Uncertainty Invariance Transformation in Continuous Case

In this work, a general procedure for transforming a possibility distribution into a probability density function, in the continuous case, is proposed, in a way that the resulting distribution contains the same uncertainty as the original distribution. A significant aspect of this approach is that it makes use of Uncertainty Invariance Principle which is itself a general procedure for going from an initial representation of uncertainty to a new representation.

[1]  C. Gupta A note on the transformation of possibilistic information into probabilistic information for investment decisions , 1993 .

[2]  George J. Klir,et al.  A MATHEMATICAL ANALYSIS OF INFORMATION-PRESERVING TRANSFORMATIONS BETWEEN PROBABILISTIC AND POSSIBILISTIC FORMULATIONS OF UNCERTAINTY , 1992 .

[3]  Éloi Bossé,et al.  Approximation techniques for the transformation of fuzzy sets into random sets , 2008, Fuzzy Sets Syst..

[4]  Ronald R. Yager,et al.  Entropy and Specificity in a Mathematical Theory of Evidence , 2008, Classic Works of the Dempster-Shafer Theory of Belief Functions.

[5]  Jagat Narain Kapur,et al.  Measures of information and their applications , 1994 .

[6]  K. D. Lee,et al.  Hybrid model for intent estimation , 2003, Sixth International Conference of Information Fusion, 2003. Proceedings of the.

[7]  Settimo Termini,et al.  A Definition of a Nonprobabilistic Entropy in the Setting of Fuzzy Sets Theory , 1972, Inf. Control..

[8]  Xiang Li,et al.  Maximum Entropy Principle for Fuzzy Variables , 2007, Int. J. Uncertain. Fuzziness Knowl. Based Syst..

[9]  D. Dubois,et al.  On Possibility/Probability Transformations , 1993 .

[10]  Bogdan Rebiasz,et al.  Fuzziness and randomness in investment project risk appraisal , 2007, Comput. Oper. Res..

[11]  Kwang-Hyun Cho,et al.  Level sets and minimum volume sets of probability density functions , 2003, Int. J. Approx. Reason..

[12]  Didier Dubois,et al.  Practical representations of incomplete probabilistic knowledge , 2006, Comput. Stat. Data Anal..

[13]  E. Lee,et al.  Comparison of fuzzy numbers based on the probability measure of fuzzy events , 1988 .

[14]  E. Lee,et al.  Analysis and simulation of fuzzy queues , 1992 .

[15]  George J. Klir,et al.  Uncertainty-Based Information , 1999 .

[16]  M. Gupta,et al.  FUZZY INFORMATION AND DECISION PROCESSES , 1981 .

[17]  G. Klir,et al.  MEASURES OF UNCERTAINTY AND INFORMATION BASED ON POSSIBILITY DISTRIBUTIONS , 1982 .

[18]  S. Chanas,et al.  Single value simulation of fuzzy variables , 1988 .

[19]  C. E. SHANNON,et al.  A mathematical theory of communication , 1948, MOCO.

[20]  Thomas M. Cover,et al.  Elements of Information Theory , 2005 .

[21]  Charles F. Hockett,et al.  A mathematical theory of communication , 1948, MOCO.

[22]  G. Klir,et al.  Uncertainty-based information: Elements of generalized information theory (studies in fuzziness and soft computing). , 1998 .

[23]  James Llinas,et al.  Hybrid framework for fusion 2+ in multi-multi air engagement , 2005, SPIE Defense + Commercial Sensing.

[24]  M. Oussalah ON THE PROBABILITY/POSSIBILITY TRANSFORMATIONS:A COMPARATIVE ANALYSIS , 2000 .

[25]  George J. Klir,et al.  A principle of uncertainty and information invariance , 1990 .

[26]  L. Zadeh Fuzzy sets as a basis for a theory of possibility , 1999 .

[27]  Siegfried Wonneberger,et al.  Generalization of an invertible mapping between probability and possibility , 1994 .