Main Article Content
There are many fuzzy information and divergence measures exist in the literature of fuzzy Information Theory. Inequalities play important role for finding the relations. Here, we will introduce some new information inequalities on fuzzy measures and their applications in pattern recognition. Also established relations between new and well known fuzzy divergence measures with help of the fuzzy $f$-divergence measure and jensen’s inequality.
This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.
R. Beran , Minimum Hellinger distance estimates for parametric models Ann.Statist.5 (1977), 445-463.
D. Bhandari and N.R Pal, Some new information measures for fuzzy sets. Information Sciences, 67(3), (1993), 209-228.
A. Bhattacharyya , Some Analogues to the Amount of Information and Their uses in Statistical Estimation, Sankhya, 8(1946), 1-14.
P. K. Bhatia and S. Singh, Three families of generalized fuzzy directed divergence, AMO-Advanced Modeling and Optimization, 14(3) (2012) 599-614.
J. Burbea and C.R.Rao, On Convexity of Some Divergence measures based on entropy functions,IEEE Transe.on.inform.theory ,IT-28 (1982), 489-495.
I. Csisza, On Topological Properties of f-Divergences. Studia Math. HunHungarica, Vol. 2,1967, 329-339.
I. Csiszar, Information-type measures of diverence of probability functions and indirect observations. studia Sci. Math. 2(1961). 299-318.
D. Wu and Jerry M. Mendel, Uncertainty measures for interval type-2 fuzzy sets, Information Sciences: an International Journal, 177 (23), p.5378-5393,2007
S. S. Dragomir, J. Sunde and C. Buse, New Inequalities for Jeffreys Divergence measure,Tamusi Oxford Journal of Mathematical Sciences, 16(2)(2000), 295-309.
S. S. Dragomir, Bounds of f-divergences under likelihood Ratio Constraints No.3, 205-223, 48(2003).
M. Ghosh, D. Das, C. Chakraborty and A.K. Roy, Automated leukocyte recognition using fuzzy divergence, Micron, 41 (2010) 840-846.
D. S. Hooda and D. Jain, The generalized fuzzy measures of directed divergence, total ambiguity and information improvement, Investigations in Mathematical Sciences, 2 (2012) 239-260.
E. Hellinger, Neue Begrundung der Theorie quadratischen Formen von unendlichenvielen Veranderlichen, J. Reine Aug. Math.,136(1909), 210-271.
K. C. Jain and Ram Naresh Saraswat, New Information Inequality and its application in establishing relation among various f-divergence measures, Journal of the Applied Mathematics, Statistics and Informatics, 8 (2012), No. 1.
K. C. Jain and R. N. Saraswat, Some well-known inequalities and its applications in information theory" Jordan Journal of Mathematics and Statistics. 2013, 157-167.
K. C. Jain and R. N. Saraswat, Some Bounds of Information Divergence Measures in Terms of Relative-Arithmetic Divergence Measure" International Journal of Applied Mathematics and Statistics, 32 (2) (2013), 48-58.
K. C. Jain and A. Srivastava, On Symmetric Information Divergence Measures of Csiszar's f-Divergence Class, Journal of Applied Mathematics, Statistics and Informatics (JAMSI),3(1)(2007),85-102.
A. Kaufmann, Introduction to the Theory of Fuzzy Sets - Vol. 1: Fundamental Theoretical Elements. 1975. Academic Press, New York.
S. Kullback and R. A. Leibler, On information and suciency, The Annals of Mathematical Statistics 22(1) (1951) 79-86.
A. Luca De. and S. Termini, A definition of non-probabilistic entropy in the setting of fuzzy sets theory. Information and Control. (1972) v20. 301-312.
Loo and S. G., Measures of fuzziness. Cybernetica. (1997) v20. 201-210.
S. Montes, I. Couso, P. Gil and C. Bertoluzza, Divergence measures between fuzzy sets, International Journal of Approximate Reasoning, 30 (2002) 91-105.
O. Parkash, P. K. Sharma and S. Kumar, Two new measures of fuzzy divergence and their properties. SQU Journal for Science, 11 (2006) 69- 77.
K. Pearson, On the criterion that a give system of deviations from the probable in the case of correlated system of variables in such that it can be reasonable supposed to have arisen from random sampling,Phil. Mag., 50(1900),157-172.
F. Osterreicher, Csiszar's f-Divergence, Basic Properties, pre-print, 2002.
Ram Naresh Saraswat and Ajay Tak, New f-divergence and Jensen ostrowski's type inequalities, Tamkang journal of mathematics, 50(1), (2019), 111-118.
R. Sibson, Information Radius,Z,Wahrs.undverw.geb.(14)(1969),149-160.
C. E. Shannon, A mathematical theory of communication, The Bell Syst. Tech. Journal 27(3) (1948) 379-423.
I. J. Taneja and Prenesh kumar, Relative information of type s, Csiszar's f-divergence, and information inequalities, Information sciences 166 (2004) 105-125.
I. J. Taneja, New Developments in generalized information measures, Chapter in: Advances in imaging and Electron Physics, Ed. P.W. Hawkes 91 (1995),37-135.
I. J. Taneja, Pranesh Kumar, Generalized non-symmetric divergence measures and inequalities.
V. P. Tomar and A. Ohlan, Sequence of inequalities among fuzzy mean divergence divergence measures and their applications, Springer Plus, 3:623 (2014) 1-20.
F. Topse, Some inequalities for information divergence and related measures of discrimination.Res.Coll.RGMIA2 (1999), 85-98.
L. A. Zadeh, Probability measures of fuzzy events. Journal of Mathematical Analysis and Applications. v23. 421-427.
L. A. Zadeh, Toward a generalized theory of uncertainty (GTU): an outline, Information Sciences|Informatics and Computer Science: An International Journal, Vol. 172 No.1-2, 1-40, 2005.