Restricted equivalence functions

Bustince, Humberto; Barrenechea, Edurne; Pagola, Miguel

doi:10.1016/j.fss.2006.03.018

Cited by 153 publications

(84 citation statements)

References 23 publications

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“…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%

“…(1) c is a subsethood measure, (2) if N satisfies N4 and N8, then c is a VY -subsethood measure, (3) if N satisfies N4 and N8, then c is a * -subsethood measure, (4) if N satisfies N4 and N5, then c is a VY -subsethood measure, (5) if N satisfies N4 and N5, then c is a * -subsethood measure, (6) if N satisfies N4, N7 and N8, then c is a DI-subsethood measure. …”

Section: Proposition 29 Given a Discrete Universementioning

confidence: 99%

See 1 more Smart Citation

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: E(x Y) E(y Z)) ≥ E(x Z)mentioning

confidence: 99%

Section: Proposition 29 Given a Discrete Universementioning

confidence: 99%

Relationships Among Several Fuzzy Measures

He¹,

Li²

2016

Handbook of Fuzzy Sets Comparison - Theory, Algorithms and Applications

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show abstract

“…The construction method of IV-REFs used in this paper, which is based on the construction method of REFs introduced in [39], is the following one:…”

Section: Interval-valued Fuzzy Setsmentioning

confidence: 99%

A Compact Evolutionary Interval-Valued Fuzzy Rule-Based Classification System for the Modeling and Prediction of Real-World Financial Applications With Imbalanced Data

Sanz

Bernardo

Herrera

et al. 2015

IEEE Trans. Fuzzy Syst.

142

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“…In 2006, Bustince et al 5 proposed the concept of restricted equivalence function, which arises from the concept of fuzzy equivalence and from the properties usually demanded from the measures used for comparing images 6,7 . …”

Section: (N2) If X Y Then N(x) N(y)mentioning

confidence: 99%

“…Fan et al 11 gave a general definition of similarity measure and discussed some properties of similarity measure. Bustince et al 5 proposed the concept of restricted equivalence function and then used this function to construct similarity measure 5,6 .…”

Section: Introductionmentioning

confidence: 99%