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Öğe Analysis of signals with inexact data by using interval-valued functions(Springernature, 2022) Levent, Halise; Yilmaz, YilmazMathematically, a signal is a function of an independent variable t and it contains information about the behavior of the physical quantity. In real life, sometimes a signal value in a time t may not be known exactly. This paper presents a new mathematical method for processing of such a non-deterministic signal by using interval-valued functions which is called as its model interval signal. If the properties of a signal are completely unknown then we cannot perform the processing of these signals such as determining the autocorrelation function of the non-deterministic signal. Especially, in this work, we give an application to estimate the autocorrelation function of a signal with inexact data. For this purpose we use some new mathematical methods so called quasilinear functional analysis. Our studies give approximative result, although there are no definite results for such signals. We think that it's better than not having any information.Öğe Complex Interval Matrix and Its Some Properties(2023) Levent, Halise; Yılmaz, YılmazIn this paper, we present the notion of complex interval matrix. Further, we discuss the algebraic structure of the set of all $(mtimes n)$ complex interval matrices by using tools of quasilinear functional analysis. Finally, we put a norm on the space of the complex interval matrices and we calculate the norm of a complex interval matrices.Öğe Inner Product Fuzzy Quasilinear Spaces and Some Fuzzy Sequence Spaces(Hindawi Ltd, 2022) Yilmaz, Yilmaz; Bozkurt, Hacer; Levent, Halise; Cetinkaya, Uemitt has been shown that the class of fuzzy sets has a quasilinear space structure. In addition, various norms are defined on this class,and it is given that the class of fuzzy sets is a normed quasilinear space with these norms. In this study, we first developed thealgebraic structure of the class of fuzzy setsF(Rn)and gave definitions such as quasilinear independence, dimension, and thealgebraic basis in these spaces. .en, with special norms, namely,?u?q = ( integral(1)(0)(sup(x is an element of[u]alpha)?x?)(q)d alpha)(1/q )where 1 <= q <=infinity, we stated that (F(R-n),?u?(q))is a complete normed space. Furthermore, we introduced an inner product in this space for the case q=2. .e innerproduct must be in the form = integral(1)(0)<[u](alpha),[v](alpha)>(K(Rn))d alpha=integral(1)(0){(Rn)d alpha:a is an element of[u](alpha),b is an element of[v](alpha)}. Foru,v is an element of F(Rn). We alsoproved that the parallelogram law can only be provided in the regular subspace, not in the entire ofF(Rn).Finally, we showed thata special class of fuzzy number sequences is a Hilbert quasilinear space.Öğe Inner-product quasilinear spaces with applications in signal processing(Tbilisi Centre Math Sci, 2021) Yilmaz, Yilmaz; Levent, HaliseIf certain characteristics of a non-deterministic signal are known, can some approximate results be obtained concerning the frequency, deterministic autocorrelation or other characteristics of the signal? The mathematical techniques we have developed allow us to obtain some approximate estimations of this type. In this way we use some new mathematical methods so called quasilinear functional analysis. Interval analysis also in the scope of this area and we use complex interval-valued signals in calculations. Especially, in this work, we give some special properties and results of inner-product quasilinear spaces which are generalizations of classical inner-product spaces. By this results we give easy examples of approximate estimations of deterministic autocorrelation of some semi non-deterministic signals or signals with inexact data. Further, we have constructed the space Il(2) and we have showed that Il(2) is an inner-product quasilinear space. This space provides a basis for an estimation of deterministic autocorrelation of the signals with inexact data.Öğe On the Algebra of Interval Vectors(2023) Yılmaz, Yılmaz; Levent, Halise; Bozkurt, HacerIn this study, we examine some important subspaces by showing that the set of n-dimensional interval vectors is a quasilinear space. By defining the concept of dimensions in these spaces, we show that the set of $n$-dimensional interval vectors is actually a $(n_{r},n_{s})$-dimensional quasilinear space and any quasilinear space is $left( n_{r},0_{s}right) $-dimensional if and only if it is $n$-dimensional linear space. We also give examples of $(2_{r},0_{s})$ and $(0_{r},2_{s})$-dimensional subspaces. We define the concept of dimension in a quasilinear space with natural number pairs. Further, we define an inner product on some spaces and talk about them as inner product quasilinear spaces. Further, we show that some of them have Hilbert quasilinear space structure.Öğe Some Important Classes of the Continuous and Complex Interval-Valued Functions(2023) Levent, Halise; Yılmaz, YılmazThis paper presents some important classes of the continuous functions defined from the set of real numbers to the space of complex intervals. These function spaces have an algebraic structure named as a quasilinear space which is suggested by Aseev in 1986. In this work, we analysis the quasilinear structure on the classes of the continuous and complex interval-valued functions. Further, we show that these spaces are the normed ?-spaces. Finally, we examine the dimension of these function spaces.
