Some new information measures for fuzzy sets

Bhandari, Dinabandhu; Pal, Nikhil R.

doi:10.1016/0020-0255(93)90073-u

Cited by 319 publications

(168 citation statements)

References 14 publications

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“…Therefore, the fuzzy entropy N (p(A), q(A)) is in accord with the one given by Zeng and Li [44]. (2) In conditions of (1), if n = 1, then we have…”

Section: Example 17 Consider the Fuzzy Equivalence E(x Y)supporting

confidence: 75%

“…This dissimilarity measure is indeed a distance measure in the sense of Liu [43] in case it is symmetrical and satisfies the triangular inequality. Based on logarithm operation, Bhandari and Pal [2] defined a divergence measure between fuzzy sets. In [32], Montes et al introduced a new axiomatic definition for divergence measure.…”

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

confidence: 99%

“…(1) c is a subsethood measure, (2) if N satisfies N4, N6 and N9, then c is a VY -subsethood measure, (3) if N satisfies N4 and N9, then c is a * -subsethood measure, (4) if N satisfies N4, N5 and N6, 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, N6 and N9, then c is a DI-subsethood measure.…”

Section: B)mentioning

confidence: 99%

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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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“…Therefore, the fuzzy entropy N (p(A), q(A)) is in accord with the one given by Zeng and Li [44]. (2) In conditions of (1), if n = 1, then we have…”

Section: Example 17 Consider the Fuzzy Equivalence E(x Y)supporting

confidence: 75%

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

confidence: 99%

Section: B)mentioning

confidence: 99%

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Relationships Among Several Fuzzy Measures

He¹,

Li²

2016

Handbook of Fuzzy Sets Comparison - Theory, Algorithms and Applications

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“…Characterization and quantification of fuzziness are important issues that affect the management of uncertainty in many system models and designs. The fact that the entropy of a fuzzy set is a measure of the fuzziness of that fuzzy set has been established by previous researchers [14,16]. Liu proposed the axiomatic definitions of entropy, distance measure, and similarity measure, and discussed the relations between these three concepts.…”

Section: Introductionmentioning

confidence: 99%

Relation between Certainty and Uncertainty with Fuzzy Entropy and Similarity Measure

Lee¹,

Zhai²

2014

Journal of the Korea Convergence Society

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We survey the relation of fuzzy entropy measure and similarity measure. Each measure represents features of data uncertainty and certainty between comparative data group. With the help of one-to-one correspondence characteristics, distance measure and similarity measure have been expressed by the complementary characteristics. We construct similarity measure using distance measure, and verification of usefulness is proved. Furthermore analysis of similarity measure from fuzzy entropy measure is also discussed.•

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“…Design of fuzzy entropy for calculation of uncertainty has been studied by numerous researchers [1][2][3]. Most of results were concentrated in the designing of fuzzy entropies [1,2], and many parts of them also showed the implicit results of fuzzy entropies [1]. Hence, to apply real data explicit fuzzy entropy has to be needed.…”

Section: Introductionmentioning

confidence: 99%

Mutual Information Analysis with Similarity Measure

Wang¹,

Lee²

2010

International Journal of Fuzzy Logic and Intelligent Systems

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Discussion and analysis about relative mutual information has been carried out through fuzzy entropy and similarity measure. Fuzzy relative mutual information measure (FRIM) plays an important part as a measure of information shared between two fuzzy pattern vectors. This FRIM is analyzed and explained through similarity measure between two fuzzy sets. Furthermore, comparison between two measures is also carried out.

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Some new information measures for fuzzy sets

Cited by 319 publications

References 14 publications

Relationships Among Several Fuzzy Measures

Relationships Among Several Fuzzy Measures

Relation between Certainty and Uncertainty with Fuzzy Entropy and Similarity Measure

Mutual Information Analysis with Similarity Measure

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