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In this paper, we propose a numerical method based on the F-transform for solving a certain type of partial differential equations (PDEs) with Dirichlet boundary conditions and initial conditions. We show how the PDEs after the application of the Crank-Nicolson scheme for time discretization can be approximated by a system of linear equations with the direct F-transform components as their variables...
Fuzzy relational compositions based on fuzzy quantifiers naturally do not preserve all the properties that are preserved for “standard” fuzzy relational compositions and, in many cases, the property is preserved only in a weaker form. For example, the associativity, that is preserved in the standard case derived from the universal and the existential quantifiers, generally does not hold for the case...
In this paper, we reformulate the fuzzy transform of higher degree (Fm-transform) proposed originally for an approximation of continuous functions to the discrete case. We introduce two types of Fm-transform which components are defined using polynomials in the first case and using specific values of these polynomials in the second case. We provide an analysis of basic properties of Fm-transform.
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 is decomposed into two constituents: the trend-cycle and random noise. We will demonstrate that using the F-transform we can reduce the variability of random noise which consequence is an extraction of the trend-cycle.
In the first part of this contribution, we proposed extensional fuzzy numbers and a working arithmetic for them that may be abstracted to so-called many identities algebras (MI-algebras, for short). In this second part, we show that the proposed MI-algebras give a framework not only for the arithmetic of extensional fuzzy numbers, but also for other arithmetics of fuzzy numbers and even more general...
Up to our best knowledge, distinct so far existing arithmetics of fuzzy numbers, usually stemming from the Zadeh's extensional principle, do not preserve some of the important properties of the standard arithmetics of classical (real) numbers. Obviously, although we cannot expect that a generalization of standard arithmetic will preserve precisely all its properties however, at least the most important...
Data smoothing is an important step within a data processing procedure that allows one to stress the most important pattern of a function relation between a studied object and given variables. Recently, Holčapek and Tichý (2011) suggested a smoothing filter based on fuzzy transform approach of Perfilieva (2004) and compared it to Nadaraya-Watson estimator. However, within the analysis only one independent...
In this contribution, we study a very important semantic property of generalized quantifiers called the monotonicity for fuzzy quantifiers of type 〈1,1〉 defined using fuzzy measures and Sugeno type of fuzzy integrals. We show that fuzzy integrals can ensure under some natural conditions the monotonicity of fuzzy quantifiers. Finally, we propose the concept of concave fuzzy quantifiers and prove that...
In the classical set theory, there is the well known correspondence between the equipollence of finite sets and the equality of natural numbers expressing their cardinalities. In the fuzzy set theory, an equivalent correspondence between the equipollence of finite fuzzy sets and the equality of generalized cardinals has been proposed in [1]. This paper is devoted to the situation when we consider...
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