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Accurate measurement of the incidence of poverty is essential for monitoring the performance of countries against poverty. In poverty measurement, the global poverty line (GPL) is usually converted to national equivalents in local currencies, with the available purchasing power parities (PPPs) from the World Bank’s International Comparison Program (ICP), instead of the exchange rate. This approach is often criticized for various limitations, and the poverty PPPs are recommended to be estimated from modifications of the ICP framework as a conversion factor of the GPL. This study employs a sample of price data in 2015 and the approximate expenditure budgets of poor households to estimate the regional poverty PPPs in China. The results show that the estimates of regional poverty PPPs with different aggregating methods are very similar, and the price levels for the poor in the more-developed regions are usually high, while those in the less-developed regions are relatively low. The urban poverty PPPs of four regions are greater than 1 (with Beijing = 1), while the rural poverty PPPs of seven regions are greater than 1. The series of regional poverty PPPs are obtained by extrapolation and reveal that there is a price convergence phenomenon among regions during the period. With the regional poverty PPPs, the urban and rural regional poverty lines (RPLs) across China are estimated, based on the World Bank’s GPL.

We extend and unify several Hardy type inequalities to functions whose values are positive semi-definite operators. In particular, our methods lead to the operator versions of Hardy–Hilbert's and Godunova's inequalities. While classical Hardy type inequalities hold for parameter values p > 1, it is typical that the operator versions hold only for 1 < p ≤ 2, even for functions with values in 2 × 2 matrices.

The present paper develops a weighted least-square dissimilarity approach to address the Multiple Criteria ABC inventory classification problem, when the different criteria ranking makes impossible to achieve a group consensus. The proposed approach effectively eliminates drawbacks regarding subjective judgements of multiple decision makers on the criteria importance, and comprehensively aggregates all rankings of the criteria importance to provide a more reasonable and effective classification mechanism. The common weights associated with all rankings are determined. An illustrative example is presented to compare the performance of our approach with the existing studies.

Recently, there has been a rapid increase in the volume of medical image repositories because of the maximized utilization of digitized image data in hospitals. As a result, there is a complexity in querying and handling such large databases, which has led to the development of a novel Content-Based Medical Image Retrieval (CBMIR) technique. In this work, the CBMIR technique is developed using three types of visual features (i.e., color, texture and shape) along with 12 distance measures, and is optimized with the Crossover-Gravitational Search Algorithm (CRO-GSA). For ease, we named this technique Content-Based Medical Image Retrieval using Visual features with CRO-GSA (CBMIRVC). The initial step of our CBMIRVC technique is to extract three types of visual features from the images. Then, each type of feature is employed with a suitable distance measure, which is used for the computation of image similarities between the medical images in the database and a provided query image. The optimization of our proposed CBMIRVC technique is done by the CRO-GSA algorithm. This algorithm optimizes the CBMIRVC technique by identifying the optimal combinations of visual features and similarity measures. Additionally, optimal weights are computed in accordance with the three types of features for the three similarities. Experimental validations were done using retrieved cancer-related and endoscopic color images from databases holding numerous image categories. The experimental outcome shows that our proposed CBMIRVC technique outperforms other conventional image retrieval techniques by effectively retrieving similar images from large databases.

Many medical specialists used Computer Aided Diagnostic (CAD) systems as a second opinion to detect breast masses. The poor visualization of mass images makes it difficult to identify precisely. To segment the lesions from the mammograms is a difficult task due to different shapes, sizes, and locations of the masses. The motivation of this study is to develop a method that can segment breast mass lesions from mammogram images. The objective is to perform the segmentation of the breast mass mammogram images more precisely at an early stage. Breast mass segmentation is always a basic requirement in computer-aided diagnosis systems. In this study segmentation of the masses abnormalities from the mammogram images is performed by using the Skipping Dilated semantic segmentation approach. The study uses class weights and Dilation factor using semantic Convolutional Neural Network (CNN). It overcomes the class misbalance in tumors and background class, that affect the mean Intersection over Union (MIOU), and weighted-IOU (WIOU) by using class weights. Secondly, dilation convolution magnifies the receptive field exposure that enriches the convolutional operation with context attentiveness. Two public datasets of mammography INbreast and CBIS-DDSM are used. The WIOU of Skipping Dilated Semantic CNN for INbreast is 98.51% and CBIS-DDSM is 94.82% achieved.

The aim of this work is to develop a new compatibility for the uncertain multiplicative linguistic preference relations and determine the optimal weights of decision makers (DMs), which are very suitable to deal with group decision making (GDM) problems involving uncertain multiplicative linguistic preference relations. First, the concepts of compatibility degree and compatibility index for the two uncertain multiplicative linguistic preference relations are proposed. Then we prove the property that the synthetic uncertain linguistic preference relation is of acceptable compatibility under the condition that uncertain multiplicative linguistic preference relations given by DMs are all of acceptable compatibility with a specific linguistic preference relation, which is the scientific basis of using the uncertain multiplicative linguistic preference relations in the GDM. Next, in order to determine the weights of decision makers, we construct an optimal model based on the criterion of minimizing the compatibility index. Finally, we develop an application of the optimal weights approach compared with the equal weights approach where we analyze a GDM regarding the selection of investment.

The integrity of a graph $G$ is defined as the minimum value of $\left|S\right|+m(G-S)$ taken over all $S\subseteq V(G)$, where $m(H)$ denotes the maximum cardinality of a component of graph $H$. In this paper, we investigate bounds on the maximum and minimum values of the weighted version of this parameter. We also consider the same question for the related parameter vertex-neighbor-integrity.

Evaluating sustainable conceptual designs is a crucial part of the development of new products in various sectors because it contributes to the survival and prosperity of companies. Such designs must be compatible with a product’s functional requirements and be sustainable in economic, environmental, and social terms. Various criteria, some qualitative and others quantitative, are considered when evaluating sustainable conceptual designs; some criteria may also have sub-criteria, and these criteria and sub-criteria may differ in importance. How to effectively evaluate various criteria and sub-criteria and weight them are the major research problem. This study developed an analytic hierarchy process (AHP)-based ELECTRE I method to resolve the evaluation problem; the method entails a two-level hierarchical structure to depict the relationships between the major criteria and sub-criteria and their corresponding weights, with weights obtained through an AHP. Furthermore, an extension based on the addition of net concordance value and net adjusted discordance value is proposed for ranking alternative designs; this extension yields more distinguishable results than the method of [Nijkamp and Van Delft Multi-Criteria Analysis and Regional Decision-Making, Vol. 8 (Springer Science & Business Media, 1977)], and the proposed extension in the ELECTRE I method captures more information in the modified summation matrix when aggregating values in the concordance matrix and the modified discordance matrix, representing an advantage over the method of [Zhang et al. Virtual network embedding using node multiple metrics based on simplified ELECTRE method, IEEE Access6 (2018) 37314–37327]. In addition, to demonstrate the feasibility of the proposed method, the example of the evaluation and selection of sustainable conceptual designs in the furniture manufacturing industry is presented. Finally, a numerical comparison is made to show the advantages of the proposed method.

Univariate regression trees have representation problems for non-orthogonal regression functions. Ensembles of univariate regression trees have better representational power. In some cases, weighted ensembles have shown better performance than unweighted ensembles. In this paper, we study the properties of ensembles of regression trees by using regression classification models. We propose a theoretical framework to study the representational power of infinite-sized weighted ensembles, consisting of randomised finite-sized regression trees. We show for some datasets that the weighted ensembles may have better representational power than unweighted ensembles, but the performance is highly dependent on the weighting scheme and the properties of datasets. Our model cannot be used for all the datasets. However, for some datasets, we can accurately predict the experimental results of ensembles of regression trees.

To reduce the effect of environment factor against mass measurement of high accuracy, robot system with three-axis motion, data acquisition of environment parameters and function of remote communication is developed for realizing automatic remote measurement of high accurate weights. The system consists of function of automatic centering, combined weights to be load and unload, combined comparison measurement and function of automatic measuring for temperature, humidity and air pressure. Weights from 1 mg to 10 g are determined by the system with method of direct comparison and combined comparison. The experimental results show extended uncertainty of direct comparison and combined comparison from 1 mg to 10 g is better than 4.3 μg (k=2).

According to Annex B.7.4 of OIML R111-1, equipment for measuring volume of weights mass ranging from 1 kg to 20 kg including three methods of hydrostatic comparison is described. The equipment consists of a robot arm for transferring weights, a liquid bath, a mass comparator with 26.1 kg of maximum capacity and 1 mg of readability, glass housing, two weight exchangers including in air and in liquid, two weight holders including in air and in liquid, and a controller. The equipment will enable to perform automatically volume measurements.

The paper presents a simple and robust Multicriteria Decision Aiding Technique based on the use of statistical instruments. The objective is twofold: firstly, to provide a statistical tool to interpret enquiries on large samples of customers or clients facing multicriteria choices of some products or brands. Secondly, to help decision makers in making multicriteria choices in ranking alternatives corresponding to different preference profiles.

The following sections are included:

• Introduction
• Preliminaries
• Dyadic operators
• Digression: one weight inequalities
• Testing conditions
• Bump conditions
• Separated bump conditions
• References

Let 1 < p < +∞ and let v be a weight on (0, +∞) such that v(x)x^ρ is equivalent to a non-decreasing function on (0, +∞) for some ρ ≥ 0. Let A be the averaging operator given by , x ∈ (0, +∞), and let L^p(v) denote the weighted Lebesgue space of all measurable functions f on (0, +∞) for which . Then the following statements are equivalent:

(i) A is bounded on L^p(v);

(ii) A is bounded on L^p-ε(v) for some ε ∈ (0,p - 1);

(iii) A is bounded on L^p(v^1+ε) for some ε > 0;

(iv) A is bounded on L^p(v(x)x^ε) for some ε > 0.

Moreover, if A is bounded on L^p(v), then A is bounded on L^q(v) for all q ∈ [p, +∞).

We also show that the boundedness of the averaging operator A on the space L^p(v) implies that, for all r > 0, the weight v^1-p′ satisfies the reverse Hölder inequality over the interval (0, r) with respect to the measure dt, while the weight v satisfies the reverse Hölder inequality over the interval (r, +∞) with respect to the measure t^-p dt.

Assume moreover that p ≤ q < +∞ and that w is a weight on (0, +∞) such that

Then the operator A is bounded on L^p(v) if and only if the operator A : L^p(v) → L^q(w) is bounded. This enables us to transfer our results on the boundedness of the operator A mentioned above to the case when the operator A acts between two weighted Lebesgue spaces L^p(v) and L^q(w).