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Purpose: The purpose of this study is to provide individualized concept structure analysis based on the comparisons with concept structure of expert. Fuzzy clustering can distinguish characteristics of concept structures on assessment of examination for registered nurse. Design/methodology/approach: This study adds a regulating factor of covariance matrix to each class in objective function and deletes the constraint of the determinant of covariance matrices. The fuzzy covariance matrices in the Mahalanobis distance with recursive process iteratively can be directly derived by minimizing the objective function and can overcome the drawback of Euclidean distance. Hence, we could extend the distance measure to alternative distance. Findings: To get a more stable partition clustering algorithm, this study replaces all the covariance matrices with the same common covariance matrix and solves the problem of the singular problem for the inverse covariance matrix. Each cluster of data can easily describe features of knowledge structures. Manage the knowledge structures of assessment of examination for registered nurse to construct the model of features in the pattern recognition completely. Practical implications: Provide the empirical data for concepts of Professional and Technical Examination for Registered Nurse from junior college students of learning deficiencies. The results show that students with different response patterns and total score own varied concept structures. Originality/value: Based on the findings and results, some suggestions and recommendations for future research are provided. Integrated algorithm could improve the assessment methodology of cognition diagnosis and manage the knowledge structures of Professional and Technical Examination for Registered Nurse's concepts easily. [ABSTRACT FROM AUTHOR]

Purpose: Fuzzy algorithms of Gath-Geva (GG) and Gustafson-Kessel (GK) based on Mahalanobis distance can improve those limitations of spherical structural clusters, but GG algorithm can only be used for the data with multivariate normal distribution. GK algorithm is limited by that it must know the distribution of data. An improved supervised clustering algorithm based on fuzzy c-means (FCM) has been proposed. Methodology: We take a new threshold value and a new convergent algorithm to improve those limitations of GG and GK algorithms, delete the constraint of the determinants of covariance matrices in the GK algorithm, and replace the covariance matrix with the correlation matrix which exists in the objective function. Findings: The experimental results of real data sets show that our proposed new algorithm can promote clustering accuracies and get better performance. Value: The popular FCM algorithm based on Euclidean distance function converges to a local minimum of the objective function, which can only be used to detect spherical structural clusters. Adding fuzzy covariance matrices in their distance measure was not directly derived from the objective function. But it is not stable enough when some of its covariance matrices are not equal. Hence, different initializations may lead to different results. [ABSTRACT FROM AUTHOR]