# Fuzzy multidimensional scaling

##### Citations

249 citations

129 citations

### Cites background or methods from "Fuzzy multidimensional scaling"

...The paper by Hébert et al. (2007) is devoted to the construction of multidimensional scaling techniques, when the dissimilarity matrix is imprecisely observed....

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...In the paper by Groenen et al. (2007), one of the models also considered by Hébert et al. (2007) is studied in more detail....

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16 citations

### Cites background from "Fuzzy multidimensional scaling"

...…Masson (2004b), D’Urso and Giordani (2005), Giordani and Kiers (2006) and Calcagnì et al. (2016) Multidimensional scaling Denoeux and Masson (2000) and Hébert et al. (2006) Self-organizing maps D’Urso et al. (2014) Clusterwise regression analysis D’Urso and Santoro (2006) Correspondence analysis…...

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10 citations

10 citations

### Cites background from "Fuzzy multidimensional scaling"

...However, treating this imprecision usually leads to an increased computational costs, as shown by various authors in the past [6,7,3]....

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##### References

12,530 citations

8,942 citations

### "Fuzzy multidimensional scaling" refers methods in this paper

...Concepts of fuzzy correlation were introduced in Liu and Kao (2002) and Hébert et al. (2003); Denœux et al. (2005) to measure the degree of association between fuzzy-valued attributes, by applying the extension principle (Zadeh, 1975)....

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...Applying the extension principle (Zadeh, 1975), the fuzzy distance between two fuzzy regions R̃i et R̃j can be defined as: µ d̃ij (w) = sup x,y∈Rp min(µ R̃i (x), µ R̃j (y)), (20) where the supremum is computed under the constraint ‖x−y‖ = w....

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4,561 citations

### "Fuzzy multidimensional scaling" refers methods in this paper

...In this case, the disparities are computed using a transformation referred to as isotonic regression (Kruskal, 1964) which insures that dij ≤ dkl whenever δij ≤ δkl. This nonmetric or ordinal approach will not be considered further in this paper, although a nonmetric MDS procedure for interval-valued data was proposed in Denoeux and Masson (2000)....

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...In this case, the disparities are computed using a transformation referred to as isotonic regression (Kruskal, 1964) which insures that dij ≤ dkl whenever δij ≤ δkl....

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2,238 citations

### Additional excerpts

...If R̃i and R̃j are multidimensional fuzzy numbers (Kaufmann and Gupta, 1991, page 146), each α-cut of d̃ij is a closed interval αd̃ij = [ αd̃−ij, αd̃+ij], whose bounds are respectively the minimum and maximum distances between the α-cuts of R̃i and R̃j....

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