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In this study, we investigated the relationship between similarity measures and entropy for fuzzy sets. First, we developed fuzzy entropy by using the distance measure for fuzzy sets. We pointed out that the distance between the fuzzy set and the corresponding crisp set equals fuzzy entropy. We also found that the sum of the similarity measure and the entropy between the fuzzy set and the corresponding crisp set constitutes the total information in the fuzzy set. Finally, we derived a similarity measure from entropy and showed by a simple example that the maximum similarity measure can be obtained using a minimum entropy formulation.

- Publication
- IEICE TRANSACTIONS on Information Vol.E92-D No.9 pp.1783-1786

- Publication Date
- 2009/09/01

- Publicized

- Online ISSN
- 1745-1361

- DOI
- 10.1587/transinf.E92.D.1783

- Type of Manuscript
- LETTER

- Category
- Computation and Computational Models

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Sang-Hyuk LEE, Keun Ho RYU, Gyoyong SOHN, "Study on Entropy and Similarity Measure for Fuzzy Set" in IEICE TRANSACTIONS on Information,
vol. E92-D, no. 9, pp. 1783-1786, September 2009, doi: 10.1587/transinf.E92.D.1783.

Abstract: In this study, we investigated the relationship between similarity measures and entropy for fuzzy sets. First, we developed fuzzy entropy by using the distance measure for fuzzy sets. We pointed out that the distance between the fuzzy set and the corresponding crisp set equals fuzzy entropy. We also found that the sum of the similarity measure and the entropy between the fuzzy set and the corresponding crisp set constitutes the total information in the fuzzy set. Finally, we derived a similarity measure from entropy and showed by a simple example that the maximum similarity measure can be obtained using a minimum entropy formulation.

URL: https://global.ieice.org/en_transactions/information/10.1587/transinf.E92.D.1783/_p

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@ARTICLE{e92-d_9_1783,

author={Sang-Hyuk LEE, Keun Ho RYU, Gyoyong SOHN, },

journal={IEICE TRANSACTIONS on Information},

title={Study on Entropy and Similarity Measure for Fuzzy Set},

year={2009},

volume={E92-D},

number={9},

pages={1783-1786},

abstract={In this study, we investigated the relationship between similarity measures and entropy for fuzzy sets. First, we developed fuzzy entropy by using the distance measure for fuzzy sets. We pointed out that the distance between the fuzzy set and the corresponding crisp set equals fuzzy entropy. We also found that the sum of the similarity measure and the entropy between the fuzzy set and the corresponding crisp set constitutes the total information in the fuzzy set. Finally, we derived a similarity measure from entropy and showed by a simple example that the maximum similarity measure can be obtained using a minimum entropy formulation.},

keywords={},

doi={10.1587/transinf.E92.D.1783},

ISSN={1745-1361},

month={September},}

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TY - JOUR

TI - Study on Entropy and Similarity Measure for Fuzzy Set

T2 - IEICE TRANSACTIONS on Information

SP - 1783

EP - 1786

AU - Sang-Hyuk LEE

AU - Keun Ho RYU

AU - Gyoyong SOHN

PY - 2009

DO - 10.1587/transinf.E92.D.1783

JO - IEICE TRANSACTIONS on Information

SN - 1745-1361

VL - E92-D

IS - 9

JA - IEICE TRANSACTIONS on Information

Y1 - September 2009

AB - In this study, we investigated the relationship between similarity measures and entropy for fuzzy sets. First, we developed fuzzy entropy by using the distance measure for fuzzy sets. We pointed out that the distance between the fuzzy set and the corresponding crisp set equals fuzzy entropy. We also found that the sum of the similarity measure and the entropy between the fuzzy set and the corresponding crisp set constitutes the total information in the fuzzy set. Finally, we derived a similarity measure from entropy and showed by a simple example that the maximum similarity measure can be obtained using a minimum entropy formulation.

ER -