Abstract

Abstract

Abstract
We investigate the fuzzy clustering of interval time series using wavelet variances and covariances; in particular, we use a fuzzy c-medoids clustering algorithm. Traditional hierarchical and non-hierarchical clustering methods lead to the identification of mutually exclusive clusters whereas fuzzy clustering methods enable the identification of overlapping clusters, implying that one or more series could belong to more than one cluster simultaneously. An interval time series (ITS) which arises when interval-valued observa-tions are recorded over time is able to capture the variability of values within each interval at each time point. This is in contrast to single-point information available in a classical time series. Our main contribution is that by combining wavelet analysis, interval data analysis and fuzzy clustering, we are able to capture information which would otherwise have not been contemplated by the use of traditional crisp clustering methods on classical time series for which just a single value is recorded at each time point. Through simulation studies, we show that under some circumstances fuzzy c-medoids clustering performs better when applied to ITS than when it is applied to the corresponding traditional time series. Applications to exchange rates ITS and sea-level ITS show that the fuzzy clustering method reveals different and more meaningful results than when applied to associated single-point time series.

Abstract
We propose a Multi-Agent framework to analyze the dynamics of organizational survival in cooperation networks. Firms can decide to cooperate horizontally (in the same market) or vertically with other firms that belong to the supply chain. Cooperation decisions are based on economic variables. We have defined a variant of the density dependence model to set up the dynamics of the survival in the simulation. To validate our model, we have used empirical outputs obtained in previous studies from the automobile manufacturing sector. We have observed that firms and networks proliferate in the regions with lower marginal costs, but new networks keep appearing and disappearing in regions with higher marginal costs.

Abstract
This paper introduces a partitioning clustering method for objects described by interval data. It follows the dynamic clustering approach and uses an L-2 distance. Particular emphasis is put on the standardization problem where we propose and investigate three standardization techniques for interval-type variables. Moreover, various tools for cluster interpretation are presented and illustrated by simulated and real-case data.

Abstract
This paper compares different approaches to the multivariate analysis of interval data, focusing on discriminant analysis. Three fundamental approaches are considered. The first approach assumes an uniform distribution in each observed interval, derives the corresponding measures of dispersion and association, and appropriately defines linear combinations of interval variables that maximize the usual discriminant criterion. The second approach expands the original data set into the set of all interval description vertices, and proceeds with a classical analysis of the expanded set. Finally, a third approach replaces each interval by a midpoint and range representation. Resulting representations, using intervals or single points, are discussed and distance based allocation rules are proposed. The three approaches are illustrated on a real data set.