Relations among similarity measure, subsethood measure and fuzzy entropy

Li, Yingfang; Qin, Keyun; He, Xiaoqiong

doi:10.1080/18756891.2013.780726

Cited by 13 publications

(7 citation statements)

References 30 publications

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“…Several similarity measures for practical use have been proposed in the literature [4,5,10,16,20,25,27,29,30,34,35,37,38,43]. When we review to these similarity measures, we find that most of them satisfy the above-mention conditions demanded from similarity measures.…”

Section: Fuzzy Measures For the Comparison Of Fuzzy Sets: Similarity mentioning

confidence: 97%

Relationships Among Several Fuzzy Measures

He¹,

Li²

2016

Handbook of Fuzzy Sets Comparison - Theory, Algorithms and Applications

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In fuzzy set theory, similarity measure, divergence measure, subsethood measure and fuzzy entropy are four basic concepts. They surface in many fields, such as image processing, fuzzy neural networks, fuzzy reasoning, fuzzy control, and so on. The similarity measure describes the degree of similarity of fuzzy sets A and B. The divergence measure describes the degree of difference of fuzzy sets A and B. The subsethood measure (also called inclusion measure) is a relation between fuzzy sets A and B, which indicates the degree to which A is contained in B. The entropy of a fuzzy set is the fuzziness of that set.

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Section: Fuzzy Measures For the Comparison Of Fuzzy Sets: Similarity mentioning

confidence: 97%

Relationships Among Several Fuzzy Measures

He¹,

Li²

2016

Handbook of Fuzzy Sets Comparison - Theory, Algorithms and Applications

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“…The relationships among fuzzy logic entropy, similarity, and subsethood measures are studied and calculated based on their definitions by (Li, Qin, & He, 2013). The transformation of these measures has been calculated by using new formulae.…”

Section: Related Workmentioning

confidence: 99%

Design of a hybrid measure for image similarity: a statistical, algebraic, and information-theoretic approach

Al-Janabi

Hussain

Shnain

et al. 2019

European Journal of Remote Sensing

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Image similarity or distortion assessment is fundamental to a wide range of applications throughout the field of image processing and computer vision. Many image similarity measures have been proposed to treat specific types of image distortions. Most of these measures are based on statistical approaches, such as the classic SSIM. In this paper, we present a different approach by interpolating the information theory with the statistic, because the information theory has a high capability to predict the relationship among image intensity values. Our unique hybrid approach incorporates information theory (Shannon entropy) with a statistic (SSIM), as well as a distinctive structural feature provided by edge detection (Canny). Correlative and algebraic structures have also been utilized. This approach combines the best features of Shannon entropy and a joint histogram of the two images under test, and SSIM with edge detection as a structural feature. The proposed method (ISSM) has been tested versus SSIM and FSIM under Gaussian noise, where good results have been obtained even under a wide range of PSNR. Simulation results using the IVC and TID2008 image databases show that the proposed approach outperforms the SSIM and FSIM approaches in similarity and recognition of the image. ARTICLE HISTORY

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“…However, these studies did not agree on any axioms that must be required for such functions. Different axiomatic definitions of fuzzy similarity measures exist [12,14,16,17,18,23,24,26,35], but these axiomatic definitions depend on the contexts in which they are constructed. According to some studies of fuzzy similarity measures, a reasonable fuzzy similarity measure for pattern recognition must satisfy the following three conditions at least.…”

Section: Examplementioning

confidence: 99%

“…However, previous researchers do not agree about any axioms that must be required by such functions. Thus, different axiomatic definitions of fuzzy similarity measures exist [12,14,16,17,18,23,24,26,35] and these axiomatic definitions depend on the contexts in which they were constructed. According to some existing definitions of fuzzy similarity measures, we know that the reflexivity (N (A, A) = 1), symmetry (N (A, B) = N (B, A)), boundary condition (N (X, ∅) = 1), and monotonicity (N (A, C) ≤ min (N (A, B), N(B, C)) when A ⊆ B ⊆ C) are standard properties of fuzzy similarity measures.…”

Section: Introductionmentioning

confidence: 99%