Most typical values for fuzzy sets

The classical definitions of 'expected value' and 'standard deviation' lead to quantities which generally fail to represent any 'typical' feature of a given data set, whenever it consists of more than one cluster. The use of the fuzzy expected value (FEV) as a 'typical' grade of membership within a fuzzy set, may occasionally also lead to improper results. Other quantities like the clustering fuzzy expected value (CFEV) hardly deviate from the set average both conceptually and numerically and cannot represent a typical value of the given data. In this work a new quantity - the most typical value (MTV) for n-dimensional sets is defined. A given fuzzy set in R-n is first clustered and replaced by a finite set of clusters, each represented by the cluster center and its size. This set of ordered pairs is then replaced by a single vector - the most typical value of the fuzzy set. (C) 1997 EIsevier Science B.V.