Generalized Point Estimators for Fuzzy Multivariate Data

Abstract

Data analysis methods are necessary tools in evaluating and better understanding the information of interest.  However, there are limitations in applying standard statistical methods to specific data analyses.  The data obtained from different sources are often clouded by imprecision and uncertainty.  To overcome this problem, data analysis methods have to be generalized to capture the data uncertainty through statististical methods for fuzzy data.  The existing methods are based on the extension principle or require other generalized procedures, such as the calculation of statistics, the extimation of parameters, and the construction of fuzzy confidence regions.  The development of these methods to evaluate univariate data has been flourished.  However, to solve complex real-world problems, these methods have to be extended and generalized to handle multivariate fuzzy data.  In this research, the methods of generalized point estimators, i.e. sample mean, variance-covariance, and correlation coefficient, are extended for the multivariate case through concepts of fuzzy vector and combined fuzzy sample.