7.     POSTSCRIPT

The applications of the new information theory show that the theory is more suitable for dealing with what is meant by ¡°information¡± in common language  , and for optimizing various information processes. However, for optimizing economic forecast, such as the forecast of a stock index, information value may be a better criterion in some cases than information criterion. Recently, the author  found a new generalized entropy that can be applied to optimize portfolio  (Lu, 1997). On the new portfolio theory,  a very practical measure of information value  for a class of cases is defined.,  It promises an increase in capital appreciation because of information.   Since information value, such as the information value of storm forecast is very relative and generally changes from person to person,   information criterion is still proper in many cases.  About information value criterion based on the generalized entropy,  further research is proceeding.      

 

 Many theories in economics, such as efficient market theory, game theory, rational expectation theory, asymmetric information theory (Sengupta, 1993), are based on information concept. However, the problem remains as how do we measure information and information value in economic fields. It is believed that the information economics, including the  afore mentioned theories, can be  improved with the help of the new information and information value theory.

 

ACKNOWLEDGMENT

The author gratefully acknowledges guidance from Professors Pei-Zhuang Wang, Cheng-Zhong Luo, and Hong-Xing Li,  Professors  of Fuzzy Mathematics Research group at Beijing Normal University, and editorial assistance  of Dr. Gordon Chen,  at  Niagara College, Canada.

¡¡

References

Aczel,  J. and Forte,  B. (1986), ¡° Generalized entropies and the  maximum entropy  principle, In: Bayesian Entropy and Bayesian Methods in Applied Statistics, edited by J. H. Justice,  Cambridge  University Press, Cambridge, pp. 95-100.

Bar-Hillel, Y. and Carnap, R. (1952),  ¡°An outline of a theory  of semantic information,¡± Tech. Rep. No., 247, Research Lab. of  Electronics, MIT.

Berger, T. (1971), Rate Distortion Theory, Englewood Cliffs, N.J.: Prentice-Hall.

Brillouin, L. (1962) Science and Information Theory,  Academic Press, New York.

Chen, K. J. (1982),  How Does God Play Dices (in Chinese), Sichuan People's Publishing House, Chendu.

De Luca, A. and Termini S. (1972), ¡°A definition of nonprobabilistic entropy in the setting of fuzzy sets, Infor. Contr. 20, pp.301-312.

Gottinger, H. W.(1975),  ¡°Lecture notes on concepts and Measures of information,¡± In: Information Theory: New trends and Open Problems, edited by G. Longo, Springer Verlag, CISM.

Helstron, C. W. (1976), Quantum Detection and Estimation Theory, Academic Press, New York.

 Higashi, M. and Klir, G. (1982), ¡°Measures of uncertainty and  information based on possibility distributions, Internat. J.  General Systems, 9, pp.4358.

 Jumarie, J. (1987),  ¡±Subjectivity: human communication¡±,  in:   System and Control Encyclopedia, edited by M. G. Singh,  Pergamon Press, pp. 4696-4698.

 Kullback, S. (1959), Information and Statistics, John Wiley & Sons Inc., New York.

  Lu, C. G. (1989),  ¡°Decoding model of colour vision and verifications,¡± (in Chinese) ACTA OPTIC SINICA, 9(2), 158-163.

  Lu, C. -G. (1991a),  ¡°Reform of  Shannon's  Formulas,¡±(in Chinese)  J. of China Institute of Communication , 12(2). pp.95-96.

  Lu, C. -G. (1991b),  ¡°The consistency of a generalized information theory  with Popper's theory of scientific evolution,¡±(in Chinese)J. of Changsha University,  7(2),  pp.41-46.

  Lu, C. -G. (1994), ¡°Meanings of generalized entropy and generalized mutual information for coding,(in Chinese) J. of China Institute of Communication, 15(6), pp.37-44.

  Lu, C. -G. (1997), ¡°Entropic theory of portfolio and risk control¡±,(in Chinese) China Futures, 4(6), pp. 44-48.

  Popper, K. R. (1968), Conjectures and Refutations: The Growth of  Scientific Knowledge, Harper & Row, Publishers, New York and Evanston.

  Reichenbach, H. (1982),  ¡°The logical foundation of the concept of probability,¡±  In: Logical Empiricism, edited by Q. Hong, Business and Affairs Press, Peking.

  Rosie, A. M. (1978),  Information and Communication Theory,  People's Post and Telecommunication Press, Beijing.

  Sengupta, J. K. (1993), Economics of Information and Efficiency, Kluwer Academic Publishers, Dordrecht.

  Shannon, C. E.(1949), ¡°The Mathematical theory of communication,¡±  In: The Mathematical Theory of  Communication, edited by C. E. Shannon and W. Weaver, University of  Illinois Press, Urbana.

  Theil, H. (1967), Economics and Information Theory, North-Holland, Amsterdam.

  Weaver, W. (1949),  ¡°Recent contributions to the mathematical theory of communication,¡± In: The Mathematical Theory of  Communication, edited by C. E. Shannon and W. Weaver, University of Illinois Press, Urbana.

  Wang, P. -Z. (1987),  ¡°Random sets in Fuzzy Set theory, In: System & Control Encyclopedia, edited by M. G. Singh, Pergamon Press, pp.3945-3947.

  Zadeh, L. A. (1965), ¡°Fuzzy sets,¡±  Infor. Contr., 8, pp.338-353.

  Zadeh, L. A. (1986), ¡°Probability measures of fuzzy events,¡±  Journal of Mathematical Analysis and Applications, 23, pp.421-427.