A sensitivity analysis approach to introducing weight factors into decision functions in fuzzy multicriteria decision making

Kaymak, Uzay; Lemke, H.R. van Nauta

doi:10.1016/s0165-0114(96)00336-3

Cited by 43 publications

(13 citation statements)

References 10 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In order to take the different size of clusters into account, Beringer and Hüllermeier propose to generalize this approach by using a weighted t-norm aggregation [15]:…”

Section: Other Measuresmentioning

confidence: 99%

“…We define a fuzzy equivalence relation on X in terms of a similarity measure on the associated membership vectors (15). Generally, this relation is of the form…”

Section: Definitionmentioning

confidence: 99%

“…Roughly speaking, this is due to the fact that, by mapping elements to their membership vectors (15), some information about the partition itself is lost. In particular, it is possible that two partitions, even though they are not identical, cannot be distinguished in terms of the distances between these vectors.…”

Section: Formal Propertiesmentioning

confidence: 99%

See 2 more Smart Citations

Comparing Fuzzy Partitions: A Generalization of the Rand Index and Related Measures

Hüllermeier

Rifqi

Henzgen

et al. 2012

IEEE Trans. Fuzzy Syst.

104

View full text Add to dashboard Cite

In this paper, we introduce a fuzzy extension of a class of measures for comparing clustering structures, namely measures that are based on the number of concordant and the number of discordant pairs of data points. This class includes the well-known Rand index but also commonly used alternatives, such as the Jaccard measure. In contrast to previous proposals, our extension exhibits desirable metrical properties. Apart from elaborating on formal properties of this kind, we present an experimental study in which we compare different fuzzy extensions of the Rand index and the Jaccard measure.

show abstract

“…In order to take the different size of clusters into account, Beringer and Hüllermeier propose to generalize this approach by using a weighted t-norm aggregation [15]:…”

Section: Other Measuresmentioning

confidence: 99%

“…We define a fuzzy equivalence relation on X in terms of a similarity measure on the associated membership vectors (15). Generally, this relation is of the form…”

Section: Definitionmentioning

confidence: 99%

See 1 more Smart Citation

Comparing Fuzzy Partitions: A Generalization of the Rand Index and Related Measures

Hüllermeier

Rifqi

Henzgen

et al. 2012

IEEE Trans. Fuzzy Syst.

104

View full text Add to dashboard Cite

show abstract

“…Thus, one might think of weighting (13) by the relative size w ı = |C ı |/n, where n is the number of objects (data streams), that is, to replace (13) in (12) by m(w ı , s ı ). This comes down to using a weighted t-norm aggregation instead of a simple one [22]:…”

Section: Similarity Between Cluster Modelsmentioning

confidence: 99%

Fuzzy Clustering of Parallel Data Streams

Beringer

Hüllermeier

2007

Advances in Fuzzy Clustering and Its Applications

View full text Add to dashboard Cite

The management and processing of so-called data streams has recently become a topic of active research in several fields of computer science, notably database systems and data mining. A data stream can roughly be thought of as a transient, continuously increasing sequence of time-stamped data. In this paper, we consider the problem of clustering parallel streams of real-valued data, that is to say, continuously evolving time series. More specifically, we are interested in grouping data streams the evolution over time of which is similar in a specific sense. In order to maintain an up-to-date clustering structure, it is necessary to analyze the incoming data in an online manner, tolerating not more than a constant time delay. For this purpose, we develop an efficient online version of the fuzzy C-means clustering algorithm. A fuzzy approach appears to be particularly useful for this type of application, in which the clustering structure is subject to continuous changes.

show abstract

“…For , the maximum operator is obtained and, hence, the volume prototype becomes the smallest hypersphere that encloses the cluster volume (hyperellipsoid). It is known that the unbiased aggregation for measurements in a metric space is obtained for [18]. The averaging operator (16) then reduces to the geometric mean, so that the prototype radius is given by (17) Hence, this selection for the radius leads to a spherical prototype that preserves the volume of the cluster.…”

Section: Extended Gk and Fcm Algorithmsmentioning

confidence: 99%

Fuzzy clustering with volume prototypes and adaptive cluster merging

Kaymak

Setnes

2002

IEEE Trans. Fuzzy Syst.

129

View full text Add to dashboard Cite

Abstract-Two extensions to the objective function-based fuzzy clustering are proposed. First, the (point) prototypes are extended to hypervolumes, whose size can be fixed or can be determined automatically from the data being clustered. It is shown that clustering with hypervolume prototypes can be formulated as the minimization of an objective function. Second, a heuristic cluster merging step is introduced where the similarity among the clusters is assessed during optimization. Starting with an overestimation of the number of clusters in the data, similar clusters are merged in order to obtain a suitable partitioning. An adaptive threshold for merging is proposed. The extensions proposed are applied to Gustafson-Kessel and fuzzy c-means algorithms, and the resulting extended algorithm is given. The properties of the new algorithm are illustrated by various examples.

show abstract

A sensitivity analysis approach to introducing weight factors into decision functions in fuzzy multicriteria decision making

Cited by 43 publications

References 10 publications

Comparing Fuzzy Partitions: A Generalization of the Rand Index and Related Measures

Comparing Fuzzy Partitions: A Generalization of the Rand Index and Related Measures

Fuzzy Clustering of Parallel Data Streams

Fuzzy clustering with volume prototypes and adaptive cluster merging

Contact Info

Product

Resources

About