theory is developed to establish the fact that they are universal approximators. Based on this theory, an algorithm, which can actually construct a BFLS approximating a given continuous function with an arbitrary degree of accuracy, is described. We then show that BFLSs satisfy more critical properties which are the best approximation property and the interpolation property. We complete the paper with a series of numerical comparisons between the approximation performances of BFLSs and other classes of widely used fuzzy logic systems. These comparisons confirm that BFLSs perform best in all the cases studied.