American Journal of Applied Mathematics and Statistics
ISSN (Print): 2328-7306 ISSN (Online): 2328-7292 Website: http://www.sciepub.com/journal/ajams Editor-in-chief: Mohamed Seddeek
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American Journal of Applied Mathematics and Statistics. 2014, 2(2), 73-76
DOI: 10.12691/ajams-2-2-4
Open AccessArticle

Some New Generalizations of Fuzzy Average Code Word Length and their Bonds

M.A.K. Baig1, , Mohd Afzal Bhat1 and Mohd Javid Dar1

1University of Kashmir, Hazratbal, Srinagar, India

Pub. Date: February 27, 2014

Cite this paper:
M.A.K. Baig, Mohd Afzal Bhat and Mohd Javid Dar. Some New Generalizations of Fuzzy Average Code Word Length and their Bonds. American Journal of Applied Mathematics and Statistics. 2014; 2(2):73-76. doi: 10.12691/ajams-2-2-4

Abstract

In this communication, we propose a new generalizations of fuzzy average codeword length La and study its particular cases. The results obtained not only generalize the existing fuzzy average code word length but all the known results are the particular cases of the proposed length. Some new fuzzy coding theorems have also been proved.

Keywords:
fuzzy set generalized fuzzy entropy generalized fuzzy average godeword length information Bounds

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References:

[1]  Bhandari, N. R. Pal, Some new information measures for fuzzy sets, Information Sciences 1993; Vol. 67, No. 3: pp. 209-228.
 
[2]  Campbell, L.L., A coding theorem and Renyi’s entropy, Information and Control 1965; Vol. 8: pp. 423-429.
 
[3]  De Luca, S. Termini, A Definition of Non-probabilistic Entropy in the Setting of fuzzy sets theory, Information and Control 1972; Vol.20: pp.301-312.
 
[4]  Havrada, J. H., Charvat, F., Quantification methods of classificatory processes, the concepts of structural α entropy, Kybernetika 1967; Vol.3: pp. 30-35.
 
[5]  J.N.Kapur, Measures of Fuzzy Information, Mathematical Science Trust Society, New Delhi; 1997.
 
[6]  Kapur, J. N., A generalization of Campbell’s noiseless coding theorem, Jour. Bihar Math, Society 1986; Vol.10: pp.1-10.
 
[7]  Kapur, J. N., Entropy and Coding, Mathematical Science Trust Society, New Delhi; 1998.
 
[8]  Lowen, R., Fuzzy Set Theory–Basic Concepts, Techniques and Bibliography, Kluwer Academic Publication. Applied Intelligence 1996; Vol. 31, No. 3: pp.283-291.
 
[9]  Mathai, A.M., Rathie, P.N., Basic Concept in Information Theory and Statistics. Wiley Eastern Limited, New Delhi; 1975.
 
[10]  Pal, Bezdek, Measuring Fuzzy Uncertainty, IEEE Trans. of fuzzy systems 1994; Vol. 2, No. 2: pp.107-118.
 
[11]  Renyi, A., On measures of entropy and information. Proceedings 4th Berkeley Symposium on Mathematical Statistics and Probability 1961; Vol.1: pp.541-561.
 
[12]  Shannon, C. E., A mathematical theory of communication. Bell System Technical Journal 1948; Vol.27: pp.379-423, 623-659.
 
[13]  Sharma, B.D., Taneja, I. J., Entropies of typeα, β and other generalized measures of information theory, Matrika 1975; Vol.22: pp. 205-215.
 
[14]  Zadeh, L. A., Fuzzy Sets, Inform, and Control 1966; Vol.8: pp.94-102.