Weighted Correlation Coefficient Research Articles

Correlation Coefficients of Probabilistic Hesitant Fuzzy Elements and Their Applications to Evaluation of the Alternatives

Correlation coefficient is one of the broadly use indexes in multi-criteria decision-making (MCDM) processes. However, some important issues related to correlation coefficient utilization within probabilistic hesitant fuzzy environments remain to be addressed. The purpose of this study is introduced a MCDM method based on correlation coefficients utilize probabilistic hesitant fuzzy information. First, the covariance and correlation coefficient between two PHFEs is introduced, the properties of the proposed covariance and correlation coefficient are discussed. In addition, the northwest corner rule to obtain the expected mean related to the multiply of two PHFEs is introduced. Second, the weighted correlation coefficient is proposed to make the proposed MCDM method more applicable. And the properties of the proposed weighted correlation coefficient are also discussed. Finally, an illustrative example is demonstrated the practicality and effectiveness of the proposed method. An illustrative example is presented to demonstrate the correlation coefficient propose in this paper lies in the interval [−1, 1], which not only consider the strength of relationship between the PHFEs but also whether the PHFEs are positively or negatively related. The advantage of this method is it can avoid the inconsistency of the decision-making result due to the loss of information.

Statistical Analysis for Quality Adjustment of the Analytical Curve for Determination of Pesticide Multiresidue in Pineapple Samples

This work describes the development of an analytical methodology based on the modified QuEChERS method and GC/MS detection involving the analysis of 38 pesticides in pineapple from a local market in Fortaleza-Brazil. Matrix-standard calibration and heteroscedasticity have been studied by a weighted least squares linear regression model application. The analytical curves for most of the analytes (except cyproconazole and pyraclostrobin) presented heteroscedasticity by weighted least square regression (WLS). The weighted correlation coefficient values were in the range of 0.9690 to 0.9987 (linear range of 0.03 to 0.50 mg kg−1). The calibration curves obtained by applying regression by ordinary least squares (OLS) showed relative errors of approximately 32.3% for fenpropathrin, 23.1% for buprofezin, 17.4% for methyl parathion, and 13.9% for ametryn. Analysis of commercial pineapple samples revealed the presence of methyl parathion, buprofezin, ametryn, and fenpropathrin at 0.023 ± 0.0037, 0.013 ± 0.0047, 0.043 ± 0.0156, and 0.031 ± 0.0049 mg kg−1, respectively.

The Relationship Between Clinical and Personal Recovery in Patients With Schizophrenia Spectrum Disorders: A Systematic Review and Meta-analysis.

Patients describe experiencing personal recovery despite ongoing symptoms of psychosis. The aim of the current research was to perform a meta-analysis investigating the relationship between clinical and personal recovery in patients with schizophrenia spectrum disorders. A comprehensive OvidSP database search was performed to identify relevant studies. Correlation coefficients of the relationship between clinical and personal recovery were retrieved from primary studies. Meta-analyses were performed, calculating mean weighted effect sizes for the association between clinical and personal recovery, hope, and empowerment. Additionally, associations between positive, negative, affective symptoms, general functioning, and personal recovery were investigated. The results show that heterogeneity across studies was substantial. Random effect meta-analysis of the relationship between symptom severity and personal recovery revealed a mean weighted correlation coefficient of r = -.21 (95% CI = -0.27 to -0.14, P < .001). We found the following mean weighted effect size for positive symptoms r = -.20 (95% CI = -0.27 to -0.12, P < .001), negative symptoms r = -.24 (95% CI = -0.33 to -0.15, P < .001), affective symptoms r = -.34 (95% CI = -0.44 to -0.24, P < .001) and functioning r = .21 (95% CI = -0.09 to 0.32, P < .001). The results indicate a significant small to medium association between clinical and personal recovery. Psychotic symptoms show a smaller correlation than affective symptoms with personal recovery. These findings suggest that clinical and personal recovery should both be considered in treatment and outcome monitoring of patients with schizophrenia spectrum disorders.

Psychometric properties of scales used for grading the severity of bronchial obstruction in pediatrics: A systematic review and meta-analysis.

In pediatrics, identifying the severity of bronchial obstruction in an early manner is a decisive factor. To assess the psychometric properties of the scales for grading the severity of bronchial obstruction in pediatric patients. This was a systematic review of studies on the validity and reliability of scales for grading the severity of bronchial obstruction conducted in infants and children younger than 3 years old. The search was conducted in Medline, WoS, EMBASE, SciELO, and Google Scholar. The correlation coefficient corresponding to each article was included in a random effects model to establish the criterion validity and reliability using the weighted averages of coefficients as per the sample size. A total of 9 articles were included, which accounted for 2699 children; 3 articles had an adequate or excellent methodological quality. Four articles established the concurrent criterion validity considering oxygen saturation, with a weighted correlation coefficient of -0.627 (95% confidence interval [CI]: -0.767 to -0.431, p < 0.001); 2 articles established the convergent criterion validity, with a weighted correlation coefficient of 0.809 (95% CI: 0.721 to 0.871, p < 0.001); 6 articles established the inter-observer reliability, with a weighted correlation coefficient of0.500for kappa and 0.891 for the intraclass correlation coefficient. The assessment of psychometric properties to support the use of scales for grading the construct "severity of bronchial obstruction" showed a moderate to adequate criterion validity. The percentage of agreement among observers in terms of the studied measure (severity of bronchial obstruction) was adequate; however, weaknesses such as the article design should be taken into account since it may affect the internal validity of results.

Correlation Between Posttraumatic Growth and Posttraumatic Stress Disorder Symptoms Based on Pearson Correlation Coefficient: A Meta-Analysis.

The literature on posttraumatic growth (PTG) is burgeoning, with the inconsistencies in the literature of the relationship between PTG and posttraumatic stress disorder (PTSD) symptoms becoming a focal point of attention. Thus, this meta-analysis aims to explore the relationship between PTG and PTSD symptoms through the Pearson correlation coefficient. A systematic search of the literature from January 1996 to November 2015 was completed. We retrieved reports on 63 studies that involved 26,951 patients. The weighted correlation coefficient revealed an effect size of 0.22 with a 95% confidence interval of 0.18 to 0.25. Meta-analysis provides evidence that PTG may be positively correlated with PTSD symptoms and that this correlation may be modified by age, trauma type, and time since trauma. Accordingly, people with high levels of PTG should not be ignored, but rather, they should continue to receive help to alleviate their PTSD symptoms.

Correlation Coefficient for the Interval-valued Neutrosophic Hesitant Fuzzy Set and Its Use in Multi-attribute Decision Making

Interval-valued neutrosophic hesitant fuzzy set (INHFS) is a generalization of the fuzzy set (FS) that is designed for some practical situations in which each element has different truth membership hesitant function, indeterminacy membership hesitant function and falsity membership hesitant function, and permits the membership degrees to have a set of possible interval values. In this paper, we develop the correlation coefficient and the weighted correlation coefficient for INHFSs and study their properties. Then, an approach to multi- attribute decision making (MADM) within the framework of INHFS is developed by the weighted correlation coefficient. Finally, a practical application of the developed approach to the problem of investment is given, and the result shows that our approach is reasonable and effective in dealing with decision making (DM) problems.

Correlation Coefficient between Dynamic Single Valued Neutrosophic Multisets and Its Multiple Attribute Decision-Making Method

Based on dynamic information collected from different time intervals in some real situations, this paper firstly proposes a dynamic single valued neutrosophic multiset (DSVNM) to express dynamic information and operational relations of DSVNMs. Then, a correlation coefficient between DSVNMs and a weighted correlation coefficient between DSVNMs are presented to measure the correlation degrees between DSVNMs, and their properties are investigated. Based on the weighted correlation coefficient of DSVNMs, a multiple attribute decision-making method is established under a DSVNM environment, in which the evaluation values of alternatives with respect to attributes are collected from different time intervals and are represented by the form of DSVNMs. The ranking order of alternatives is performed through the weighted correlation coefficient between an alternative and the ideal alternative, which is considered by the attribute weights and the time weights, and thus the best one(s) can also be determined. Finally, a practical example shows the application of the proposed method.

Investigation of PM2.5 mass concentration over India using a regional climate model

Seasonal variation of PM2.5 (Particulate Matter <2.5 μm) mass concentration simulated from WRF-Chem (Weather Research and Forecasting coupled with Chemistry) over Indian sub-continent are studied. The simulated PM2.5 are also compared with the observations during winter, pre-monsoon, monsoon and post-monsoon seasons of 2008. Higher value of simulated PM2.5 is observed during winter followed by post-monsoon, while lower values are found during monsoon. Indo-Gangetic Basin (IGB) exhibits high amount of PM2.5 (60− 200 μg m−3) throughout the year. The percentage differences between model simulated and observed PM2.5 are found higher (40− 60%) during winter, while lower (< 30%) during pre-monsoon and monsoon over most of the study locations. The weighted correlation coefficient between model simulated and observed PM2.5 is 0.81 at the significance of 98%. Associated RMSE (Root Mean Square Error) is 0.91 μg m−3. Large variability in vertically distributed PM2.5 are also found during pre-monsoon and monsoon. The study reveals that, model is able to capture the variabilities in spatial, seasonal and vertical distributions of PM2.5 over Indian region, however significant bias is observed in the model. PM2.5 mass concentrations are highest over West Bengal (82± 33 μg m−3) and the lowest in Jammu & Kashmir (14± 11 μg m−3). Annual mean of simulated PM2.5 mass over the Indian region is found to be 35± 9 μg m−3. Higher values of PM2.5 are found over the states, where the reported respiratory disorders are high. WRF-Chem simulated PM2.5 mass concentration gives a clear perspective of seasonal and spatial distribution of fine aerosols over the Indian region. The outcomes of the study have significant impacts on environment, human health and climate.

Distance Measure and Correlation Coefficient for Linguistic Hesitant Fuzzy Sets and Their Application

Linguistic hesitant fuzzy sets (LHFSs) permit the decision maker to apply several linguistic terms with each having several membership degrees to denote his/her preference of one thing. This type of fuzzy sets can well address the qualitative and quantitative cognitions of the decision maker as well as reflect his/her hesitancy, uncertainty and inconsistency. This paper introduces a distance measure between any two LHFSs and then defines a correlation coefficient of LHFSs. Considering the application of LHFSs, the weighted distance measure and the weighted correlation coefficient of LHFSs are defined. To address the interactions between elements in a set, the Shapley weighted distance measure and the Shapley weighted correlation coefficient are presented. It is worth noting that when the elements are independent, they degenerate to the associated weighted distance measure and the weighted correlation coefficient, respectively. After that, their application to pattern recognition is studied. Furthermore, an approach to multi-attribute decision making under linguistic hesitant fuzzy environment is developed. Meanwhile, numerical examples are offered to show the concrete application of the developed procedure.

Generalised intuitionistic fuzzy entropy and weighted correlation with application in multi-attributes decision-making

The present paper introduces generalised entropy for intuitionistic fuzzy entropy of order α with the evidences of its validity along with some of its properties. The proposed measure is a generalisation of the entropy given by De Luca and Termini (1972). It has been used to determine weights of both experts and attributes in intuitionistic fuzzy environment using decision matrices in multi-attributes decision-making problem with unknown weights. Further, weighted correlation coefficient is defined using the proposed entropy measure and correlation coefficients between alternatives and ideal point are determined. The value of correlation coefficient is used to rank the alternative and the alternative with greatest weighted correlation coefficient is selected as an optimal solution. Finally, an illustrative example describes its application on multi-attributes decision-making problem with undefined weights.

An Improved Weighted Correlation Coefficient Based on Integrated Weight for Interval Neutrosophic Sets and its Application in Multicriteria Decision-making Problems

An Improved Weighted Correlation Coefficient Based on Integrated Weight for Interval Neutrosophic Sets and its Application in Multicriteria Decision-making Problems

Postural Symmetry Evaluation Using Wavelet Correlation Coefficients Calculated for the Follow-Up Posturographic Trajectories

The paper presents an original method enabling postural symmetry evaluation using weighted averages of the wavelet correlation coefficients obtained individually for the corresponding x and y components of the cantered follow-up posturographic trajectories registered during the clockwise and counterclockwise visual stimulations. In the process the x and y components of both trajectories undergo 7-stage db2 discrete wavelet decomposition. The correlations of the detail coefficients are evaluated at all levels of the decomposition structure whereas the correlations of the approximation coefficients are calculated only at its last level. Applied weighting factors constitute the sums of energies of the reconstructed details or approximations corresponding to a particular level of decomposition. The ultimate measure of postural symmetry in the herein presented method is the quantity based on the vector distance of the point whose coordinates constitute the values of the obtained weighted correlation coefficients (individually for the x and y components), from the point representing the state of ideal symmetry. This quantity assumes the values within the range of [0,1], where 1 is identified with the maximum postural symmetry dynamics whereas the value of 0 represents the state of maximum anti-symmetry dynamics (analysed trajectories are out of phase by π [rad]). The applicability of the herein presented method was verified in the process of postural symmetry evaluation carried out in the group of 30 patients rehabilitated after total hip arthroplasty.DOI: http://dx.doi.org/10.5755/j01.eie.22.5.16349

Correlating eligibility criteria generalizability and adverse events using Big Data for patients and clinical trials.

Randomized controlled trials can benefit from proactive assessment of how well their participant selection strategies during the design of eligibility criteria can influence the study generalizability. In this paper, we present a quantitative metric called generalizability index for study traits 2.0 (GIST 2.0) to assess the a priori generalizability (based on population representativeness) of a clinical trial by accounting for the dependencies among multiple eligibility criteria. The metric was evaluated on 16 sepsis trials identified from ClinicalTrials.gov, with their adverse event reports extracted from the trial results sections. The correlation between GIST scores and adverse events was analyzed. We found that the GIST 2.0 score was significantly correlated with total adverse events and serious adverse events (weighted correlation coefficients of 0.825 and 0.709, respectively, with P < 0.01). This study exemplifies the promising use of Big Data in electronic health records and ClinicalTrials.gov for optimizing eligibility criteria design for clinical studies.

Correlation Coefficients of Intuitionistic Hesitant Fuzzy Sets and Their Applications to Clustering Analysis

An intuitionistic hesitant fuzzy set (IHFS) consists of hesitancy function intuitionistic fuzzy elements, which consists the membership degree and the non membership degree, supporting a more exemplary and flexible access to assign values for each element in the domain, and can handle this kind of hesitancy in this situation. It can be seen as a powerful tool to express uncertain information in the process of group recommendation. Therefore, we propose a correlation coefficient between IHFSs as a further extension of existing correlation coefficients for hesitant fuzzy sets and intuitionistic fuzzy sets and apply it to group recommendation under intuitionistic hesitant fuzzy environments. Through the weighted correlation coefficient between each item and the ideal item, the ranking order of all items can be identified and the best item can be easily identified as well. Finally, a practical example of a movie recommendation is given to demonstrate the practicality and effectiveness of the developed approach.

A Novel Correlation Coefficients between Pythagorean Fuzzy Sets and Its Applications to Decision-Making Processes

Pythagorean fuzzy set (PFS) is one of the most successful in terms of representing comprehensively uncertain and vague information. Considering that the correlation coefficient plays an important role in statistics and engineering sciences, in this paper, after pointing out the weakness of the existing correlation coefficients between intuitionistic fuzzy sets (IFSs), we propose a novel correlation coefficient and weighted correlation coefficient formulation to measure the relationship between two PFSs. Pairs of membership, nonmembership, and hesitation degree as a vector representation with the two elements have been considered during formulation. Numerical examples of pattern recognition and medical diagnosis have been taken to demonstrate the efficiency of the proposed approach. Results computed by the proposed approach are compared with the existing indices.

Criterion-related validity of perceived exertion scales in healthy children: a systematic review and meta-analysis.

Physiological parameters used to measure exercise intensity are oxygen uptake and heart rate. However, perceived exertion (PE) is a scale that has also been frequently applied. The objective of this study is to establish the criterion-related validity of PE scales in children during an incremental exercise test. Seven electronic databases were used. Studies aimed at assessing criterion-related validity of PE scales in healthy children during an incremental exercise test were included. Correlation coefficients were transformed into z-values and assessed in a meta-analysis by means of a fixed effects model if I2 was below 50% or a random effects model, if it was above 50%. wenty-five articles that studied 1418 children (boys: 49.2%) met the inclusion criteria. Children's average age was 10.5 years old. Exercise modalities included bike, running and stepping exercises. The weighted correlation coefficient was 0.835 (95% confidence interval: 0.762-0.887) and 0.874 (95% confidence interval: 0.794-0.924) for heart rate and oxygen uptake as reference criteria. The production paradigm and scales that had not been adapted to children showed the lowest measurement performance (p < 0.05). Measuring PE could be valid in healthy children during an incremental exercise test. Child-specific rating scales showed a better performance than those that had not been adapted to this population. Further studies with better methodological quality should be conducted in order to confirm these results.

High correlation of VAS pain scores after 2 and 6weeks of treatment with VAS pain scores at 12weeks in randomised controlled trials in rheumatoid arthritis and osteoarthritis: meta-analysis and implications.

BackgroundResearchers in clinical trials in rheumatoid arthritis (RA) and osteoarthritis (OA) often measure pain levels with a visual analogue scale (VAS). Of interest to clinical practice and future clinical trial design are associations of change from baseline (CFB) between time points with predictive ability of earlier response for long-term treatment benefit. We assessed the association and predictive ability of CFB in VAS pain between 2, 6 and 12 weeks in randomised controlled trials (RCTs) of non-steroidal anti-inflammatory drugs (NSAIDs).MethodsAggregated VAS pain data at baseline and CFB at 2, 6 and 12 weeks were collected from a systematic literature review of 176 RCTs in OA and RA. The predictive ability of earlier assessments for longer-term pain reduction was estimated using correlation and regression analyses. Analysis was performed using the R software package for statistical programming, version 3.1.1.ResultsAppropriate data were available from 50 RCTs (22,854 patients). Correlations between time points were high (weighted correlation coefficients between 2 and 6 weeks, 0.84; between 2 and 12 weeks, 0.79; and between 6 and 12 weeks, 0.96). CFB at 6 weeks was highly predictive and close to CFB at 12 weeks (regression coefficient 0.9, 95 % confidence interval 0.9–1.0). CFB at 2 weeks was significantly associated with CFB at 12 (0.8, 0.7–0.8) and 6 weeks (0.9, 0.8–1.0).ConclusionsThe results showed that early analgesic response measured by VAS for pain beyond 2 weeks of treatment with a particular NSAID is likely to be predictive of response at 12 weeks. Failure to achieve desired pain relief in OA and RA after 2 weeks should trigger reassessment of dosage and/or analgesic.Electronic supplementary materialThe online version of this article (doi:10.1186/s13075-016-0972-7) contains supplementary material, which is available to authorized users.

Correlation coefficient of single-valued neutrosophic hesitant fuzzy sets and its applications in decision making

As a combination of the hesitant fuzzy set (HFS) and the single-valued neutrosophic set (SVNS), the single-valued neutrosophic hesitant fuzzy set (SVNHFS) is an important concept to handle uncertain and vague information existing in real life, which consists of three membership functions including hesitancy, as the truth-hesitancy membership function, the indeterminacy-hesitancy membership function and the falsity-hesitancy membership function, and encompasses the fuzzy set, intuitionistic fuzzy set (IFS), HFS, dual hesitant fuzzy set (DHFS) and SVNS. Correlation and correlation coefficient have been applied widely in many research domains and practical fields. This paper, motivated by the idea of correlation coefficients derived for HFSs, IFSs, DHFSs and SVNSs, focuses on the correlation and correlation coefficient of SVNHFSs and investigates their some basic properties in detail. By using the weighted correlation coefficient information between each alternative and the optimal alternative, a decision-making method is established to handling the single-valued neutrosophic hesitant fuzzy information. Finally, an effective example is used to demonstrate the validity and applicability of the proposed approach in decision making, and the relationship between the each existing method and the developed method is given as a comparison study.

A New Type of Compositive Information Entropy for IvIFS and Its Applications

We first show the interval-valued intuitionistic fuzzy entropy which reflects intuitionism and fuzziness of interval-valued intuitionistic fuzzy set (IvIFS) based on interval-valued intuitionistic fuzzy cross-entropy. As for intuitionism and fuzziness of IvIFS, we propose interval-valued intuitionistic entropy and interval-valued fuzzy entropy, respectively. Furthermore, we establish the interval-valued span entropy describing the uncertainty of membership degree and nonmembership degree and show some concrete measure formulas. Combining intuitionistic factor, fuzzy factor, and span factor, we ultimately put forward the axiomatic definition of the compositive entropy and give a measure formula of compositive entropy. In addition, the effectiveness of the compositive entropy measure is illuminated by comparison with other entropy measures. Furthermore, the compositive entropy is applied to multiple attributes’ decision-making by using the weighted correlation coefficient between IvIFSs and pattern recognition by a similarity measure transformed from the compositive entropy.

Relationship Between FEV1 and Patient-Reported Outcomes Changes: Results of a Meta-Analysis of Randomized Trials in Stable COPD.

Background: This meta-analysis assessed the relationship between change from baseline (CFB) in spirometric measurements (trough forced expiratory volume in 1 second [FEV1] and FEV1 area under the curve [AUC]) and patient-reported outcomes (St. George's Respiratory Questionnaire total score [SGRQ] CFB, Transition Dyspnea Index [TDI] and exacerbation rates) after 6-12 months' follow-up, using study treatment-group level data. Methods: A systematic literature search was performed for randomized controlled trials of ≥24 weeks duration in adults with chronic obstructive pulmonary disease (COPD). Studies reporting ≥1 spirometric measurement and ≥1 patient-reported outcome (PRO) at baseline and at study endpoint were selected. The relationships between PROs and spirometric endpoints were assessed using Pearson correlation coefficient and meta-regression. Results: Fifty-two studies (62,385 patients) were included. Primary weighted analysis conducted at the last assessment showed a large significant negative correlation (r, -0.68 [95% confidence interval (CI); -0.77, -0.57]) between trough FEV1 and SGRQ. Improvement of 100 mL in trough FEV1 corresponded to a 5.9 point reduction in SGRQ. Similarly, a reduction of 4 points on SGRQ corresponded to 40 mL improvement in trough FEV1 (p<0.001). The weighted correlation coefficients of trough FEV1 with TDI, exacerbation rate (all) and exacerbation rate (moderate/severe) at last assessment point were 0.57, -0.69 and -0.57, respectively (all p<0.05). For the analyses excluding placebo groups, the correlations of FEV1 with SGRQ and TDI were lower but significant. Conclusions: A strong association exists between changes in spirometric measurements and changes in PROs.