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Original Articles

MEASURES OF UNCERTAINTY AND INFORMATION BASED ON POSSIBILITY DISTRIBUTIONS

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Pages 43-58 | Received 12 May 1982, Accepted 12 Aug 1982, Published online: 31 May 2007

References

  • J. Acwl , and Z. Daroczy , On Measures of Information and Their Characterizations. Academic Press , New York , 1973 .
  • J. Arael , B. Forte , and C.T. Ng , “ Why the Shannon and Hartley entropies are [natural]. ” Advances in Applied Probability , 6 , 1974 , pp. 131 – 146 .
  • W. R. Ashby , “ Measuring the internal information exchange in a system. ” Cybernerica , 1 , No. I , 1963 , pp. 5 – 22 .
  • W. R. Ashby , “ Two tables of identities governing information flows within large systems. ” ASC Communications , 1 , No. 2 . 1969 , pp. 3 – 8 .
  • W. R. Ashby , “ Information flows within co—ordinated systems. ” In; Progress of Cybernetics , edited by J. Rose , Gordon and Breach , London , 1970 , pp. 57 – 64 .
  • W. R. Ashby , “ Systems and their informational measures. ” In Trends in General Systems Theory , edited by G. 1. Kiit , John Wiley , New York , 1972 , pp. 78 – 97 .
  • D. E Boekee , J. C. A. Van Der Lubbe , “ The R—nonn information measure. ” Information, and Control , 45 , No. 2 , 1980 , pp. 136 – 155 .
  • L. Brillouin , Science and Information Theory. Academic Press. New York. 1956 .
  • L. Brtllouin , Scientific Uncertainty and Inforjnniion. Academic Press , New York , 1964 .
  • G. Broekan , ” On the representation and identification of structure systems. ” International Journal of Systems Science. 9 , No. 11 . 1978 , pp. 1271 – 1293 .
  • R. E. CavtHo , J. Kir , “ A conceptual foundation for systems problem soNing. ” International Journal of Systems Science , 9 , No. 2 . 1978 . pp. 219 – 236 .
  • R L. Cartllo and G. J. KJir , “ Systems of overall possibilities reconstruction aspects. ” In Applied Systems and Cybernetics , edited by G. E. Lasker , Pergamon Press , New York , 1981 , pp. 939 – 946 .
  • R E. Csvallo and G. J. Klir , “ Reconstruction of postibilislic behavior systems. ” Futxy Seis and Systems , 8 , No. 2 , August 1982 , pp. 175 – 197 .
  • C. Cherry , On Human Communication. The M.I.T. Press , Cambridge , Mass. , 1957 .
  • R. Christensen , Foundations of inductive Reasoning Entropy. Lincoln . Mass , 1980 .
  • R. Giristensen , Entropy Minimax Source Sourcebooks , Vol. 1–4 . Entropy, Lincoln. Mass , 1981 .
  • R. C. Cottant , “ Detecting subsystems of a complex system. ” IEEE Trans, on Sytttms, Man, and Cybernetics , SMC–2 , No. 4 , 1972 , pp 550 – 553 .
  • R. C. ConariL “ Measuring the strength of intervariabk relations. ” Kybernetes. 2 , No. 1 , 1973 . pp. 47 – 51 .
  • R. C. Conant , “ Laws of information which govern systems ” IEEE Tram, on Systems, Man, and Cybernetics , SMC–6 , No. 4 . 1976. pp. 240 – 255 .
  • R. C. Conant , “ Structural modelling using a simple information measure ,” International Journal of Systems Science , 11 , No, 6 , June 1980 , pp 721 – 730 .
  • Z. Daroczy , “ Generalized information functions. ” Information and Control , 16 , No. I , 1970 , pp. 36 – 51 .
  • D. Dubois and H. Prade , Fuzzy Sets and Systems Theory and Applications. Academic Press , New York , 1980 .
  • B. Forte , “ On the amount of information given by an experiment. ” In; Proc. of the Colloquium on Informtaian Theory , edited by A. Renyi , Janus Bolyai Mathematical Society , Budapest , 1968 , pp. 149 – 166 (VoL 1 ).
  • B. Forte , “ Why Shannon entropy. ” Symposia Mathematical XV , Academic Press , New York , 1975 . pp. 137 – 151 .
  • R. V. L. Hartley , “ Transmission of information. ” The Bell Systems Technical Journal , 7 , 1928 . pp. 535 – 563 .
  • EL Hisdalc. “ Conditional possibilities, independence and noninteraction. ” Fuzzy Sets and Systems , 1, No. 4 , 1978 , pp. 283 – 297 .
  • E. T. Jayncs , “ Where do we stand on maiimiim entropy? ” In The Maximum Entropy Formalism , edited by R. L Levine and M. Tribua , MIT Press , Cambridge , Mass , 1979 . pp. 15 – 118 .
  • G. J. Klir , On the representation of activity arrays. International Journal of General Systems , 1 Nat 3 , 1975 , pp. 149 – 168 .
  • G. J. Klir , “ General systems problem solving methodology. ” In Modelling and Simulation Methodology. edited by B. Zdgter et aL , North—Holland , Amsterdam. 1979 .
  • A N. Kolmogorov , Foundations of the Theory of Probability. Chelsea , New York , 1950 .
  • A.N. Kolmogorov , Three approaches to the quantitative definition of information. ” Problems of Information Transmission , 1 , No. 1 , 1965 , pp. 1 – 7 .
  • H. T. Nguyen , “ On conditional possibility distributions. ” Fuzzy Sets and Systems , I . No. 4 . October 1978 . pp. 299 – 309 .
  • H. T. Nguyen , “ Toward a calculus of the mathematical notion of possibility. ” In Advances in Futty Set Theory and Applications , edited by M. M. Gupta, R. K. Ragndc and R. R Yager , North—Holland , New York . 1979 , pp. 235 – 246 .
  • M. L. Puri , and D. Ralescu , “ A possibility measure is not a fuzzy measure. ” Furry Sets and Systems , 7 , No. 3 , 1981 pp. 311 – 313 .
  • A. Renyi , “ On measures of entropy and information. ” Proc. 4th Berkeley Symp. on Math. Stat, and Prob. , Univ. of California Press. Berkeley , 1960 , pp. 547 – 561 .
  • A. Renyi , Probability Theory. North—Holland , Amsterdam , 1970 (Appendix “Introduction to information theory,” pp. 540 – 616 .
  • C. L. Shannon , “ A mathematical theory of communication. ” The Bell System Technical Journal , 27 , July and October , 1948 . pp. 379 – 423 , 623 – 656 .
  • J. E. Shore and R. W. Johnson , “ Auomattc derivation of the principle of maiiminn entropy and the principle of minimum cross—entropy. ” IEEE Trans, on Information Theory. IT–24 , No. I , 1980 , pp. 26 – 37 .
  • Special Issue of the International Journal of General Systems on fXtconstructability Analysis , VoL 7 . No. I . 1981 (Brockstra, Cavallc, Conant, Klir, KrippendoriTL) .
  • M. Sugeno , “ Fuzzy measures and fuzzy integrals a survey. ” In Fuzzy Automata and Decision Processes. edited by M. M. Gupta. North—Holland , New York. 1977 , pp. 89 – 101 .
  • S. Wannabe , “ Information theoretical analysis of multivariate correlations. ” IBM Journal of Research aid Development , 4 , No. 1 . 1960 , pp. 66 – 81 .
  • S. Watanabe , Knowing and Guessing. John Wiley , New York . 1969 .
  • S. Watanabe , “ Pattern recognition as a guest for minimum entropy. ” Pattern Recognition , 13 , No. 5 , 1981 , pp. 381 – 387 .
  • R R. Yager , “ Measuring tranquility and anxiety in decision making an application of fuzzy sets. ” Technical Report No. RRY 79–03. lona College, School of Business Adminsiration, New Rocnclle , New York , 1979 .
  • R R. Yager , “ Measuring tranquility and anxiety in decision making ” International Journal of General Systems , 8 , No. 3 . 1981 PP 139 – 146 .
  • R R. Yager , “ Aspects of pombtlistic uncertainty. ” intern. J. of Man—Machine Studies , 11 No. 3 , April 1980 , pp. 283 – 298 .
  • R R. Yager , “ A foundabon for a theory of possibuity. ” Journal of Cybernetics , 10 , Nos. 1–3 , 1980 , pp. 177 – 204 .
  • L. A. Zadeh , “ Fuzzy sets as a bass for a theory of possibility. ” Fuzzy Sets and Systems , I , No. I . 1978 , pp. 3 – 28 .
  • L. A. Zadeh , “ PRUF—a meaning representation— language for natural languages. ” International Journal of Man—Machine Studies , 10 , No. 4 , 1978 , pp, 395 – 460 .
  • †This work was supported by the National Science Foundation under Grant No. ECS-8006590

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