Article
Measures of fit in multiple correspondence analysis of crisp and fuzzy coded data
SSRN Electronic Journal
01/2008;
DOI: 10.2139/ssrn.1107815
Source: RePEc
 Citations (5)

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ABSTRACT: This article provides a largely nontechnical discussion of the acquisition of membership values in fuzzy set analyses. First the basic properties of a membership are discussed. Then the three common strategies of membership assignmentâ€”direct subjective assign ment, indirect subjective assignment, and transformationâ€”are critically examined in turn. Examples are used to illustrate the techniques. The connection with existing psy chometric and statistical methods is particularly emphasized, focusing on the notion of a membership value as a random variable as a means to assess uncertainty in assignment.Sociological Methods & Research 05/2005; 33(4):462496. DOI:10.1177/0049124105274498 · 1.52 Impact Factor 
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ABSTRACT: The multiple correspondence analysis (MCA) is a descriptive and multidimensional method which can investigate several empirical situations, each situation being described by a categorical variable set. This paper shows how the fuzzy sets principle can be used to transform raw continuous data into categorical. The transformation is considered in two main stages: data characterizing and data coding. The data characterizing is performed to build analysis variables from complex empirical variables, such as multidimensional signals, using fuzzy windowing of the time and/or the space axes. The analysis variables are indicators summarizing the information within the so obtained windows. The data coding is performed to build homogeneous analysis variables, i.e. variables that are based on a qualitative scale using fuzzy windowing. Both methodological and practical aspect are considered in this paper through two examples. The first example considers the comparative analysis of force and force derivative signals in several load lifting conditions. The second example considers the analysis and the modelling of individual agreements between a graphical view showing two bargraphs and the assertion the height of the first bar is large and the height of the second is large, the agreement being given through an interval.Fuzzy Sets and Systems 11/1999; 107(3):255275. DOI:10.1016/S01650114(97)003175 · 1.88 Impact Factor 
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ABSTRACT: A general coefficient measuring the similarity between two sampling units is defined. The matrix of similarities between all pairs of sample units is shown to be positive semidefinite (except possibly when there are missing values). This is important for the multidimensional Euclidean representation of the sample and also establishes some inequalities amongst the similarities relating three individuals. The definition is extended to cope with a hierarchy of characters.Biometrics 12/1971; 27(44):857871. DOI:10.2307/2528823 · 1.52 Impact Factor
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