Comparison of Crisp and Fuzzy Classification Trees Using Chi-Squared ImpurityMeasure on Simulated Data

Classification trees are one of the most popular choices in classification and discriminant analysis. One chief reason is that they are distribution free methods. Recently, with the introduction of fuzzy theory,fuzzy classification trees are gaining popularity. In this paper we use Pearson’s chi-squared impurity measure to compare the performance of crisp and fuzzy classification trees. This is done using simulated data. The data used consisted of two sets of observations from multivariate normal distributions. The first set of data were from two 3-variate normal populations with different mean vectors and common dispersion matrix. From each of the two populations 5000 samples were generated. 1000 samples out of the 5000 were used to create the trees. The remaining 4000 samples from each population were used to test the trees. The second set of data were from three 4-variate normal populations with different mean vectors and common dispersion matrix. A similar sampling and testing procedure as for the case of first set of data was employed. Computations were implemented using R statistical package. Using the Pearson’s chi-squared statistic for testing homogeneity in contingency tables showed that fuzzy classification trees algorithm makes two subnodes more heterogeneous than the crisp classification algorithm. Therefore fuzzy classification trees allocated observations to the correct population with fewer errors than did crisp classification tree

A Comparative Study of Chi-Square Goodness-of-Fit Under Fuzzy Environments

Testing goodness-of-fit plays a vital role in data analysis.  This problem seems to be much more complicated in the presence of vague data.  In this paper, the chi-square goodness-of-fit under trapezoidal fuzzy numbers (tfns.) is proposed using alpha cut interval method.  And the ranking grades of tfns. are also used to compute the chi-square test statistic.  The proposed technique is illustrated with two different numerical examples along with different methods of ranking grades for a concrete comparative study. Keywords: Chi-square Test, Fuzzy Sets, Trapezoidal Fuzzy Numbers, Alpha Cut, Ranking Function, Graded Mean Integration Representation

Analysis of the Learning Process through Eye Tracking Technology and Feature Selection Techniques

In recent decades, the use of technological resources such as the eye tracking methodology is providing cognitive researchers with important tools to better understand the learning process. However, the interpretation of the metrics requires the use of supervised and unsupervised learning techniques. The main goal of this study was to analyse the results obtained with the eye tracking methodology by applying statistical tests and supervised and unsupervised machine learning techniques, and to contrast the effectiveness of each one. The parameters of fixations, saccades, blinks and scan path, and the results in a puzzle task were found. The statistical study concluded that no significant differences were found between participants in solving the crossword puzzle task; significant differences were only detected in the parameters saccade amplitude minimum and saccade velocity minimum. On the other hand, this study, with supervised machine learning techniques, provided possible features for analysis, some of them different from those used in the statistical study. Regarding the clustering techniques, a good fit was found between the algorithms used (k-means ++, fuzzy k-means and DBSCAN). These algorithms provided the learning profile of the participants in three types (students over 50 years old; and students and teachers under 50 years of age). Therefore, the use of both types of data analysis is considered complementary.European Project “Self-Regulated Learning in SmartArt” 2019-1-ES01-KA204-065615

Exploring a Relationship Between Quality Control Procedure and Select Input Factors for Statutory Financial Audit

The study identifies 12 critical issues based on Standards on Auditing issued by the Institute of Chartered Accountants of India relating to using the work of internal auditors, auditors’ expert and external confirmations and that may influence quality control procedure for statutory financial audit. Opinions of 227 CAs and 146 Students pursuing Chartered Accountancy course on these variables have been gathered and empirically analysed with the help of Chi-Square test of homogeneity, Mann-Whitney test, Pearson’s Correlation Coefficient (r) and t test and suitable conclusions are drawn. Keywords: Internal Auditor, External Confirmations, Auditors’ Expert, Chi-Square, Mann-Whitney, Pearson’s Correlation Coefficient, t test

Certification of a Reference Material with Eschericia Coli O157 (NCTC 12900) at a level of 4 Colony forming Unit per Material Sphere, IRMM-351

This report describes the certification of a reference material (IRMM-351) of Escherichia coli O157. Certified Reference Materials (CRMs) for microbiological analysis are indispensable tools for development and validation of detection methods and for the implementation and support of internal and external quality control in the area of microbiological analysis. Each vial contains one material sphere of E. coli O157. The homogeneity and stability (at 4 °C, -20 °C and -70 °C) of the batch was assessed by monitoring colony forming units (cfu) on nutrient agr (NA) and eterohemolysin agar (EhlyA) of selected vials by colony counting. The material is not stable at 4 °C but no instability was detected when stored at -20 °C for up to 12 months and at -70 °C for up to 54 months. The batch was characterised by six laboratories to determine a certified value of cfu per vial on NA and EhlyA. The certified value is 4 cfu on both agars with an expanded uncertainty of 2 using a coverage factor k = 2, corresponding to a level of confidence of about 95 %. DNA sequence analysis of the coding region for the fliC gene identified the material as E. coli O157.JRC.D.2-Reference material

Certification of a Reference Material with Salmonella Enteritidis (NCTC 12694) at a Level of 5 Colony Forming Units on Nutrient Agar and 4 Colony Forming Units on Xylose Lysine Deoxycholate Agar, IRMM-352

This report describes the certification of a reference material (IRMM-352) of Salmonella Enteritidis. Certified Reference Materials (CRMs) for microbiological analysis are indispensable tools for development and validation of detection methods and for the implementation and support of internal and external quality control in the area of microbiological analysis. Each vial contains one material sphere of S. enteritidis. The homogeneity and stability (at 4 °C, -20 °C and -70 °C) of the batch was assessed by monitoring colony forming units (cfu) on nutrient agar (NA) and xylose lysine deoxycholate (XLD) agar of selected vials by colony counting. The material is not stable at 4 °C byt no instability was detected when stored at -20 °C for up to 12 months and at -70 °C for up to 54 months. The batch was characterised by six laboratories to determine a certified value of cfu per vial on NA and XLD agar. A quite considerable performance difference of both agars was observed. The certified value is 5 cfu on NA with an expanded uncertainty of 2 and 4 cfy on XLD agar with an expanded incertainty of 2 using a coverage factor k = 2, corresponding to a level of confidence of about 95 %. DNA sequence analysis of the coding region for the sefA gene identified the material as S. enteritidis.JRC.D.2-Reference material