Some picture fuzzy Bonferroni mean operators with their application to multicriteria decision making

In this paper, we extend the Bonferroni mean (BM) operator with the picture fuzzy numbers (PFNs) to propose novel picture fuzzy aggregation operators and demonstrate their application to multicriteria decision making (MCDM). On the basis of the algebraic operational rules of PFNs and BM, we introduce some aggregation operators: the picture fuzzy Bonferroni mean, the picture fuzzy normalized weighted Bonferroni mean, and the picture fuzzy ordered weighted Bonferroni mean. Then, a new picture fuzzy MCDM method is proposed with the help of the proposed operators. Lastly, a practical application of proposed model is given to verify the developed model and related results of the proposed model is compared with the results of the existing models to indicate its applicability.     

Convergence analysis of the alternating RGLS algorithm for the identification of the reduced complexity Volterra model

In this paper we provide a convergence analysis of the alternating RGLS (Recursive Generalized Least Square) algorithm used for the identification of the reduced complexity Volterra model describing stochastic non-linear systems. The reduced Volterra model used is the 3rd order SVD-PARAFC-Volterra model provided using the Singular Value Decomposition (SVD) and the Parallel Factor (PARAFAC) tensor decomposition of the quadratic and the cubic kernels respectively of the classical Volterra model. The Alternating RGLS (ARGLS) algorithm consists on the execution of the classical RGLS algorithm in alternating way. The ARGLS convergence was proved using the Ordinary Differential Equation (ODE) method. It is noted that the algorithm convergence canno׳t be ensured when the disturbance acting on the system to be identified has specific features. The ARGLS algorithm is tested in simulations on a numerical example by satisfying the determined convergence conditions. To raise the elegies of the proposed algorithm, we proceed to its comparison with the classical Alternating Recursive Least Squares (ARLS) presented in the literature. The comparison has been built on a non-linear satellite channel and a benchmark system CSTR (Continuous Stirred Tank Reactor). Moreover the efficiency of the proposed identification approach is proved on an experimental Communicating Two Tank system (CTTS).     

A Lattice Approach to Image Segmentation

After a formal definition of segmentation as the largest partition of the space according to a criterion σ and a function f, the notion of a morphological connection is reminded. It is used as an input to a central theorem of the paper (Theorem 8), that identifies segmentation with the connections that are based on connective criteria. Just as connections, the segmentations can then be regrouped by suprema and infima. The generality of the theorem makes it valid for functions from any space to any other one. Two propositions make precise the AND and OR combinations of connective criteria. The soundness of the approach is demonstrated by listing a series of segmentation techniques. One considers first the cases when the segmentation under study does not involve initial seeds. Various modes of regularity are discussed, which all derive from Lipschitz functions. A second category of examples involves the presence of seeds around which the partition of the space is organized. An overall proposition shows that these examples are a matter for the central theorem. Watershed and jump connection based segmentations illustrate this type of situation. The third and last category of examples deals with cases when the segmentation occurs in an indirect space, such as an histogram, and is then projected back on the actual space under study. The relationships between filtering and segmentation are then investigated. A theoretical chapter introduces and studies the two notions of a pulse opening and of a connected operator. The conditions under which a family of pulse openings can yield a connected filter are clarified. The ability of segmentations to generate pyramids, or hierarchies, is analyzed. A distinction is made between weak hierarchies where the partitions increase when going up in the pyramid, and the strong hierarchies where the various levels are structured as semi-groups, and particularly as granulometric semi-groups. The last section is based on one example, and goes back over the controversy about “lattice” versus “functional” optimization. The problem is now tackled via a case of colour segmentation, where the saturation serves as a cursor between luminance and hue. The emphasis is put on the difficulty of grouping the various necessary optimizations into a single one.     

H∞-control with measurement-feedback for Pritchard-Salamon systems

In this paper we extend the finite-dimensional results for the H_∞-control problem with measurement-feedback to a large class of infinite-dimensional systems, allowing for a certain type of unboundedness in the input and output operators (the Pritchard-Salamon class). The main result of the paper relates the solvability to the suboptimal H_∞-control problem to the existence of stabilizing solutions to certain operator Riccati equations. Furthermore, a characterization of all suboptimal controllers is given.     

Nonlinear adaptive algorithms for equalisation in mobile satellite communications

This paper considers the equalisation problem in Quadrature Phase-Shift Keying (QPSK) modulated signals which have been distorted by the passage through a transmission channel. The channel is modelled as a Rician fading channel to simulate the behaviour of the transmission channel in the mobile satellite context. The equalisation is treated as the generalisation of the channel behaviour, and some algorithms with the structure of an artificial neural network using the Multilayer Perceptron, Volterra Series and Radial Basis Function are described. Results for the BER performance of typical transversal equalisers, with Square-Root Kalman adaptation algorithm, and algorithms with artificial neural network structure are also reported and evaluated. Improved performance is exhibited by the artificial neural network approaches.     

On parity problems and the functional-link artificial neural network

This paper contains the proof of a theorem on the capability of functional-link artificial neural networks both to represent and to learn the n-dimensional parity problem. The result is obtained by an embedding of the problem into a space of dimension 2ⁿ — 1. It is shown that the Volterra expansion of the data in n-dimensions provides the necessary transformation. By computing the parity function, it is shown that a suitable set of neural network weights can be deduced. Finally, it is demonstrated that 2ⁿ — 1 is the minimum embedding dimension for the problem.The contribution of A Zuderell of the University of Innsbruck is acknowledged.     

Convergence of iterated boolean sums of simultaneous approximants

Explicit error estimates are given for the iterated Boolean sum of a sequence of simultaneous approximants; the rate of convergence is shown to be improved for smooth functions. The general results are applied in the case of the Bernstein, Durrmeyer and Stancu operators.     

毫米波谐波振荡器的多模Volterra级数分析

本文基于Ｖｏｌｔｅｒｒａ级数和非线性转移函数理论，提出了一种分析毫米波谐波振荡器的新方法一多模Ｖｏｌｔｅｒｒａ级数法，并给出了描述其非线性特性的决定方程，通过求解一组非线性代数方程，便可计算出谐波振荡器的振荡频和幅度。文中给出了分析实例并与谐波平衡法等进行了比较，结果表明：这种方法具有理论严密、准确性高，适用范围广等特点特别是利用一次决定方程的结果作为其它非线性数值分析方法的初始估值，可大大地节约     

毫米波谐波振荡器的Volterra级数分析法

本文基于Ｖｏｌｔｅｒｒａ级数法和非线性转移函数理论，提出了一种分析毫米波谐波振荡器的新方法，给出了描述其非线性特性的决定方程，通过求解一组非线性代数方程，便可计算出谐波振荡器的振荡频率和幅度。文中给出了具体分析实例，并与谐波平衡法等进行了比较，结果表明：这种方法具有理论严密、准确性高、适用范围广等特点，特别是利用一次决定方程的结果作为其它非线性数值分析方法的初始估值，则可大大地节约计算时间，并容易