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Full-Text Articles in Physical Sciences and Mathematics
Necessary And Sufficient Conditions For Generalized Uniform Fuzzy Partitions, Michal Holčapek, Irina Perfilieva, Vilém Novák, Vladik Kreinovich
Necessary And Sufficient Conditions For Generalized Uniform Fuzzy Partitions, Michal Holčapek, Irina Perfilieva, Vilém Novák, Vladik Kreinovich
Departmental Technical Reports (CS)
The fundamental concept in the theory of fuzzy transform (F-transform) is that of fuzzy partition. The original definition assumes that each two fuzzy subsets overlap in such a way that sum of membership degrees in each point is equal to 1. However, this condition can be generalized to obtain a denser fuzzy partition that leads to improvement of approximation properties of F-transform. However, a problem arises how one can effectively construct such type of fuzzy partitions. We use a generating function having special properties and it is not immediately clear whether it really defines a general uniform fuzzy partition. In …
Filtering Out High Frequencies In Time Series Using F-Transform, Vilém Novák, Irina Perfilieva, Michal Holčapek, Vladik Kreinovich
Filtering Out High Frequencies In Time Series Using F-Transform, Vilém Novák, Irina Perfilieva, Michal Holčapek, Vladik Kreinovich
Departmental Technical Reports (CS)
In this paper, we will focus on the application of fuzzy transform (F-transform) in the analysis of time series. We assume that the time series can be decomposed into three constituent components: the trend-cycle, seasonal component and random noise. We will demonstrate that by using F-transform, we can approximate the trend-cycle of a given time series with high accuracy.