Author

# Christian Döring

Bio: Christian Döring is an academic researcher from Otto-von-Guericke University Magdeburg. The author has contributed to research in topics: Fuzzy clustering & Fuzzy set. The author has an hindex of 8, co-authored 9 publications receiving 483 citations.

##### Papers

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TL;DR: An approach to possibilistic fuzzy clustering that avoids a severe drawback of the conventional approach, namely that the objective function is truly minimized only if all cluster centers are identical, is explored.

175 citations

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TL;DR: An encompassing, self-contained introduction to the foundations of the broad field of fuzzy clustering is presented, with special emphasis on the interpretation of the two most encountered types of gradual cluster assignments: the fuzzy and the possibilistic membership degrees.

117 citations

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11 May 200778 citations

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TL;DR: An extension of the Gath and Geva algorithm is developed that introduces a class-specific probability for missing values in order to appropriately assign incomplete data points to clusters.

57 citations

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27 Jun 2004TL;DR: This work proposes a new fuzzy clustering approach based on a probabilistic distance measure that can be avoided which ties in the vulnerability to favor one type of attributes.

Abstract: In many applications the objects to cluster are described by quantitative as well as qualitative features. A variety of algorithms has been proposed for unsupervised classification if fuzzy partitions and descriptive cluster prototypes are desired. However, most of these methods are designed for data sets with variables measured in the same scale type (only categorical, or only metric). We propose a new fuzzy clustering approach based on a probabilistic distance measure. Thus a major drawback of present methods can be avoided which ties in the vulnerability to favor one type of attributes.

26 citations

##### Cited by

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TL;DR: A new model called possibilistic-fuzzy c-means (PFCM) model, which solves the noise sensitivity defect of FCM, overcomes the coincident clusters problem of PCM and eliminates the row sum constraints of FPCM.

Abstract: In 1997, we proposed the fuzzy-possibilistic c-means (FPCM) model and algorithm that generated both membership and typicality values when clustering unlabeled data. FPCM constrains the typicality values so that the sum over all data points of typicalities to a cluster is one. The row sum constraint produces unrealistic typicality values for large data sets. In this paper, we propose a new model called possibilistic-fuzzy c-means (PFCM) model. PFCM produces memberships and possibilities simultaneously, along with the usual point prototypes or cluster centers for each cluster. PFCM is a hybridization of possibilistic c-means (PCM) and fuzzy c-means (FCM) that often avoids various problems of PCM, FCM and FPCM. PFCM solves the noise sensitivity defect of FCM, overcomes the coincident clusters problem of PCM and eliminates the row sum constraints of FPCM. We derive the first-order necessary conditions for extrema of the PFCM objective function, and use them as the basis for a standard alternating optimization approach to finding local minima of the PFCM objective functional. Several numerical examples are given that compare FCM and PCM to PFCM. Our examples show that PFCM compares favorably to both of the previous models. Since PFCM prototypes are less sensitive to outliers and can avoid coincident clusters, PFCM is a strong candidate for fuzzy rule-based system identification.

1,118 citations

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01 Nov 2007TL;DR: A clustering algorithm based on k-mean paradigm that works well for data with mixed numeric and categorical features is presented and a new cost function and distance measure based on co-occurrence of values is proposed.

Abstract: Use of traditional k-mean type algorithm is limited to numeric data. This paper presents a clustering algorithm based on k-mean paradigm that works well for data with mixed numeric and categorical features. We propose new cost function and distance measure based on co-occurrence of values. The measures also take into account the significance of an attribute towards the clustering process. We present a modified description of cluster center to overcome the numeric data only limitation of k-mean algorithm and provide a better characterization of clusters. The performance of this algorithm has been studied on real world data sets. Comparisons with other clustering algorithms illustrate the effectiveness of this approach.

621 citations

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TL;DR: In this review, the basic mathematical framework of fuzzy set theory will be described, as well as the most important applications of this theory to other theories and techniques.

Abstract: Since its inception in 1965, the theory of fuzzy sets has advanced in a variety of ways and in many disciplines. Applications of this theory can be found, for example, in artificial intelligence, computer science, medicine, control engineering, decision theory, expert systems, logic, management science, operations research, pattern recognition, and robotics. Mathematical developments have advanced to a very high standard and are still forthcoming to day. In this review, the basic mathematical framework of fuzzy set theory will be described, as well as the most important applications of this theory to other theories and techniques. Since 1992 fuzzy set theory, the theory of neural nets and the area of evolutionary programming have become known under the name of ‘computational intelligence’ or ‘soft computing’. The relationship between these areas has naturally become particularly close. In this review, however, we will focus primarily on fuzzy set theory. Applications of fuzzy set theory to real problems are abound. Some references will be given. To describe even a part of them would certainly exceed the scope of this review. Copyright © 2010 John Wiley & Sons, Inc.
For further resources related to this article, please visit the WIREs website.

493 citations

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TL;DR: An overview of numerical possibility theory is proposed, showing that some notions in statistics are naturally interpreted in the language of this theory and providing a natural definition of a subjective possibility distribution that sticks to the Bayesian framework of exchangeable bets.

411 citations

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TL;DR: Experiments with synthetic and real data sets show that the proposed ECM (evidential c-means) algorithm can be considered as a promising tool in the field of exploratory statistics.

359 citations