Towards general measures of comparison of objects

Bouchon‐Meunier, Bernadette; Rifqi, Maria; Bothorel, Sylvie

doi:10.1016/0165-0114(96)00067-x

Cited by 266 publications

(150 citation statements)

References 18 publications

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“…Such a work will meet a general framework for measures of similarity between fuzzy sets we have already proposed [2,9], providing a qualitative view of similarities associated with such numerical evaluations of similarities.…”

Section: Resultsmentioning

confidence: 99%

“…in the form of Equation (2). Furthermore, f and g satisfy the conditions required in (ii): they are strictly increasing, and f (0) = g(0) = 0.…”

Section: Representation Theoremsmentioning

confidence: 97%

“…Following the links to the concept of similarity in cognitive science, especially in the process of categorization, the seminal work proposed by Tversky [12] has often been considered as a reference for the description of a general framework: it embeds numerous similarity measures and enables the user to make an appropriate choice of a specific similarity measure when facing a particular problem to solve. In [2,9] we have proposed a general form for comparison measures, including similarity measures, compatible with Tversky's model, i.e. such that the proposed classes of measures satisfy the basic axioms introduced by Tversky.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Towards a Conscious Choice of a Similarity Measure: A Qualitative Point of View

Bouchon‐Meunier

Coletti

Lesot

et al. 2009

Lecture Notes in Computer Science

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Abstract. In many applications, such as case based reasoning, data mining or analogical reasoning, the choice of a particular measure of similarity is crucial. In this paper, we propose to study similarity measures from the point of view of the ordering relation they induce on object pairs. Using a classic method in measurement theory, introduced by Tversky, we establish necessary and sufficient conditions for the existence of a specific numerical measure, or a class of measures, to represent a given ordering relation, depending on the axioms this relation satisfies. The interest is particularly focused on different conditions of independence.

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Section: Resultsmentioning

confidence: 99%

“…in the form of Equation (2). Furthermore, f and g satisfy the conditions required in (ii): they are strictly increasing, and f (0) = g(0) = 0.…”

Section: Representation Theoremsmentioning

confidence: 97%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Towards a Conscious Choice of a Similarity Measure: A Qualitative Point of View

Bouchon‐Meunier

Coletti

Lesot

et al. 2009

Lecture Notes in Computer Science

Self Cite

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“…In his well-known paper on similarity, Tversky (1977) comes up via an axiomatic approach to the following general forms of similarity index between crisp sets (A\B denotes set-difference A∩B c ): Bouchon- Meunier et al (1996) have tried to extend this approach to the comparison of fuzzy sets, using evaluations of intersection and differences of fuzzy sets. They propose comparison indices of the form f(e(F∩G), e(F\G), e(G\F)).…”

Section: Building Comparison Indicesmentioning

confidence: 99%

Fuzzy Sets: History and Basic Notions

Dubois¹,

Ostasiewicz

Prade³

2000

The Handbooks of Fuzzy Sets Series

138

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Abstract. This paper is an introduction to fuzzy set theory. It has several purposes. First, it tries to explain the emergence of fuzzy sets from an historical perspective. Looking back to the history of sciences, it seems that fuzzy sets were bound to appear at some point in the 20th century. Indeed, Zadeh's works have cristalized and popularized a concern that has appeared in the first half of the century, mainly in philosophical circles. Another purpose of the paper is to scan the basic definitions in the field, that are required for a proper reading of the rest of the volume, as well as the other volumes of the Handbooks of Fuzzy Sets Series. This Chapter also contains a discussion on operational semantics of the generally too abstract notion of membership function. Lastly, a survey of variants of fuzzy sets and related matters is provided.

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“…The next step consists in estimating the matching between this fuzzy representation and the other region. Among all possible fuzzy measures, we choose as a criterion a M-measure of satisfiability [16] defined as:…”

Section: Graph Representation Of Images Including Spatial Relationsmentioning

confidence: 99%

Kernel Fusion for Image Classification Using Fuzzy Structural Information

Aldea

Fouquier

Atif³

et al.

Advances in Visual Computing

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Abstract. Various kernel functions on graphs have been defined recently. In this article, our purpose is to assess the efficiency of a marginalized kernel for image classification using structural information. Graphs are built from image segmentations, and various types of information concerning the underlying image regions as well as the spatial relationships between them are incorporated as attributes in the graph labeling. The main contribution of this paper consists in studying the impact of fusioning kernels for different attributes on the classification decision, while proposing the use of fuzzy attributes for estimating spatial relationships.

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Towards general measures of comparison of objects

Cited by 266 publications

References 18 publications

Towards a Conscious Choice of a Similarity Measure: A Qualitative Point of View

Towards a Conscious Choice of a Similarity Measure: A Qualitative Point of View

Fuzzy Sets: History and Basic Notions

Kernel Fusion for Image Classification Using Fuzzy Structural Information

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