Distance and similarity measures of Pythagorean fuzzy sets based on the Hausdorff metric with application to fuzzy TOPSIS

Pythagorean fuzzy sets (PFSs) were proposed by Yager in 2013 to treat imprecise and vague information in daily life more rigorously and efficiently with higher precision than intuitionistic fuzzy sets. In this paper, we construct new distance and similarity measures of PFSs based on the Hausdorff metric. We first develop a method to calculate a distance between PFSs based on the Hasudorff metric, along with proving several properties and theorems. We then consider a generalization of other distance measures, such as the Hamming distance, the Euclidean distance, and their normalized versions. On the basis of the proposed distances for PFSs, we give new similarity measures to compute the similarity degree of PFSs. Some examples related to pattern recognition and linguistic variables are used to validate the proposed distance and similarity measures. Finally, we apply the proposed methods to multicriteria decision-making by constructing a Pythagorean fuzzy Technique for Order Preference by Similarity to an Ideal Solution and then present a practical example to address an important issue related to social sector. Numerical results indicate that the proposed methods are reasonable and applicable and also that they are well suited in pattern recognition, linguistic variables, and multicriteria decision-making with PFSs.     

Chest X-ray enhancement to interpret pneumonia malformation based on fuzzy soft set and Dempster–Shafer theory of evidence

Image enhancement algorithms are commonly used to increase the contrast and visual quality of low-dose x-ray images. This paper proposes an automated enhancement method using soft fuzzy sets with a new decision-making scheme based on Dempster-Shafer theory of evidence for the visual interpretation of pneumonia malformation in low-dose x-ray images, called as XEFSDS. The XEFSDS model first generates an original source x-ray image into a complementary image, then each original and complement image is applied to the characterized image object and background areas of fuzzy space. The S-function is utilized to define fuzzy soft sets for the classification of gray level ambiguity in both images, and hence a decision criterion via Dempster-Shafer approach and fuzzy interval has been adapted to discriminate uncertainties on the pixel intensity and the spatial information. Modified membership grade operations have been performed on each object/background area, and Werner’s AND/OR operator (an aggregation operator) has been utilized to build a new membership function from two modified membership functions. Finally, an enhanced image is obtained from the new membership function via defuzzification. Experiments on different pneumonia X-ray images demonstrate that the XEFSDS scheme produces better results than the existing methods. To show the advantages of the XEFSDS scheme, we have executed a segmentation based examination on enhanced image for the detection of pneumonia malformation as well as abnormal lobe (lobar pneumonia) or bronchopneumonia.     

Integrated rough VIKOR for customer-involved design concept evaluation combining with customers’ preferences and designers’ perceptions

Customer-involved design concept evaluation (DCE) allows customers to take part in evaluating the design alternatives to get more popular design concept. Traditional customer-involved DCE methods still focus on the collection of customer responses and only consider cost and benefit characteristics of design criteria in multi-criteria decision-making (MCDM) based evaluation process. Few studies have customized the decision-making algorithms specifically aimed at customers’ preferences. This paper further explores the customers’ influences in the early stages of the product design development, and proposes a new rough number based MCDM model (i.e., VIKOR) incorporating customers’ preferences for design specifications along with designers’ perceptions for the characteristics of design criteria (cost and benefit) to perform concept evaluation under subjective environment, and this proposed method is named as integrated rough VIKOR (IR-VIKOR). The objective of this study is to identify the best design concept which maximizes the satisfactions of expectations from most customers as well as conforms to the characteristics of design criteria. Firstly, Shannon entropy is used to obtain the weightings and relative importance ratings of design criteria from the customers’ preferences. Secondly, the customers’ preferences for design attribute values, the importance ratings of design criteria and the characteristics of design criteria are combined together to define the ideal solutions to calculate the rough evaluation index of each design alternative in IR-VIKOR, and finally the ranking result is provided by IR-VIKOR to determine the best design concept. A practical design example is introduced to illustrate the evaluation process of this proposed method, and the empirical comparisons are further carried out to validate its superiority for DCE. Through the sensitivity analysis experiments including i) inside IR-VIKOR, and ii) between IR-VIKOR and other classical MCDM methods, the proposed method is proved to be a reliable and feasible customer-involved DCE approach.     

基于工业机器人的液压支架导向套柔性制造系统

自动化技术在小批量多品种的产品制造中，存在兼容难、换产时间长、人工干预多等问题，导致生产线难以高效率运行。设计的柔性制造系统，在充分分析了导向套不同结构、不同规格的基础上，以一套六关节机器人和行走地轨作为物流搬运设备，同时负责3台数控设备、自动辊道上料设备、自动堆垛下料设备、翻转机构、打标机构及抽检机构的上下料，并通过使用机器人双工位卡爪、机床六爪卡盘、自动刀补等卡具及技术，实现了一键换产，极大提高了制造系统的柔性。     

面向文本数据的正则化交叉验证方法

面向文本数据建模时,交叉验证方法是特征选择及模型比较任务中的常用方法。许多研究表明,文本数据模型的性能估计对交叉验证的数据切分方式较为敏感,不合理的切分方式可能会导致不稳定的性能估计值,使得实验结果可复现性差。该文试图论证基于多次重复(m次)的2折交叉验证,通过引入对训练集、验证集分布差异的约束,所构造的正则化m×2交叉验证方法(简记为m×2 BCV)可以改善模型的性能指标的估计,适宜于模型比较。该文首先针对文本数据引入训练集与验证集分布差异的卡方度量,基于该度量构建数据切分的正则化条件,以最大化模型性能指标的信噪比为目标,给出了满足正则化条件的m×2 BCV的数据切分优化算法。最后,以自然语言处理中汉语框架语义角色标注任务为例,验证了基于m×2 BCV方法的有效性。     

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.     

On lattice ordered soft sets

Certain type of linguistic terms such as satisfactory, good, very good and excellent have an order among them. In this paper we introduce a new concept of soft sets with some order among the parameters. Some properties of lattice ordered soft sets are given. Lattice ordered soft sets are very useful in particular type of decision making problems where some order exists among the elements of parameters set.     

From sustainability to sustainizability

Following the recent introduction of the Sustainability over Sets (SOS) concept as a sustainability analysis tool with broad flexibility in incorporating human input, in this work, the concepts of Sustainizability (SIZ) and Sustainizability over Sets (SIZOS) are introduced, as novel frameworks for sustainable system synthesis. Springing off the conceptual foundation of sustainability, SIZ (and SIZOS) refers to the existence of allowable external actions, and/or design changes that can render sustainable (sustainable over a set) an unsustainable (unsustainable over a set) system. Utilizing earlier mathematical results for SOS, rigorous necessary and sufficient conditions for SIZOS are presented. Two case studies, on a two-dimensional biological waste treatment system, and a three-dimensional food chain system, are then presented to illustrate the developed necessary and sufficient conditions for SIZOS.