On ideal convergence of double sequences in probabilistic normed spaces

The notion of ideal convergence is a generalization of statistical convergence which has been intensively investigated in last few years.For an admissible ideal ∮N× N,the aim of the present paper is to introduce the concepts of ∮-convergence and ∮*-convergence for double sequences on probabilistic normed spaces(PN spaces for short).We give some relations related to these notions and find condition on the ideal ∮ for which both the notions coincide.We also define ∮-Cauchy and ∮*-Cauchy double sequences on PN spaces and show that ∮-convergent double sequences are ∮-Cauchy on these spaces.We establish example which shows that our method of convergence for double sequences on PN spaces is more general.     

Lattice valued intuitionistic fuzzy sets

In this paper a new definition of a lattice valued intuitionistic fuzzy set (LIFS) is introduced, in an attempt to overcome the disadvantages of earlier definitions. Some properties of this kind of fuzzy sets and their basic operations are given. The theorem of synthesis is proved: For every two families of subsets of a set satisfying certain conditions, there is an lattice valued intuitionistic fuzzy set for which these are families of level sets. The research supported by Serbian Ministry of Science and Technology, Grant No. 1227.     

On the Mazur-Ulam theorem in non-Archimedean fuzzy normed spaces

We prove that the Mazur-Ulam theorem holds under some conditions in non-Archimedean fuzzy normed space.     

On the law S ( S ( x , y ), T ( x , y )) = S ( x , y ) of fuzzy logic

Motivated by some functional models arising in fuzzy logic, when classical boolean relations between sets are generalized, we study the functional equation S(S(x, y), T(x, y)) = S(x, y), where S is a continuous t-conorm and T is a continuous t-norm. Some interesting methods for solving this type of equations are introduced.     

Stability of Pexiderized quadratic functional equation in intuitionistic fuzzy normed space

The object of the present paper is to determine the stability of the Hyers-Ulam-Rassias type theorem concerning the Pexiderized quadratic functional equation in intuitionistic fuzzy normed spaces (IFNS).     

About the statistical uniform convergence

In this work we study the concept of statistical uniform convergence. We generalize some results of uniform convergence in double sequences to the case of statistical convergence. We also prove a basic matrix theorem with statistical convergence.     

On convergence theory in fuzzy topological spaces and its applications

In this paper we introduce and study new concepts of convergence and adherent points for fuzzy filters and fuzzy nets in the light of the Q-relation and the Q-neighborhood of fuzzy points due to Pu and Liu [28]. As applications of these concepts we give several new characterizations of the closure of fuzzy sets, fuzzy Hausdorff spaces, fuzzy continuous mappings and strong Q-compactness. We show that there is a relation between the convergence of fuzzy filters and the convergence of fuzzy nets similar to the one which exists between the convergence of filters and the convergence of nets in topological spaces.     

Subcategories of Filter Tower Spaces

The concept of a convergence tower space, or equivalently, a convergence approach space is formulated here in the context of a Cauchy setting in order to include a completion theory. Subcategories of filter tower spaces are defined in terms of axioms involving a general t-norm, T, in order to include a broad range of spaces. A T-regular sequence for a filter tower space is defined and, moreover, it is shown that the category of T-regular objects is a bireflective subcategory of all filter tower spaces. A completion theory for subcategories of filter tower spaces is given.     

On the order conditions of fuzzy convergence classes

By means of the order structure of the related lattice, the LIMINF condition of fuzzy convergence classes is proposed in this paper, which reflects the essential difference between fuzzy convergence classes and ordinary convergence classes. The relationship between the LIMINF condition and two related conditions proposed by Liu and Wang respectively are discussed. The theory of fuzzy convergence classes based on LIMINF condition is established for topological molecular lattices, L-topological spaces (in the sense of Chang or Lowen), weakly induced spaces, and induced spaces.     

Controlling the space with preassigned responses

It is shown that large classes of control systems, which include certain systems of the typex+A(t)x=B(t)u, can be handled in such a way that the control functionsu(t) are actually associated with responsesx(t) that belong to known families of functions. In particular, it is possible, for a variety of perturbationsB(t)u and operatorsA(t) with convex domains, to have responses that are line segments joining the origin to the reachable states.The present approach establishes the fact that a vast number of results from functional analysis concerning ranges of operators can be effectively applied to the general theory of control. It is also rather significant that the present theory does not necessarily require the solvability of the associated Cauchy problem.The operatorsB(t)u do not have to be invertible inu. However, it is shown that continuous controlsu(t) can be obtained for a variety of problems whenB ^–1(t)u exists and is continuous int.     

Fuzzy Relation Equations for Compression/Decompression Processes of Colour Images in the RGB and YUV Colour Spaces

We use particular fuzzy relation equations for compression/decompression of colour images in the RGB and YUV spaces, by comparing the results of the reconstructed images obtained in both cases. Our tests are made over well known images of 256×256 pixels (8 bits per pixel in each band) extracted from Corel Gallery. After the decomposition of each image in the three bands of the RGB and YUV colour spaces, the compression is performed using fuzzy relation equations of “min - →_t” type, where “t” is the Lukasiewicz t-norm and “→_t” is its residuum. Any image is subdivided in blocks and each block is compressed by optimizing a parameter inserted in the Gaussian membership functions of the fuzzy sets, used as coders in the fuzzy equations. The decompression process is realized via a fuzzy relation equation of max-t type. In both RGB and YUV spaces we evaluate and compare the root means square error (RMSE) and the consequentpeak signal to noise ratio (PSNR) on the decompressed images with respect to the original image under several compression rates.     

Convergence of fourier series with respect to multiplicative systems and the p-fluctuation continuity modulus

We obtain some sufficient conditions for convergence of series of the Fourier coefficients with respect to multiplicative systems for functions of bounded p-fluctuation. In some cases we establish the unimprovability of these conditions.     

On general two-scale convergence and its application to the characterization of <Emphasis Type="Italic">G</Emphasis>-limits

We characterize some G-limits using two-scale techniques and investigate a method to detect deviations from the arithmetic mean in the obtained G-limit provided no periodicity assumptions are involved. We also prove some results on the properties of generalized two-scale convergence.     

On the convergence rate of Newton interior-point methods in the absence of strict complementarity

In the absence of strict complementarity, Monteiro and Wright [7] proved that the convergence rate for a class of Newton interior-point methods for linear complementarity problems is at best linear. They also established an upper bound of 1/4 for the Q ₁-factor of the duality gap sequence when the steplengths converge to one. In the current paper, we prove that the Q ₁ factor of the duality gap sequence is exactly 1/4. In addition, the convergence of the Tapia indicators is also discussed.This author was supported in part by NSF Coop. Agr. No. CCR-8809615 and AFOSR 89-0363 and the REDI Foundation.This author was supported in part by NSF Coop. Agr. No. CCR-8809615, AFOSR 89-0363, DOE DEFG05-86ER25017 and ARO 9DAAL03-90-G-0093.Visiting member of the Center for Research on Parallel Computations, Rice University, Houston, Texas, 77251-1892. This author was supported in part by DOE DE-FG02-93ER25171.     

On statistical approximation of a general class of positive linear operators extended in q-calculus

In this paper we present a general class of positive linear operators of discrete type based on q-calculus and we investigate their weighted statistical approximation properties by using a Bohman–Korovkin type theorem. We also mark out two particular cases of this general class of operators.     

On the convergence of finite linear predictors of stationary processes

It is shown that the finite linear least-squares predictor of a multivariate stationary process converges to its Kolmogorov-Wiener predictor at an exponential rate, provided that the entries of its spectral density matrix are smooth functions. Also, the same rate of convergence holds for the partial sums of the Kolmogorov-Wiener predictor.     

On integration of vector functions with respect to vector measures

We study integration of Banach space-valued functions with respect to Banach space-valued measures. We focus our attention on natural extensions to this setting of the Birkhoff and McShane integrals. The corresponding generalization of the Birkhoff integral was first considered by Dobrakov under the name S*-integral. Our main result states that S*-integrability implies McShane integrability in contexts in which the later notion is definable. We also show that a function is measurable and McShane integrable if and only if it is Dobrakov integrable (i.e. Bartle *-integrable).     

Collapsing to Riemannian manifolds with boundary and the convergence of the eigenvalues of the Laplacian

We prove that the eigenvalues of the Laplacian acting on functions converge to those of the limit manifold for a special collapsing family of closed Riemannian manifolds without curvature bounds. The proof uses L ²-analysis.Dedicated to Professor Hajime Urakawa on his sixtieth birthday.The author is partially supported by the Grant-in-Aid for Scientific Research No. 16740026 of the Japan Society for the Promotion of Science.     

On the fundamental convergence in the (C) mean in problems of information fusion

The Choquet integral can be regarded as one of aggregation operators being used in information fusion. In this study, we offer an interpretation of sequences of measurable functions and the Choquet integral in the framework of information fusion. Based on an efficiency measure space, we also define a new concept of a fundamental convergence in the (C) mean of sequences of measurable functions and discuss its theoretical underpinnings along with related interpretation issues as well as deliver some new results. Furthermore, an application of this concept is discussed in the context of information fusion. More specifically, based on the theoretical investigations, this idea is applied to the determination of a measurable function being used in the Choquet integral.