REFERENCES. Aczel, J. and Daroczy, Z. (1963). Characterisierung der entropien positiver ordnung

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1 REFERENCES Aczel, J. and Daroczy, Z. (1963). Characterisierung der entropien positiver ordnung under Shannonschen entropie. Acta Mathematica Hungarica 14: Aczel, J. and Daroczy, Z. (1975). On Measures of Information and their Characterizations. pp Academic Press, New York. Aggarwal, N. L. and Picard, C.F. (1978).Functional equations and information measures with preference. Kybernetika 14: Ang, W. K. and Jowitt, P.W. (2005). Some new insights on informational entropy for water distribution networks. Engineering Optimization 37: Asadi, M., Ebrahimi, N., Hamedani, G.G. and Soofi, S. (2004). Maximum dynamic entropy models. Applied Probability 41: Belis, M. and Guiasu, S. (1968). A quantitative-qualitative measure of information in cybernetic systems. IEEE Transactions on Information Theory 14: Bhandari, D. and Pal, N.R. (1993). Some new information measures for fuzzy sets. Information Sciences 67: Bhandari, D., Pal, N.R. and Majumder, D.D. (1992). Fuzzy divergence, probability measure of fuzzy events and image thresholding. Pattern Recognition Letters 1: Bhattacharya, A. (1943). On a measure of divergence between two statistically populations defined by their probability distributions. Bulletin of the Calcutta Mathematical Society 35: Brissaud, J.B. (2005). The meaning of entropy. Entropy 7: Burbea, J. (1984). The convexity with respect to Gaussian distributions of divergence of order α. Utilities Math 26:

2 Burbea, J. and Rao, C.R. (1982). On the convexity of some divergence measures based on entropy functions. IEEE Transactions on Information Theory 28: Burg, J.P. (1972). The relationship between maximum entropy spectra and maximum likelihood spectra. In: Childrers, D.G.(ed). Modern Spectral Analysis. pp Burgin, M. (2003). Information theory: A multifaceted model of Information. Entropy 5: Cai, H., Kulkarni, S. and Verdu, S. (2006). Universal divergence estimation for finitealphabet sources. IEEE Transactions on Information Theory 52: Chakrabarti, C.G. (2005). Shannon entropy: axiomatic characterization and application. International Journal of Mathematics and Mathematical Sciences 17: Chen, Y. (2006). Properties of quasi-entropy and their applications. Journal of Southeast University Natural Sciences 36: De Luca, A. and Termini, S. (1972). A definition of non-probabilistic entropy in setting of fuzzy set theory. Information and Control 20: Dragomir, S. S. (2005). Some general divergence measures for probability distribution. Acta Mathematica Hungarica 109: Dragomir, S. S. and Gluscevic, V. (2001). New estimates of the Kullback and Leibler distance and applications. Inequality Theory Applications 1: Dubois, D. and Prade, H. (1983). On distances between fuzzy points and their use for plausible reasoning. Proceedings of International Conference on Systems, Man and Cybernetics pp Dubois, D. and Prade, H. (2000). Fundamentals of Fuzzy Sets. pp Kluwer Academic Publishers, Boston. 192

3 Ebanks, B.R. (1983). On measures of fuzziness and their representations. Journal of Mathematical Analysis and Applications 94: Ebrahimi, N., Soofi, E.S. and Zahedi, H. (2004). Information properties of order statistics and spacings. IEEE Transactions on Information Theory 50: Emptoz, H. (1981). Non-probabilistic entropies and indetermination process in the setting of fuzzy set theory. Fuzzy Sets and Systems 5: Fan, J.L., Ma, Y.L. and Xie, W.X. (2001). On some properties of distance measure. Fuzzy Sets and Systems 117: Ferreri, C. (1980). Hypoentropy and related heterogeneity divergence measures. Statistica 40: Garbaczewski, P. (2006). Differential entropy and dynamics of uncertainty. Journal of Statistical Physics 123: Gross, D. and Harris, C.M. (1998). Fundamentals of Queueing Theory. John Wiley and Sons, New York. Guiasu, S. (1971). Weighted entropy. Reports on Mathematical Physics 2: Guiasu, S. (1985). The relative information generating functions. Information Sciences 35: Guiasu, S. (1986). Maximum entropy condition in queuing theory. Journal of the Operational Research Society 37: Guiasu, S. and Picard, C.F. (1971). Borne in ferictur de la longuerur utile de certains codes. Comptes Rendus Mathematique Academic des Sciences Paris 273: Guiasu, S.and Shenitzer, A. (1975). The principle of maximum entropy. Mathematical Intelligencer 7:

4 Guo, X. Z. and Xin, X. L. (2006). Some new generalized entropy formulas of fuzzy sets. Journal of the Northwest University 36: Gurdial and Pessoa, F. (1977). On useful information of order α. Journal of Combinatrics Information and System Sciences 2: Gurdial, A., Petry, F. and Beaubouef, T. (2001). A note on new parametric measures of information for fuzzy sets. International Conference on Information System Security 26: Herremoes, P. and Vignat, C. (2003). An entropy power inequality for the binomial family. Journal of Inequalities in Pure and Applied Mathematics 4: 6. Havrada, J.H. and Charvat, F. (1967). Quantification methods of classification process:concept of structural α-entropy. Kybernetika 3: Herremoes, P.(2006). Interpretations of Renyi entropies and divergences. Journal of Physics A 365: Hooda,D.S. and Kapur, J. N. (2001). Crop area distributions for optimal yield. Operations Research Society of India 38: Hooda, D.S. and Tuteja, R.K. (1981). Two generalized measures of useful information. Information Sciences 23: Hu,Q.and Yu, D. (2004). Entropies of fuzzy indiscernibility relation and its operations. International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems 12: Jaynes, E.T. (1957). Information theory and statistical mechanics. Physical Review 106:

5 Jeffreys, H. (1946). An invariant form of the prior probability in estimation problems. Proceedings of the Royal Society of Edinburg Section A 186: Kandel, A. (1986) Fuzzy Mathematical Techniques with Applications. Addison-Wesley. Kapur, J.N. (1967). Generalized entropy of order α and type β. Mathematics Seminar 4: Kapur, J.N. (1980). Non-additive measures of entropy. University of Manitoba Research Report. Kapur, J.N. (1985). Some new measures of entropy and divergence. Journal of Mathematical and Physical Sciences 19: Kapur, J.N. (1986). Some new measures of directed divergence. Journal of Mathematical and Physical Sciences 20: Kapur, J.N. (1986). Four families of measures of entropy. Indian Journal of Pure and Applied Mathematics 17: Kapur, J.N. (1987). On the range of validity of certain measures of inaccuracy. Mathematics Today 5: Kapur, J.N. (1987). Maximum entropy principle in theory. Indian Journal of Management and Systems 3: Kapur, J.N. (1989). Maximum Entropy Models in Science and Engineering. Wiley Eastern, New Delhi. Kapur, J.N. (1995). Measures of Information and Their Applications. Wiley Eastern, New York. Kapur, J.N. (1997). Measures of Fuzzy Information. Mathematical Sciences Trust Society, New Delhi. 195

6 Kapur, J.N. (2001). Generalized measures of information, generalized optimization principles and their applications. In: Parkash, O.(ed). Current Trends in Information Theory, Statistics and O.R. pp1-13. Guru Nanak Dev University Press, Amritsar. Kapur, J.N., Baciu, G. and Kesavan, H.K. (1994). The minimax information measure. International Journal of System Sciences 26: Kapur, J.N. and Kesavan, H.K. (1987). The Generalized Maximum Entropy Principle. Sandford Educational Press, University of Waterloo,Canada. Kapur,J.N.and Sandip, S. (2002). Some new measures of M-Entropy. Indian Journal of Pure and Applied Mathematics 3366: Kaufmann, A. (1975). Introduction to Theory of Fuzzy Subsets. Academic Press, New York. Klir, G. J. (2004). Generalized information theory: aims, results and open problems. Reliability Engineering and System Safety 85: Klir, G.J. and Folger, T.A. (1988). Fuzzy Sets, Uncertainty and Indetermination. Prentice Hall, New York. Kosko, B. (1991). Fuzzy entropy and conditioning. Information Sciences 42: Kullback, S. (1959). Information Theory and Statistics.Wiley Eastern, New York. Kullback, S. and Leibler, R.A. (1951). On information and sufficiency. Annals of Mathematical Statistics 22: Lavenda, B. H. (2005). Mean Entropies. Open Systems & Information Dynamics 12: Liu, S.T. and Kao, C. (2002). Fuzzy measures for correlation coefficient of fuzzy numbers. Fuzzy Sets and Systems 128:

7 Longo, G. (1972). Quantitative-Qualitative Measures of Information. Springer-Verlag, New York. Loo, S.G. (1977). Measures of fuzziness. Kybernetika 20: Lowen, R. (1996). Fuzzy Set Theory-Basic Concepts, Techniques and Bibliography. Kluwer Academic Publishers, Boston. Majda, A., Kleeman, R. and Gai, D. (2002). A mathematical framework for quantifying predictability through relative entropy. Methods Applied Analysis 9: Masi, M. (2006). On the q-parameter spectrum of generalized information entropy measures with no cut-off prescriptions. Physical Letters A-357: Medhi, J.M.. (1982). Stochastic Processes. Wiley Eastern, New Delhi. Menant, C. (2003). Information and meaning. Entropy 5: Nanda, A. K. and Paul, P. (2006). Some results on generalized residual entropy. Information Sciences 176: Onicescu, O. (1966). Energie Informationelle. Comptes Rendus Mathematique. Academie des Sciences Paris Pal, N.R. and Bezdek, J.C. (1994). Measuring fuzzy uncertainty. IEEE Transaction on Fuzzy Systems 2: Parkash, O. (1998). A new parametric measure of fuzzy entropy. Information Processing and Management of Uncertainty 2: Parkash, O. (2000). On fuzzy symmetric divergence. The Fourth Asian Fuzzy System Symposium 2:

8 Parkash, O. and Gandhi, C. P. (2005). Generating measures of fuzzy entropy through fuzzy directed divergence.ultra Scientist of Physical Sciences 17: Parkash, O. and Gandhi,C. P. (2008). New measures of information based upon measures of central tendency and dispersion. International Review of Pure and Applied Mathematics 4: Parkash, O. and Gandhi, C. P. (2009). A non-parametric measure of fuzzy R-divergence and its properties. Reflections des ERA 4: Parkash, O. and Gandhi, C. P. (2009). Variation of uncertainty in steady and non-steady processes of theory. Proceedings 40 th Annual Conference ORSI (Accepted). Parkash, O., Kumar, A. and Kumar, J. (2010). New weighted measures of fuzzy entropy, their mutual relationships and monotonic properties. In: Nath. P., Taneja, G., Deora, S.S. and Rahim, Z (ed). Emerging Trends in Software Engineering pp1-10. RGN Publications, New Delhi. Parkash, O. and Mahajan, R. (2005). New generalized weighted measures of fuzzy divergence. South East Asian Journal of Mathematics and Mathematical Sciences 4 : Parkash, O. and Sharma, P.K. (2004). Measures of fuzzy entropy and their relations. International Journal of Management & Systems 20 : Parkash, O. and Sharma, P. K. (2004). Noiseless coding theorems corresponding to fuzzy entropies. Southeast Asian Bulletin of Mathematics 27: Parkash, O. and Sharma, P. K. (2005). Some new measures of fuzzy directed divergence and their generalization. Journal of the Korean Society of Mathematical Education Series B 12 :

9 Parkash, O., Sharma, P. K. and Kumar, S. (2006). Two new measures of fuzzy directed divergence and their properties. SQC Journal For Science 11: Parkash, O., Sharma, P. K. and Kumar, J. (2008). Characterization of fuzzy measures via concavity and recursivity. Oriental Journal of Mathematical Sciences 1: Parkash, O., Sharma, P. K. and Mahajan, R (2008). New measures of weighted fuzzy entropy and their applications for the study of maximum weighted fuzzy entropy principle. Information Sciences 178: Parkash, O., Sharma, P. K. and Mahajan, R (2010). Optimization principle for weighted fuzzy entropy using unequal constraints. Southeast Asian Bulletin of Mathematics 34: Parkash, O. and Singh, R. S. (1987). On characterization of useful information theoretic measures. Kybernetika 23 : Parkash, O. and Singh, Y.B. (1994). Generalized J-divergence measure and error bounds. Carribbean Journal of Mathematics & Computing. Science 4: Parkash, O. and Singh, Y.B. (1995). Generalized R-divergence measures and error. Carribbean Journal of Mathematics & Computing Science 5: Parkash, O. and Taneja, H.C. (1986). Characterization of quantitative- qualitative measure of inaccuracy for discrete generalized probability distributions. Communications in Statistics Theory and Methods 15: Parkash, O. and Tuli, R.K. (2005). On generalized measures of fuzzy directed divergence. Ultra Scientist of Physical Sciences 17: Parkash, O. and Tuli, R.K. (2006). Maximum fuzziness in different measures of entropy. International Journal of Management and Systems 22:

10 Parkash, O. and Tuli, R.K. (2007). On generalized Havrada-Charvat fuzzy entropy. In: Kapur, P.K. (ed). Quality, Reliability and Infocom Technology. pp MacMillan India. Prabhakar, B. and Gallager, R. (2003). Entropy and the timing capacity of discrete queues. IEEE Transactions on Information Theory 49: Rao, M.C., Yunmei, V.B.C. and Wang, F. (2004). Commulative residual entropy: a new measure of Information. IEEE Transactions on Information Theory 50: Rathie, P.N. and Sheng, L.T. (1981). The J-divergence of order α. Journal of Combinatrics Information and System Sciences 6: Rathie, P.N. and Taneja, I.J. (1991). Unified (r,s) entropy and its bivariate measure. Information Sciences 54: Renyi, A. (1961). On measures of entropy and information. Proceedings 4th Berkeley Symposium on Mathematical Statistics and Probability 1: Rosenfeld, A. (1985). Distance between fuzzy sets. Pattern Recognition Letters 3: Rudas, I. J. (2001). Measures of fuzziness: theory and applications. Advances in fuzzy systems and evolutionary computation. pp World Scientific and Engineering Society Press, Athens. Salicru, M. and Taneja, I. J. (1993). Connections of generalized divergence measures with Fisher information matrix. Information Sciences 72: Schroeder, M. J. (2004). An alternative to entropy in the measurement of information. Entropy 6 :

11 Sergio, V. (1998). Fifty years of Shannon theory. IEEE Transactions on Information Theory 4: Shannon, C. E.(1948). A mathematical theory of communication. Bell System Technical Journal 27: , Sharma, B.D.and Mittal, D. P. (1975). New non-additive measures of entropy for a discrete probability distributions. Journal of Mathematical Sciences 10: Sharma, B.D. and Taneja, I.J. (1975). Entropies of type (α,β) and other generalized measures of information theory. Metrica 22: Shigeru, F. (2006). Information theoretical properties of Tsallies entropies. Journal of Mathematical Physics 47: Sibson, R. (1969). Information radius. Z. Wahrs and Verw, Geb, 14: Simpson, E.H. (1949). Measuremant of diversity. Nature 163: 688. Singh, R.P.,Kumar, R. and Tuteja, R. K. (2003). Applications of Holder s inequality in information theory. Information Sciences 152: Singh, R. P. and Kumar, S. (2007). Parametric R-norm information measures. Pure and applied Mathematika Science 35: Singh, R. P. and Tomar, V. P. (2006). Fuzzy information measures through generating functions and some comparison results. Information Processing and Management of Uncertainty : Singpurwalla, N. D. and Booker, J.M. (2004). Membership functions and probability measures of fuzzy sets. Journal of the American Statistical Association 99: Taneja, H. C. (1984). On the quantitative-qualitative measure of relative information. Information Sciences 33:

12 Taneja,H.C. and Tuteja, R.K. (1984). Characterization of quantitative-qualitative measure of relative information. Information Sciences 33: Taneja, I.J. (1983). On characterization of J-divergence and its generalizations. Journal of Combinatrics Information and System Sciences 3: Taneja, I.J. (1989). On generalized information measures and their applications. Advances in Electronics and Electron Physics 76 : Taneja,I. J. (2005). Refinement inequalities among symmetric divergence measures. Australian Journal of Mathematical Analysis and Applications 2: Taneja, I. J. (2006). Bounds on triangular discrimination, harmonic mean and symmetric chi-square divergence. Journal of Concrete and Applicable Mathematics 4: Taneja, I.J., Pardo, L., Morales, D. and Menendez, M.L. (1989). On generalized information and divergence measures and their applications. A brief review Questiio 13: Taneja, I. J. and Kumar, P. (2004). Relative information of type s, Csizer s f- divergence and information inequalities. Information Sciences 166: Theil, H.(1967): Economics and Information Theory, North-Holland, Amsterdam. Topsoe, F. (2002). Maximum entropy versus risk and applications of some classical discrete distributions. IEEE Transactions on Information Theory 48: Vinocha, O.P. and Hemlata (2004). Havrada-Charvat s entropy and the probability of error. Journal of Rajasthan Academy of Physical Sciences 3: Wiener, N. (1949). The Extrapolation, Interpolation and Smoothing of Stationary Time Series with Engineering Applications. John Wiley and Sons, New York. 202

13 Xue, J., Zhang, Y. and Lin, X. (1998). Threshold selection using cross-entropy and fuzzy divergence. Electronic Imaging and Multimedia Systems II Proceedings SPIE 3561: Yager, R. R. (1979). On measures of fuzziness and negation, Part-I: membership in the unit interval. International Journal of General Systems 5: Yun, Ben Hamza and Krim, Hamid (2003). A generalized divergence measure for robust registration. IEEE Transactions On Signal Processing 51: Zadeh, L. A. (1965). Fuzzy sets. Information and Control 8: Zadeh,L.A.(1968). Probability measures of fuzzy events. Journal of Mathematical Analysis and Applications 23: Zadeh, L.A. (2002). Towards a perception-based theory of probabilistic reasoning with imprecise probabilities. Journal of Statistics and Inference 105: Zadeh, L. A. (2004). Precisiated natural language (PNL). Al Magazine 25: Zadeh, L.A. (2005). Towards a generalized theory of uncertainty (GTU)- an outline. Information Sciences 172: Zhang, Z. (2003).On a new non-shannon type information inequalities. Communications in Information and Systems 3: Zimmermann, H. J. (2001). Fuzzy Set Theory and its Applications. Kluwer Academic Publishers, Boston. Zyczkowski, K. (2003). Renyi extrapolation of Shannon entropy. Open Systems and Information Dynamics 10: