Subsethood measure: new definitions

Fan, Jiulun; Xie, Weixin; Pei, Jihong

doi:10.1016/s0165-0114(97)00275-3

Cited by 95 publications

(47 citation statements)

References 13 publications

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“…It has been pointed out in [17] that C3 is too strong when considering the relation between subsethood measure and fuzzy entropy. Therefore, Fan et al [17] thought a simpler form of definition of subsethood measure based on Young's definition.…”

Section: Relationships Between Similarity Measures and Subsethood Meamentioning

confidence: 99%

“…Therefore, Fan et al [17] thought a simpler form of definition of subsethood measure based on Young's definition. It is shown that every DI-subsethood measure is a VY -subsethood measure and therefore, it is also a * -subsethood measure.…”

Section: Relationships Between Similarity Measures and Subsethood Meamentioning

confidence: 99%

“…Considering that an axiom definition must generally be abstract and simple, Fan [17] gave the following definition. A ⊆ B ⊆ C, then c(C, A) ≤ c(B, A) and c(C, A) ≤ c(C, B).…”

Section: Relationships Between Similarity Measures and Subsethood Meamentioning

confidence: 99%

See 2 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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Section: Relationships Between Similarity Measures and Subsethood Meamentioning

confidence: 99%

Section: Relationships Between Similarity Measures and Subsethood Meamentioning

confidence: 99%

See 1 more Smart Citation

Relationships Among Several Fuzzy Measures

He¹,

Li²

2016

Handbook of Fuzzy Sets Comparison - Theory, Algorithms and Applications

View full text Add to dashboard Cite

show abstract

“…Therefore, Fan et al 12 thought a simpler form of definition of subsethood measure based on Young's definition.…”

Section: Co-published By Atlantis Press and Taylor And Francismentioning

confidence: 99%

“…Young 30 gave four axioms for these measures. Later, Fan et al 12 modified one of Young's axioms. Finally, in 2006 Bustince et al 4 modified two of Young's axioms and proposed a new class of subsethood measure called fuzzy DIsubsethood measure.…”

Section: Introductionmentioning

confidence: 99%