Geographical data analysis via mountain function

In this paper we report an application of fuzzy arithmetic to the reduction of geographical data sets. The proposed technique builds a "summary" of the data within a given subregion in the form of a suitable fuzzy real number. The membership function of this number is obtained with a procedure that resembles the mountain function method introduced by Yager and Filev [IEEE Trans Syst. Man, Cybern Aug. 1994, 24(8), 1279-1284]. The proposed approach is computationally efficient, theoretically sound, and quite robust in terms of experimental noise. In addition, it does not require any statistical assumption about the distribution of the data. The summarization technique reported has been successfully used in modeling a real terrain from collections of sparse elevation data on a terrain. Comparisons with similar approaches are also reported. (C) 1999 John Wiley & Sons, Inc.