On Generalized Fuzzy Mean Code Word Lengths

Dhara Singh Hooda; Arunodaya Raj Mishra; Divya Jain

doi:doi:10.11648/j.ajam.20140204.13

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On Generalized Fuzzy Mean Code Word Lengths

Dhara Singh Hooda, Arunodaya Raj Mishra, Divya Jain

Published in American Journal of Applied Mathematics (Volume 2, Issue 4)

Received: 21 July 2014 Accepted: 9 August 2014 Published: 30 August 2014

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Abstract

In present communication, a generalized fuzzy mean code word length of degree β has been defined and its bounds in the term of generalized fuzzy information measure have been studied. Further we have defined the fuzzy mean code word length of type (α,β) and its bounds have also been studied. Monotonic behavior of these fuzzy mean code word lengths have been illustrated graphically by taking some empirical data.

Published in	American Journal of Applied Mathematics (Volume 2, Issue 4)
DOI	10.11648/j.ajam.20140204.13
Page(s)	127-134
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2024. Published by Science Publishing Group

Keywords

Entropy, Fuzzy Entropy, Codeword Length, Decipherable Code, Crisp Set, Hölder’s Inequality

References

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[2]	A. Renyi, “On measures of entropy and information”, Proceedings 4th Berkeley Symposium on Mathematical Statistics and Probability, 1 (1961), 547-561.
[3]	B. D. Sharma and D. P. Mittal, “New non- additive measures of entropy for discrete probability distributions”, J. Math. Sci (Calcutta), 10 (1975), 28-40.
[4]	B. D. Sharma and I. J. Taneja, “Three generalized additive measures of entropy”, Elec. Inform. Kybern., 13 (1977), pp. 419-433.
[5]	C. E. Shannon, “A mathematical theory of communication”, Bell Syst. Tech. J., 27 (1948), pp. 379-423 & 623-659.
[6]	D. Bhandari, N. R. Pal and D.D. Majumder, “Fuzzy divergence, probability measure of fuzzy events and image thresholding”, Pattern Recognition Letters, 1 (1992), 857-867.
[7]	D. S. Hooda and Divya Jain, “Sub additive measures of fuzzy information”, Journal of Reliability and Statistical Studies, 02 (2009), pp. 39-52.
[8]	D. S. Hooda, “On generalized measures of fuzzy entropy”, Mathematica Slovaka, 54 (2004), pp. 315-325.
[9]	J. N. Kapur, “Measures of fuzzy information”, Mathematical Science Trust Society, New Delhi (1997).
[10]	L. A. Zadeh, “Fuzzy sets”, Inform. Contr., 8 (1965), pp. 338-353.
[11]	L. G. Kraft, “A device for quantizing grouping and coding amplitude modulated pulses”, M. S. Thesis, Electrical Engineering Department, MIT (1949).
[12]	O. Prakash and P. K. Sharma, “Noiseless coding theorems corresponding to fuzzy entropies”, Southeast Asian Bulletin of Mathematics, 27 (2004), 1073-1080.

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APA Style

Dhara Singh Hooda, Arunodaya Raj Mishra, Divya Jain. (2014). On Generalized Fuzzy Mean Code Word Lengths. American Journal of Applied Mathematics, 2(4), 127-134. https://doi.org/10.11648/j.ajam.20140204.13

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ACS Style

Dhara Singh Hooda; Arunodaya Raj Mishra; Divya Jain. On Generalized Fuzzy Mean Code Word Lengths. Am. J. Appl. Math. 2014, 2(4), 127-134. doi: 10.11648/j.ajam.20140204.13

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AMA Style

Dhara Singh Hooda, Arunodaya Raj Mishra, Divya Jain. On Generalized Fuzzy Mean Code Word Lengths. Am J Appl Math. 2014;2(4):127-134. doi: 10.11648/j.ajam.20140204.13

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@article{10.11648/j.ajam.20140204.13,
  author = {Dhara Singh Hooda and Arunodaya Raj Mishra and Divya Jain},
  title = {On Generalized Fuzzy Mean Code Word Lengths},
  journal = {American Journal of Applied Mathematics},
  volume = {2},
  number = {4},
  pages = {127-134},
  doi = {10.11648/j.ajam.20140204.13},
  url = {https://doi.org/10.11648/j.ajam.20140204.13},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajam.20140204.13},
  abstract = {In present communication, a generalized fuzzy mean code word length of degree β has been defined and its bounds in the term of generalized fuzzy information measure have been studied. Further we have defined the fuzzy mean code word length of type (α,β) and its bounds have also been studied. Monotonic behavior of these fuzzy mean code word lengths have been illustrated graphically by taking some empirical data.},
 year = {2014}
}

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TY  - JOUR
T1  - On Generalized Fuzzy Mean Code Word Lengths
AU  - Dhara Singh Hooda
AU  - Arunodaya Raj Mishra
AU  - Divya Jain
Y1  - 2014/08/30
PY  - 2014
N1  - https://doi.org/10.11648/j.ajam.20140204.13
DO  - 10.11648/j.ajam.20140204.13
T2  - American Journal of Applied Mathematics
JF  - American Journal of Applied Mathematics
JO  - American Journal of Applied Mathematics
SP  - 127
EP  - 134
PB  - Science Publishing Group
SN  - 2330-006X
UR  - https://doi.org/10.11648/j.ajam.20140204.13
AB  - In present communication, a generalized fuzzy mean code word length of degree β has been defined and its bounds in the term of generalized fuzzy information measure have been studied. Further we have defined the fuzzy mean code word length of type (α,β) and its bounds have also been studied. Monotonic behavior of these fuzzy mean code word lengths have been illustrated graphically by taking some empirical data.
VL  - 2
IS  - 4
ER  -

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Author Information

Dhara Singh Hooda

Department of Mathematics, Jaypee University of Engineering and Technology, Guna, Madhya Pradesh, India
Arunodaya Raj Mishra

Department of Mathematics, Jaypee University of Engineering and Technology, Guna, Madhya Pradesh, India
Divya Jain

Department of Mathematics, Jaypee University of Engineering and Technology, Guna, Madhya Pradesh, India

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APA Style

Dhara Singh Hooda, Arunodaya Raj Mishra, Divya Jain. (2014). On Generalized Fuzzy Mean Code Word Lengths. American Journal of Applied Mathematics, 2(4), 127-134. https://doi.org/10.11648/j.ajam.20140204.13

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ACS Style

Dhara Singh Hooda; Arunodaya Raj Mishra; Divya Jain. On Generalized Fuzzy Mean Code Word Lengths. Am. J. Appl. Math. 2014, 2(4), 127-134. doi: 10.11648/j.ajam.20140204.13

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AMA Style

Dhara Singh Hooda, Arunodaya Raj Mishra, Divya Jain. On Generalized Fuzzy Mean Code Word Lengths. Am J Appl Math. 2014;2(4):127-134. doi: 10.11648/j.ajam.20140204.13

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@article{10.11648/j.ajam.20140204.13,
  author = {Dhara Singh Hooda and Arunodaya Raj Mishra and Divya Jain},
  title = {On Generalized Fuzzy Mean Code Word Lengths},
  journal = {American Journal of Applied Mathematics},
  volume = {2},
  number = {4},
  pages = {127-134},
  doi = {10.11648/j.ajam.20140204.13},
  url = {https://doi.org/10.11648/j.ajam.20140204.13},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajam.20140204.13},
  abstract = {In present communication, a generalized fuzzy mean code word length of degree β has been defined and its bounds in the term of generalized fuzzy information measure have been studied. Further we have defined the fuzzy mean code word length of type (α,β) and its bounds have also been studied. Monotonic behavior of these fuzzy mean code word lengths have been illustrated graphically by taking some empirical data.},
 year = {2014}
}

Copy | Download

TY  - JOUR
T1  - On Generalized Fuzzy Mean Code Word Lengths
AU  - Dhara Singh Hooda
AU  - Arunodaya Raj Mishra
AU  - Divya Jain
Y1  - 2014/08/30
PY  - 2014
N1  - https://doi.org/10.11648/j.ajam.20140204.13
DO  - 10.11648/j.ajam.20140204.13
T2  - American Journal of Applied Mathematics
JF  - American Journal of Applied Mathematics
JO  - American Journal of Applied Mathematics
SP  - 127
EP  - 134
PB  - Science Publishing Group
SN  - 2330-006X
UR  - https://doi.org/10.11648/j.ajam.20140204.13
AB  - In present communication, a generalized fuzzy mean code word length of degree β has been defined and its bounds in the term of generalized fuzzy information measure have been studied. Further we have defined the fuzzy mean code word length of type (α,β) and its bounds have also been studied. Monotonic behavior of these fuzzy mean code word lengths have been illustrated graphically by taking some empirical data.
VL  - 2
IS  - 4
ER  -

Copy | Download