Robust Estimation Method Based on Function Model of Successive Approximation

In measurement practice, the residuals in least squares adjustment usually show various abnormal discrete distributions, including outliers, which is not conducive to the optimization of final measured values. Starting with the physical mechanism of dispersion and outlier of repeated observation errors, this paper puts forward the error correction idea of using the approximate function model of error to approach the actual function model of error step by step, gives a new theoretical method to optimize the final measured values, and proves the effectiveness of the algorithm by the ability of responding to the true values. This new idea is expected to be the ultimate answer of robust estimation theory.

Multi-Attribute Decision-Support System Based on Aggregations of Interval-Valued Complex Neutrosophic Hypersoft Set

Hypersoft set is an emerging field of study that is meant to address the insufficiency and the limitation of existing soft-set-like models regarding the consideration and the entitlement of multi-argument approximate function. This type of function maps the multi-subparametric tuples to the power set of the universe. It focuses on the partitioning of each attribute into its attribute-valued set that is missing in existing soft-set-like structures. This study aims to introduce novel concepts of complex intuitionistic fuzzy set and complex neutrosophic set under the hypersoft set environment with interval-valued settings. Two novel structures, that is, interval-valued complex intuitionistic hypersoft set (IV-CIFHS-set) and interval-valued complex neutrosophic hypersoft set (IV-CNHS-set), are developed via employing theoretic, axiomatic, graphical, and algorithmic approaches. After conceptual characterization of essential elementary notions of these structures, decision-support systems are presented with the proposal of algorithms to assist the decision-making process. The proposed algorithms are validated with the help of real-world applications. A comprehensive inter-cum-intra comparison of proposed structures is discussed with the existing relevant models, and their generalization is elaborated under certain evaluating features.

n Adaptive Sparse Array Beamforming Algorithm Based on Approximate L0-norm and Logarithmic Cost

This paper introduces a constrained normalized adaptive sparse array beamforming algorithm based on approximate L0-norm and logarithmic cost (L0-CNLMLS). The proposed algorithm can control the sparsity of the array by introducing an approximate function of L0-norm. In addition, the introduction of logarithmic cost improves the stability of the algorithm as well as the convergence rate of the algorithm. The sparsity of the array can be controlled when adjusting related parameter in the proposed algorithm. Simulation results show the better performance of L0-CNLMLS compared with some conventional algorithms.

On Model Order Reduction of Interconnect Circuit Network: A Fast and Accurate Method

The time cost in integrated circuit simulation is an important consideration in the design. This paper investigates the model order reduction of interconnect circuit networks to facilitate numerical analysis. A novel fast and accurate time reduced order model is proposed to simplify the interconnection network structure analysis and perform a fast simulation. The novelty of this study is the use of the power function sum to extend the approximate function to replace the original system’s state function. We give several simulations to verify the effectiveness of the algorithm. The innovation of this model is due to its use of the approximate function of power series expansion to replace the state function of the original system.

An Adaptive Proximal Bundle Method with Inexact Oracles for a Class of Nonconvex and Nonsmooth Composite Optimization

In this paper, an adaptive proximal bundle method is proposed for a class of nonconvex and nonsmooth composite problems with inexact information. The composite problems are the sum of a finite convex function with inexact information and a nonconvex function. For the nonconvex function, we design the convexification technique and ensure the linearization errors of its augment function to be nonnegative. Then, the sum of the convex function and the augment function is regarded as an approximate function to the primal problem. For the approximate function, we adopt a disaggregate strategy and regard the sum of cutting plane models of the convex function and the augment function as a cutting plane model for the approximate function. Then, we give the adaptive nonconvex proximal bundle method. Meanwhile, for the convex function with inexact information, we utilize the noise management strategy and update the proximal parameter to reduce the influence of inexact information. The method can obtain an approximate solution. Two polynomial functions and six DC problems are referred to in the numerical experiment. The preliminary numerical results show that our algorithm is effective and reliable.

Approximate Solution of Bratu Differential Equations Using Trigonometric Basic Functions

In this paper, I have proposed a method for finding an approximate function for Bratu differential equations (BDEs), in which trigonometric basic functions are used. First, by defining trigonometric basic functions, I define the values of the transformation function in relation to trigonometric basis functions (TBFs). Following that, the approximate function is defined as a linear combination of trigonometric base functions and values of transform function which is named trigonometric transform method (TTM), and the convergence of the method is also presented. To get an approximate solution function with discrete derivatives of the solution function, we have determined the approximate solution function which satisfies in the Bratu differential equations (BDEs). In the end, the algorithm of the method is elaborated with several examples. In one example, I have presented an absolute error comparison of some approximate methods.

Decision making algorithmic techniques based on aggregation operations and similarity measures of possibility intuitionistic fuzzy hypersoft sets

<abstract><p>Soft set has limitation for the consideration of disjoint attribute-valued sets corresponding to distinct attributes whereas hypersoft set, an extension of soft set, fully addresses this scarcity by replacing the approximate function of soft sets with multi-argument approximate function. Some structures (i.e., possibility fuzzy soft set, possibility intuitionistic fuzzy soft set) exist in literature in which a possibility of each element in the universe is attached with the parameterization of fuzzy sets and intuitionistic fuzzy sets while defining fuzzy soft set and intuitionistic fuzzy soft set respectively. This study aims to generalize the existing structure (i.e., possibility intuitionistic fuzzy soft set) and to make it adequate for multi-argument approximate function. Therefore, firstly, the elementary notion of possibility intuitionistic fuzzy hypersoft set is developed and some of its elementary properties i.e., subset, null set, absolute set and complement, are discussed with numerical examples. Secondly, its set-theoretic operations i.e., union, intersection, AND, OR and relevant laws are investigated with the help of numerical examples, matrix and graphical representations. Moreover, algorithms based on AND/OR operations are proposed and are elaborated with illustrative examples. Lastly, similarity measure between two possibility intuitionistic fuzzy hypersoft sets is characterized with the help of example. This concept of similarity measure is successfully applied in decision making to judge the eligibility of a candidate for an appropriate job. The proposed similarity formulation is compared with the relevant existing models and validity of the generalization of the proposed structure is discussed.</p></abstract>

A new method to choose the approximate function in order to determine the correlation between the imposed and the obtained clearances in FDM

Practical experiments proved that the variation of clearance between two circular pieces simultaneously manufactured by FDM, in function of different parameters has a complex variation starting from zero when the imposed clearance has a small value and being approximated by the value of the imposed clearance when the last one has great values. This observation implies that the resulted clearance may be approximated by non-linear functions for which one has to impose some frontier conditions. In this paper we discuss the conditions which have to be fulfilled by the candidate functions, considered only by polynomial ones.

Learning solutions to a Cauchy problem for the modified Helmholtz equations using LS-SVM

Purpose The purpose of this paper is to develop a mesh-free algorithm based on the least square support vector machines method for numerical simulation of the modified Helmholtz equations. Design/methodology/approach The proposed method deals with a Cauchy problem for the modified Helmholtz equations. The algorithm converts the problem into a quadratic programming. It can be divided into three steps. First, some training points are allocated. Then, an approximate function is constructed. Finally, the shape parameters are estimated. Findings The proposed method's stability is discussed. Numerical experiments are conducted to check the efficiency of the algorithm. The proposed method is found to feasible for the ill-posed problems of the modified Helmholtz equations. Originality/value The originality lies in that the proposed method is applied to solve the modified Helmholtz equations for the first time, and the expected results are obtained.