t is the purpose of this paper to contribute to the discussion initiated bywachter about the parallelism between principal component (pc) and atypological grade of membership (gom) analysis. the author testedempirically the close relationship between both analysis in a lowdimensional framework comprising up to nine dichotomous variables and twotypologies. our contribution to the subject is also...

This paper presents partitional fuzzy clustering methods based on adaptive quadratic distances. The methods presented furnish a fuzzy partition and a prototype for each cluster by optimizing an adequacy criterion based on adaptive quadratic distances. These distances change at each algorithm iteration and can either be the same for all clusters or different from one cluster to another. Moreover...

7 This paper presents partitional fuzzy clustering methods based on adaptive quadratic distances. The methods presented furnish a fuzzy partition and a prototype for each cluster by optimizing an adequacy criterion based on adaptive quadratic distances. These 9 distances change at each algorithm iteration and can either be the same for all clusters or different from one cluster to another. More...

This paper presents a thresholding approach by performing fuzzy partition on a two-dimensional (2-D) histogram based on fuzzy relation and maximum fuzzy entropy principle. The experiments with various gray level and color images have demonstrated that the proposed approach outperforms the 2-D nonfuzzy approach and the one dimensional (1-D) fuzzy partition approach.

In this paper, the concept of hypergraph is extended to the fuzzy hypergraph. In the fuzzy hypergraph, the concepts of a-cut hypergraph, strength of edge and dual fuzzy hypergraph are developed. It is shown that the fuzzy hypergraph and a-cut hypergraph are useful to represent a fuzzy partition. An application example also shows that the strength of edge can be used to decompose the data set in...

Fuzzy clustering has been widely used for analysis of gene expression microarray data. However, most fuzzy clustering algorithms require complete datasets and, because of technical limitations, most microarray datasets have missing values. To address this problem, we present a new algorithm where genes are clustered using the Fuzzy C-Means algorithm (FCM). The fuzzy partition obtained is then u...

In recent years, many studies have been done on forecasting fuzzy time series. First-order fuzzy time series forecasting methods with first-order lagged variables and high-order fuzzy time series forecasting methods with consecutive lagged variables constitute the considerable part of these studies. However, these methods are not effective in forecasting fuzzy time series which contain seasonal...

In this work, we propose a pseudometric based on a fuzzy relation, which is itself derived from a fuzzy partition. This pseudometric is a metric in the particular case in which the fuzzy partition is composed solely by triangular fuzzy sets. We prove that these functions are indeed a pseudometric and a metric and illustrate their use in an experiment for the classification of land use in an are...

This paper introduces fuzzy clustering algorithms that can partition objects taking into account simultaneously their relational descriptions given by multiple dissimilarity matrices. The aim is to obtain a collaborative role of the different dissimilarity matrices to get a final consensus partition. These matrices can be obtained using different sets of variables and dissimilarity functions. T...