Relationship between restricted dissimilarity functions, restricted equivalence functions and normal EN-functions: Image thresholding invariant

Bustince, Humberto; Barrenechea, Edurne; Pagola, Miguel

doi:10.1016/j.patrec.2007.11.007

Cited by 141 publications

(87 citation statements)

References 36 publications

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“…The result given in Proposition 24 is just the way of constructing divergence measures proposed by Montes [32] and Bustince [8]. D(A, B) = 0, then D(A, C) = 0.…”

Section: Therefore We Have Max(d(a∪c B ∪C) D(a∩c B ∩C)) ≤ D(a B)mentioning

confidence: 89%

“…Some potential properties of fuzzy equivalencies could be considered [29]: In [6], Bustince et al presented the concept of restricted equivalence function, which arises from the concept of fuzzy equivalence and some properties usually demanded from the measures used for comparing images [7,8]. The conditions for restricted equivalence functions are stronger than those of fuzzy equivalencies.…”

Section: E(x Y) E(y Z)) ≥ E(x Z)mentioning

confidence: 99%

“…It is shown that every restricted dissimilarity function in the sense of Bustince [8] is a dissimilarity function (the reciprocal is not true). Now we consider four further axioms in terms of dissimilarity functions.…”

Section: Generating Dissimilarity Functionsmentioning

confidence: 99%

“…It should be mentioned here that in some references these functions are called distance measures [3,8,15,26,28,43], in some references these functions are called dissimilarity measures [4,12], but in other references these functions are called divergence measures [1,11,32,33]. The first axiomatic definition for distance measure was proposed by Liu in [43], where four axioms for distance measure were given.…”

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

confidence: 99%

“…This kind of divergence measure is also a divergence measure in the sense of Liu [43], based on fuzzy union and intersection. Bustince et al [8] normalized the definition of divergence measure in the sense of Liu and presented a method to construct normal divergence measures. Both of Montes' and Bustince's approaches to constructing divergence measures are based on the use of restricted dissimilarity functions.…”

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

confidence: 99%

See 4 more Smart Citations

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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“…The result given in Proposition 24 is just the way of constructing divergence measures proposed by Montes [32] and Bustince [8]. D(A, B) = 0, then D(A, C) = 0.…”

Section: Therefore We Have Max(d(a∪c B ∪C) D(a∩c B ∩C)) ≤ D(a B)mentioning

confidence: 89%

Section: E(x Y) E(y Z)) ≥ E(x Z)mentioning

confidence: 99%

Section: Generating Dissimilarity Functionsmentioning

confidence: 99%

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

confidence: 99%

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

confidence: 99%

See 3 more Smart Citations

Relationships Among Several Fuzzy Measures

He¹,

Li²

2016

Handbook of Fuzzy Sets Comparison - Theory, Algorithms and Applications

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Similarity measures of Pythagorean fuzzy sets based on the cosine function and their applications

Wei

2018

Int. J. Intell. Syst.

264

183

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In this paper, we presented 10 similarity measures between Pythagorean fuzzy sets (PFSs) based on the cosine function by considering the degree of membership, degree of nonmembership and degree of hesitation in PFSs. Then, we applied these similarity measures and weighted similarity measures between PFSs to pattern recognition and medical diagnosis. Finally, two illustrative examples are given to demonstrate the efficiency of the similarity measures for pattern recognition and medical diagnosis.

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Similarity measures, penalty functions, and fuzzy entropy from new fuzzy subsethood measures

et al. 2019

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In this study, we discuss a new class of fuzzy subsethood measures between fuzzy sets. We propose a new definition of fuzzy subsethood measure as an intersection of other axiomatizations and provide two construction methods to obtain them. The advantage of this new approach is that we can construct fuzzy subsethood measures by aggregating fuzzy implication operators which may satisfy some properties widely studied in literature. We also obtain some of the classical measures such as the one defined by Goguen. The relationships with fuzzy distances, penalty functions, and similarity measures are also investigated. Finally, we provide an illustrative example which makes use of a fuzzy entropy defined by means of our fuzzy subsethood measures for choosing the best fuzzy technique for a specific problem.

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Relationship between restricted dissimilarity functions, restricted equivalence functions and normal EN-functions: Image thresholding invariant

Cited by 141 publications

References 36 publications

Relationships Among Several Fuzzy Measures

Relationships Among Several Fuzzy Measures

Similarity measures of Pythagorean fuzzy sets based on the cosine function and their applications

Similarity measures, penalty functions, and fuzzy entropy from new fuzzy subsethood measures

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