A fuzzy approach for modelling non-stochastic heterogeneous data in engineering based on cluster analysis

Abstract

Existence of heterogeneous results for a particular measurement is a typical problem in engineering sciences. This phenomenon represents data uncertainty. It means that a precise specification of a measurement is not possible. Only a non-stochastic dataset is available. In this paper, a new methodo logy for modelling of such uncertain measurement as fuzzy variable is presented. The membership function for the unknown fuzzy variable is specified using the methods of fuzzy cluster analysis. With the help of these methods, structures in the dataset are identified and the number of elements of the dataset is partitioned into homogeneous subsets. The fuzzy cluster analysis uses gradual membership of elements to subsets. Within the heterogeneous measurement, homogenous subsets are thus detected and the respective membership values of each element to the subsets are determined. The known homogenous subsets and the associated membership values enable the determination of the membership function of the fuzzy variable which models the measurement. The different homogenous subsets are calculable through non-convex characteristics of the membership function. The above mentioned approach is explained with the help of real measured data as well as data resulted from a numerical simulation and is applied on a structural analysis problem.