183 research outputs found
Intuitionistic Fuzzy Time Series Functions Approach for Time Series Forecasting
Fuzzy inference systems have been commonly used for time series forecasting in the literature. Adaptive network fuzzy inference system, fuzzy time series approaches and fuzzy regression functions approaches are popular among fuzzy inference systems. In recent years, intuitionistic fuzzy sets have been preferred in the fuzzy modeling and new fuzzy inference systems have been proposed based on intuitionistic fuzzy sets. In this paper, a new intuitionistic fuzzy regression functions approach is proposed based on intuitionistic fuzzy sets for forecasting purpose. This new inference system is called an intuitionistic fuzzy time series functions approach. The contribution of the paper is proposing a new intuitionistic fuzzy inference system. To evaluate the performance of intuitionistic fuzzy time series functions, twenty-three real-world time series data sets are analyzed. The results obtained from the intuitionistic fuzzy time series functions approach are compared with some other methods according to a root mean square error and mean absolute percentage error criteria. The proposed method has superior forecasting performance among all methods
On the Description of Long Water Waves in Material Variables
Shallow water equations formulated in material variables are presented in this paper. In the model considered, a three-dimensional physical problem is substituted by a two-dimensional one describing a transformation of long waves in water of variable depth. The latter is obtained by means of the assumption that a vertical column of water particles remains vertical during the entire motion of the fluid. Under the assumption of small, continuous variation of the water depth, the equations for gravity waves are derived through Hamilton's principle formulated in terms of the material coordinates. This formulation ensures the conservation of mechanical energy. The approximation depends on the wave parameters as well as on the bed bathymetry. The latter may influence a solution of the model decisively; thus, one should be careful in applying the description to complicated geometries of fluid domains encountered in engineering practice
Nonlinear Interactions between Gravity Waves in Water of Constant Depth
The paper deals with interactions between water waves propagating in fluid of constant depth.
In formulation of this problem, a nonlinear character of these interactions is taken into account.
In particular, in order to simplify a solution to nonlinear boundary conditions at the free surface,
a system of material coordinates is employed as independent variables in the description of the
phenomenon. The main attention is focused on the transient solutions corresponding to fluid
motion starting from rest. With respect to the initial value problem considered, we confine
our attention to a finite fluid domain. For a finite elapse of time, measured from the starting
point, the solution in a finite fluid area mimics a solution within an infinite domain, inherent
for wave propagation problems. Because of the complicated structure of equations describing
nonlinear waves, an approximate formulation is considered, which is based on a power series
expansion of dependent variables with respect to a small parameter. Such a solution is assumed
to be accurate in describing the main features of the phenomenon. Numerical experiments are
conducted to illustrate the approximate formulation developed in this paper
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