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The idea of knowledge approximation is naturally rooted in the usual examples of approximation in our experience. More abstract approximation, at the levels of syntactic structures representing knowledge, is becoming a need in the existing knowledge management, addressing a variety of important issues. Here we propose a method and its implementation, which generalizes the unification method to the...
There are considered two cases of the real semiring with pseudo-operations: one, when pseudo-operations are defined by monotone and continuous function g (then the pseudo-integral reduces on g-integral), and the second semiring ([a, b] , max, odot) , where odot is generated. There is proven a generalization of the Jensenpsilas inequality for the pseudo-integral.
The superposition principle is a useful tool for constructing new solutions of ordinary and partial differential equations. Therefore, through this paper, we are considering the pseudo-linear superposition principle based on generated pseudo-operations of the following form: x oplus y = g-1 (g(x) + g(y)) , x odot y = g-1 (g(x)g(y)) , where g is a continuous generating function. Some possibilities...
In this paper we study uninorms with given strict underlying t-norm and t-conorm. Such uninorms are the only candidates for being represented by (additive) generator functions. We prove that representability depends exclusively on the value of the uninorm at a single point in the ldquoremainingrdquo open part of the unit square. The uninorm turns out to be representable if and only if this single...
Pseudo-integral of the interval-valued functions based on the pseudo-operations has been introduced. Some basic properties, as well as, some limit properties of the pseudo-integral of interval-valued functions have been investigated.
Copulas enabling to characterize the joint distributions of random vectors by means of the corresponding one-dimensional marginals are presented and discussed. Some properties of copulas and several construction methods, especially when a partial knowledge is available, are included. Possible applications are indicated.
In this paper a further step towards a novel approach to adaptive nonlinear control developed at Budapest Tech in the past few years is reported. Its main advantage in comparison with the complicated Lyapunov function based techniques is that it is based on simple geometric considerations on the basis of which the control task can be formulated as a fixed point problem for the solution of which a...
Previously, we introduced the notion of a TL- (SL-) evaluator [1]. In this paper we study the Choquet, Sugeno and Shilkret integrals and their level-dependent modifications as TL- (SL-) evaluators. We investigate under which conditions these integral-based evaluators are self-dual. Our work is a continuation of [1, 2, 6, 7].
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