Similarity and dissimilarity measures between fuzzy sets: A formal relational study

Couso, Inés; Garrido, Laura; Sánchez, Luciano

doi:10.1016/j.ins.2012.11.012

Cited by 77 publications

(59 citation statements)

References 37 publications

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“…If we design a similarity measure based on a distance measure, we can use a general fuzzy membership function without any limit on its shape [13][14][15]. Note that most conventional similarity measures-whether based on fuzzy number or distance measure-can be applied to overlapped data sets only [8,11,13,14,[18][19][20][21]. By "overlapped data sets" we mean data sets with the same support.…”

Section: Background and Motivationmentioning

confidence: 99%

“…Similarity measure design and investigations of its relation to dissimilarity have been carried out in the literature. Some similarity measure results are designed based on fuzzy numbers [11,12], and axiomatic similarity measures have been defined [18,19]. In addition, some similarity measures have been designed to work with non-overlapped data sets as well [22][23][24].…”

Section: Background and Motivationmentioning

confidence: 99%

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Analysis of a Similarity Measure for Non-Overlapped Data

et al. 2017

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Abstract:A similarity measure is a measure evaluating the degree of similarity between two fuzzy data sets and has become an essential tool in many applications including data mining, pattern recognition, and clustering. In this paper, we propose a similarity measure capable of handling non-overlapped data as well as overlapped data and analyze its characteristics on data distributions. We first design the similarity measure based on a distance measure and apply it to overlapped data distributions. From the calculations for example data distributions, we find that, though the similarity calculation is effective, the designed similarity measure cannot distinguish two non-overlapped data distributions, thus resulting in the same value for both data sets. To obtain discriminative similarity values for non-overlapped data, we consider two approaches. The first one is to use a conventional similarity measure after preprocessing non-overlapped data. The second one is to take into account neighbor data information in designing the similarity measure, where we consider the relation to specific data and residual data information. Two artificial patterns of non-overlapped data are analyzed in an illustrative example. The calculation results demonstrate that the proposed similarity measures can discriminate non-overlapped data.

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Section: Background and Motivationmentioning

confidence: 99%

Section: Background and Motivationmentioning

confidence: 99%

Analysis of a Similarity Measure for Non-Overlapped Data

et al. 2017

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“…Different similarity measures for fuzzy sets have been proposed in literature [17][18][19][20][21][22][23]. They can be classified into two main groups:…”

Section: Similarity Measures Between Fuzzy Setsmentioning

confidence: 99%

Rule Base Reduction Using Conflicting and Reinforcement Measures

Anzilli

Giove

2017

Multidisciplinary Approaches to Neural Computing

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“…One can find in the literature many coefficients used as similarity measures (see, e.g., [4] and references given there). Most of them are symmetric, as (3).…”

Section: Similarity Measuresmentioning

confidence: 99%

“…, (4) where α, β ≥ 0 are some fixed constants and f (A) is a measure of a set A. One may easily notice that for any two intervals A, B ∈ K c (R) by taking α = β = 1 and assuming that f ≡ λ we get the Jaccard measure (3).…”

Section: Similarity Measuresmentioning

confidence: 99%

Similarity based one-sided tests for the expected value and interval data

Grzegorzewski¹,

Ramos-Guajardo²

2015

Proceedings of the 2015 Conference of the International Fuzzy Systems Association and the European Society for Fuzzy Logic and

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A novel way for addressing one-sided hypothesis tests for the mean of unable to observe real random variables from which we have information provided in terms of interval data is proposed. For this purpose, a measure of similarity between intervals is considered and the classical one-sided hypothesis test to check whether the similarity between the expectation of a random interval and a subset of an specific unbounded interval is high enough. Asymptotic and bootstrap techniques are applied in order to study the limit distribution of the proposed test statistic. Some simulations have been carried out in order to show the empirical behavior of the test.

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Similarity and dissimilarity measures between fuzzy sets: A formal relational study

Cited by 77 publications

References 37 publications

Analysis of a Similarity Measure for Non-Overlapped Data

Analysis of a Similarity Measure for Non-Overlapped Data

Rule Base Reduction Using Conflicting and Reinforcement Measures

Similarity based one-sided tests for the expected value and interval data

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