scholarly journals Vague data analysis using neutrosophic Jarque–Bera test

PLoS ONE ◽  
2021 ◽  
Vol 16 (12) ◽  
pp. e0260689
Author(s):  
Muhammad Aslam ◽  
Rehan Ahmad Khan Sherwani ◽  
Muhammad Saleem
Keyword(s):  
Reliability And Validity ◽  
Outcome Variable ◽  
Data Set ◽  
Operational Procedure ◽  
Gold Mines ◽  
Fuzzy Environment ◽  
First Choice ◽  
Vague Data ◽  
Existing Form ◽  
Interval Valued

In decision-making problems, the researchers’ application of parametric tests is the first choice due to their wide applicability, reliability, and validity. The common parametric tests require the validation of the normality assumption even for large sample sizes in some cases. Jarque-Bera test is among one of the methods available in the literature used to serve the purpose. One of the Jarque-Bera test restrictions is the computational limitations available only for the data in exact form. The operational procedure of the test is helpless for the interval-valued data. The interval-valued data generally occurs in situations under fuzzy logic or indeterminate state of the outcome variable and is often called neutrosophic form. The present research modifies the existing statistic of the Jarque-Bera test for the interval-valued data. The modified design and operational procedure of the newly proposed Jarque-Bera test will be useful to assess the normality of a data set under the neutrosophic environment. The proposed neutrosophic Jarque-Bera test is applied and compared with its existing form with the help of a numerical example of real gold mines data generated under the fuzzy environment. The study’s findings suggested that the proposed test is effective, informative, and suitable to be applied in indeterminacy compared to the existing Jarque–Bera test.

scholarly journals ResCaps: an improved capsule network and its application in ultrasonic image classification of thyroid papillary carcinoma

2021 ◽  
Author(s):  
Xiongzhi Ai ◽  
Jiawei Zhuang ◽  
Yonghua Wang ◽  
Pin Wan ◽  
Yu Fu
Keyword(s):  
Papillary Carcinoma ◽  
Network Model ◽  
Reliability And Validity ◽  
Thyroid Papillary Carcinoma ◽  
Data Set ◽  
Ultrasonic Image ◽  
First Choice ◽  
Thyroid Papillary ◽  
Ultrasonic Images

AbstractUltrasonic image examination is the first choice for the diagnosis of thyroid papillary carcinoma. However, there are some problems in the ultrasonic image of thyroid papillary carcinoma, such as poor definition, tissue overlap and low resolution, which make the ultrasonic image difficult to be diagnosed. Capsule network (CapsNet) can effectively address tissue overlap and other problems. This paper investigates a new network model based on capsule network, which is named as ResCaps network. ResCaps network uses residual modules and enhances the abstract expression of the model. The experimental results reveal that the characteristic classification accuracy of ResCaps3 network model for self-made data set of thyroid papillary carcinoma was $$81.06\%$$ 81.06 % . Furthermore, Fashion-MNIST data set is also tested to show the reliability and validity of ResCaps network model. Notably, the ResCaps network model not only improves the accuracy of CapsNet significantly, but also provides an effective method for the classification of lesion characteristics of thyroid papillary carcinoma ultrasonic images.

scholarly journals A Mathematical Programming Model to Determine Objective Weights for the Interval Extension of TOPSIS

2018 ◽  
Vol 2018 ◽  
pp. 1-6 ◽  
Author(s):  
Hai Shen ◽  
Lingyu Hu ◽  
Kin Keung Lai
Keyword(s):  
Mathematical Programming ◽  
Input Data ◽  
Programming Model ◽  
Multiple Criteria Decision Making ◽  
Decision Makers ◽  
Mathematical Programming Model ◽  
Topsis Method ◽  
Data Set ◽  
Interval Extension ◽  
Interval Valued

Technique for Order Performance by Similarity to Ideal Solution (TOPSIS) method has been extended in previous literature to consider the situation with interval input data. However, the weights associated with criteria are still subjectively assigned by decision makers. This paper develops a mathematical programming model to determine objective weights for the implementation of interval extension of TOPSIS. Our method not only takes into account the optimization of interval-valued Multiple Criteria Decision Making (MCDM) problems, but also determines the weights only based upon the data set itself. An illustrative example is performed to compare our results with that of existing literature.

Fuzzy Reliability Appraisal Using Interval-Valued Intuitionistic Hesitant Fuzzy Element and Score Function

2021 ◽  
pp. 2140005
Author(s):  
Deepak Kumar ◽  
S. B. Singh
Keyword(s):  
Score Function ◽  
Parallel Structure ◽  
Complex Structures ◽  
Bridge Structure ◽  
Fuzzy Reliability ◽  
Numerical Illustration ◽  
Advanced Technique ◽  
Fuzzy Environment ◽  
Unit Component ◽  
Interval Valued

Here, we appraise the reliability for numerous complex structures (series structure, parallel structure and bridge structure) using accuracy and score function under fuzzy environment. The main focus of this effort is to address an advanced technique for fuzzy reliability evaluation of various complex systems having different arrangements by treating reliability of the unit/component as an interval valued intuitionistic hesitant fuzzy element. This technique helps to handle uncertainty and hesitancy in multi-attribute group decision-making related issues, specially when information occurs in interval form in fuzzy set. A numerical illustration is also included to demonstrate the proposed technique.

scholarly journals ASYMPTOTICALLY EFFICIENT ESTIMATION OF WEIGHTED AVERAGE DERIVATIVES WITH AN INTERVAL CENSORED VARIABLE

2016 ◽  
Vol 33 (5) ◽  
pp. 1218-1241 ◽  
Author(s):  
Hiroaki Kaido
Keyword(s):  
Support Function ◽  
Weighted Average ◽  
Interval Data ◽  
Efficient Estimation ◽  
Outcome Variable ◽  
Nonparametric Bounds ◽  
Regression Functions ◽  
Semiparametric Efficiency Bound ◽  
Derivatives Of ◽  
Interval Valued

This paper studies the identification and estimation of weighted average derivatives of conditional location functionals including conditional mean and conditional quantiles in settings where either the outcome variable or a regressor is interval-valued. Building on Manski and Tamer (2002, Econometrica 70(2), 519–546) who study nonparametric bounds for mean regression with interval data, we characterize the identified set of weighted average derivatives of regression functions. Since the weighted average derivatives do not rely on parametric specifications for the regression functions, the identified set is well-defined without any functional-form assumptions. Under general conditions, the identified set is compact and convex and hence admits characterization by its support function. Using this characterization, we derive the semiparametric efficiency bound of the support function when the outcome variable is interval-valued. Using mean regression as an example, we further demonstrate that the support function can be estimated in a regular manner by a computationally simple estimator and that the efficiency bound can be achieved.

scholarly journals THE INTERVAL-VALUED INTUITIONISTIC FUZZY GEOMETRIC CHOQUET AGGREGATION OPERATOR BASED ON THE GENERALIZED BANZHAF INDEX AND 2-ADDITIVE MEASURE

2015 ◽  
Vol 21 (2) ◽  
pp. 186-215 ◽  
Author(s):  
Fanyong MENG ◽  
Qiang ZHANG ◽  
Jiaquan ZHAN
Keyword(s):  
Geometric Mean ◽  
Fuzzy Measure ◽  
Entropy Measure ◽  
Additive Measure ◽  
Banzhaf Index ◽  
Intuitionistic Fuzzy ◽  
Fuzzy Environment ◽  
Operational Laws ◽  
Additive Measures ◽  
Interval Valued

Based on the operational laws on interval-valued intuitionistic fuzzy sets, the generalized Banzhaf interval-valued intuitionistic fuzzy geometric Choquet (GBIVIFGC) operator is proposed, which is also an interval-valued intuitionistic fuzzy value. It is worth pointing out that the GBIVIFGC operator can be seen as an extension of some geometric mean operators. Since the fuzzy measure is defined on the power set, it makes the problem exponentially complex. In order to overall reflect the interaction among elements and reduce the complexity of solving a fuzzy measure, we further introduce the GBIVIFGC operator w.r.t. 2-additive measures. Furthermore, if the information about weights of experts and attributes is incompletely known, the models of obtaining the optimal 2-additive measures on criteria set and expert set are given by using the introduced cross entropy measure and the Banzhaf index. Finally, an approach to pattern recognition and multi-criteria group decision making under interval-valued intuitionistic fuzzy environment is developed, respectively.

Fuzzy Clustering

2017 ◽  
pp. 40-61 ◽  
Author(s):  
Mashhour H. Baeshen ◽  
Malcolm J. Beynon ◽  
Kate L. Daunt
Keyword(s):  
Data Analysis ◽  
Service Quality ◽  
Mobile Phone ◽  
Fuzzy Clustering ◽  
Data Set ◽  
Clustering Techniques ◽  
Fuzzy C Means ◽  
Fuzzy Environment ◽  
External Variables ◽  
Fuzzy C Means Clustering

This chapter presents a study of the development of the clustering methodology to data analysis, with particular attention to the analysis from a crisp environment to a fuzzy environment. An applied problem concerning service quality (using SERVQUAL) of mobile phone users, and subsequent loyalty and satisfaction forms the data set to demonstrate the clustering issue. Following details on both the crisp k-means and fuzzy c-means clustering techniques, comparable results from their analysis are shown, on a subset of data, to enable both graphical and statistical elucidation. Fuzzy c-means is then employed on the full SERVQUAL dimensions, and the established results interpreted before tested on external variables, namely the level of loyalty and satisfaction across the different clusters established.

Semidefinite Programming-Based Method for Implementing Linear Fitting to Interval-Valued Data

2011 ◽  
Vol 1 (3) ◽  
pp. 32-46 ◽  
Author(s):  
Minghuang Li ◽  
Fusheng Yu
Keyword(s):  
Lower Bound ◽  
Semidefinite Programming ◽  
Large Scale ◽  
Experimental Studies ◽  
Optimal Solution ◽  
Data Set ◽  
Linear Fitting ◽  
Optimal Value ◽  
Fitting Model ◽  
Interval Valued

Building a linear fitting model for a given interval-valued data set is challenging since the minimization of the residue function leads to a huge combinatorial problem. To overcome such a difficulty, this article proposes a new semidefinite programming-based method for implementing linear fitting to interval-valued data. First, the fitting model is cast to a problem of quadratically constrained quadratic programming (QCQP), and then two formulae are derived to develop the lower bound on the optimal value of the nonconvex QCQP by semidefinite relaxation and Lagrangian relaxation. In many cases, this method can solve the fitting problem by giving the exact optimal solution. Even though the lower bound is not the optimal value, it is still a good approximation of the global optimal solution. Experimental studies on different fitting problems of different scales demonstrate the good performance and stability of our method. Furthermore, the proposed method performs very well in solving relatively large-scale interval-fitting problems.

scholarly journals Multiple Attribute Group Decision-Making Based on Power Heronian Aggregation Operators under Interval-Valued Dual Hesitant Fuzzy Environment

2020 ◽  
Vol 2020 ◽  
pp. 1-19
Author(s):  
Shenqing Jiang ◽  
Wei He ◽  
Fangfang Qin ◽  
Qingqing Cheng
Keyword(s):  
Decision Making ◽  
Group Decision Making ◽  
Group Decision ◽  
Aggregation Operators ◽  
Fuzzy Environment ◽  
Multiple Attribute ◽  
Special Cases ◽  
Magdm Problems ◽  
Interval Valued ◽  
Heronian Mean

In this paper, we focus on new methods to deal with multiple attribute group decision-making (MAGDM) problems and a new comparison law of interval-valued dual hesitant fuzzy elements (IVDHFEs). More explicitly, the interval-valued dual hesitant fuzzy 2nd-order central polymerization degree (IVDHFCP2) function is introduced, for the case that score values of different IVDHFEs are identical. This function can further compare different IVDHFEs. Then, we develop a series of interval-valued dual hesitant fuzzy power Heronian aggregation operators, i.e., the interval-valued dual hesitant fuzzy power Heronian mean (IVDHFPHM) operator, the interval-valued dual hesitant fuzzy power geometric Heronian mean (IVDHFPGHM) operator, and their weighted forms. Some desirable properties and their special cases are discussed. These proposed operators can simultaneously reflect the interrelationship of aggregated arguments and reduce the influence of unreasonable evaluation values. Finally, two approaches for interval-valued dual hesitant fuzzy MAGDM with known or unknown weight information are presented. An illustrative example and comparative studies are given to verify the advantages of our methods. A sensitivity analysis of the decision results is analyzed with different parameters.

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