MEASUREMENT OF POSSIBILISTIC HISTOGRAMS FROM INTERVAL DATA

References

• Artstein , Z. and R. A. Vitale [ 1975 ], “ Strong Law of Large Numbers for Random Compact Sets .” Annals of Probability , 3 , pp. 879 – 882 .
   Web of Science ®Google Scholar
• Barone Joseph , M. , Dimitar P. Filev ,Ronald R. Yager [ 1995 ], “ Mountain Method-Based Fuzzy Clustering .” Inl. J. General Systems , 23 , pp. 281 – 305 .
   Google Scholar
• de Cooman , Gert [ 1995 ], “ The Formal Analogy Between Possibility and Probability Theory .” In Foundations and Applications of Possibility Theory , edited by G. de Cooman, D. Ruan and E. E. Kerre , World Scientific , Singapore , pp. 71 – 87 .
   Google Scholar
• de Cooman , Gert [ 1997a ], “ Possibility Theory I Measure- and Integral-Theoretic Groundwork .” Int. J. General Systems , 25 ( 4 ), pp. 291 – 323 .
   Web of Science ®Google Scholar
• de Cooman , Gert [ 1997b ], “ Possibility Theory II Conditional Possibility .” Int. J. General Systems , 25 ( 4 ), pp. 325 – 351 .
   Web of Science ®Google Scholar
• de Cooman . Gert [ 1997c ], “ Possibility Theory III Possibilistic Independence .” Int. J. General Systems , 25 ( 4 ) pp. 353 – 371 .
   Web of Science ®Google Scholar
• de Cooman , Gert . D. Ruan and E. E. Kerre , eds [ 1995 ], Foundations and Applications of Possibility Theory . World Scientific , Singapore .
   Google Scholar
• David , Herbert A . [ 1981 ], Order Statistics . Wiley , New York .
   Google Scholar
• Deely , John ( 1990 ) Basics of Semiotics , Indiana UP , Bloominglon IN .
   Google Scholar
• Degroot , Morris H .and William F. Eddy [ 1983 ],“ Set-Valued Parameters and Set-Valued Statistics .” In Recent Advances in Statistics , Academic Press , pp. 175 – 195 .
   Google Scholar
• Dempster , A. P. [ 1967 ], “ Upper and Lower Probabilities Induced by a Multivalued Mapping .”' Annals of Mathematical Statistics . 38 , pp. 325 – 339 .
   Google Scholar
• Dubois , Didier and Henri Prade [ 1978 ], “ Operations on Fuzzy Numbers .” Int. J. Systems Science , 9 , pp. 613 – 626 .
   Web of Science ®Google Scholar
• Dubois , Didier and Henri Prade [ 1982 ], “ On Several Representations of an Uncertain Body of Evidence .” Fuzzy Information and Decision Processes , pp. 167 – 181 .
   Google Scholar
• Dubois , Didier and Henri Prade [ 1987 ], “ Fuzzy Numbers An Overview .” In Analysis of Fuzzy Information , CRC Press . Boca Raton , v. 1 , pp. 3 – 39 .
   Google Scholar
• Dubois , Didier , Henri Prade [ 1989 ], “ Fuzzy Sets, Probability, and Measurement .” European J. of Operational Research . 40 ( 2 ), pp. 135 – 154 ,
   Web of Science ®Google Scholar
• Dubois , Didier , Henri Prade [ 1990 ], “ Consonant Approximations of Belief Functions ,” Int. J. Approximate Reasoning , 4 , pp. 419 – 449 .
   Google Scholar
• Dubois , Didier , Henri Prade [ 1992 ], “ Evidence. Knowledge and Belief Functions .” Int. J. Approximate Reasoning , 6 ( 3 ), pp. 295 – 320 .
   Google Scholar
• Eco , Umberto [ 1986 ], Semiotics and the Philosophy of Language . Indiana U Press , Bloomfield .
   Google Scholar
• Ferson , Scott , Lev Ginzburg , Resit Akcakaya [ 1996 ], “ Whereof One Cannot Speak When Input Distribulions are Unknown .” Risk Analysis , in press .
   Google Scholar
• Fung , Robert M . Chee Yee Chong [ 1986 ], “ Metaprobability and the Dempsler-Shafer in Evidential Reasoning .” In Uncertainty in Artificial Intelligence , edited by L. N. Kanal and J. F. Lemmer , North-Holland , Amsterdam , pp. 295 – 302 .
   Google Scholar
• Gil , M. A. [ 1992 ], “ A Note on the Connection Between Fuzzy Numbers and Random Intervals .” Statistics and Probability Letters , 13 ( 4 ), pp. 311 – 319 .
   Web of Science ®Google Scholar
• Goodman , I. R. [ 1994 ], “ New Characterization of Fuzzy Logic Operators Producing Homomorphic-Like Relations with One-Point Coverages of Random Sets .” In Advances in Fuzzy Theory and Technology , edited by P. P. Wang , Bookwrighls Press , Raleigh NC , pp. 133 – 159 .
   Google Scholar
• Halmos , P. R. [ 1950 ], Measure Theory , van Nostrand , New York
   Google Scholar
• Janssen , Hugo , J. Gert de Cooman , and E. E. Kerre [ 1996 ], “ First Results for a Mathemalical Theory of Possibilistic Processes .” In Proc. 1996 European Meeting on Cybernetics and Systems Research , edited by R.Trappi , pp. 341 – 346 .
   Google Scholar
• Joslyn , Clifr [ 1992 ], “ Possibilistic Measurement and Set Statistics ,” In Proc. NAFIPS1992 , v. 2 , Puerto Vallerta , pp. 458 – 467 .
   Google Scholar
• Joslyn , Cliff [ 1993a ], “ Empirical Possibility and Minimal Information Distortion .” In Fuzzy Logic State of the Art . edited by R. Lowen and M. Roubens , Kluwer , Dordrecht , pp. 143 – 152 .
   Google Scholar
• Joslyn , Cliff [ 1993b ], “ Some New Results on Possibilistic Measurement .” In Proc. NAFIPS 1993 , Allentown PA , pp. 227 – 231 . To be reprinted in Fuzziness An Introduction to Theory and Applications, edited by M. Mcallister, SIAM Press.
   Google Scholar
• Joslyn , Cliff [ 1993c ], “ Possibilistic Semantics and Measurement Methods in Complex Systems .” In Proc. 2nd International Symposium on Uncertainty Modeling and Analysis , editted by Bilal Ayyub , IEEE Computer Society Press , pp. 208 – 215 .
   Google Scholar
• Joslyn , Cliff [ 1994a ], Possibilistic Processes for Complex Systems Modeling . UMI Disseration Services, Ann Arbor MI ( PhD dissertation , SUNY - Binghamton ).
   Google Scholar
• Joslyn , Cliff [ 1994b ], “ Possibilistic Approach to Qualitative Model-Based Diagnosis .” Telematics and Informatics . 11 ( 4 ). pp. 365 – 384 .
   Google Scholar
• Joslyn , Cliff [ 1994c ], “ On Possibilistic Automata .” In Computer Aided Systems Theory-EUROCAST 93 , edited by F. Pichlcr and R. Moreno-Didz , Springer-Verlag , Berlin , pp. 231 – 242 .
   Google Scholar
• Joslyn , Cliff [1995a], “ In Support of an Independent Possibility Theory .” In Foundations and Applications of Possibility Theory , edited by G. de Cooman, D. Ruan and E. E. Kerre , World Scientific , Singapore , pp. 152 – 164 .
   Google Scholar
• Joslyn . Cliff [ 1995b ], “ Strong Probabilistic Compatibility of Possibilistic Histograms .” In Proc. 1995 Int. Symposium on Uncertainty Modeling and Analysis , edited by Bilal Ayyub , IEEE Computer Society Press , Los Alamitos CA , pp. 383 , A17 – 22 .
   Google Scholar
• Joslyn , Cliff [ 1995c ], “ Semantic Control Systems .” World Futures , 45 , pp. 87 – 123 .
   Google Scholar
• Kendall , D. G. [ 1974 ], “ Foundations of a Theory of Random Sets .” In Stochastic Geometry , edited by E. F. Harding and D. G. Kendall , Wiley . New York , pp. 322 – 376 .
   Google Scholar
• Klir , George [ 1991 ], “ Generalized Informalion Theory .” Fuzzy Sets and Systems , 40 , pp. 127 – 142 .
   Web of Science ®Google Scholar
• Klir , George [ 1993 ], “ Developments in Uncertainty Based Information .” In Advances in Computers , v. 36 , edited by M. Yovitz , Academic Press , pp. 255 – 332 .
   Google Scholar
• Klir , George and Behzad Parviz [ 1992 ], “ Possibility-Probability Conversions An Empirical Study .” In Progress in Cybernetics and Systems , edited by R. Trappi , Hemisphere , New York , pp. 19 – 26 .
   Google Scholar
• Klir , George Bo Yuan [ 1995 ], Fuzzy Sets and Fuzzy Logic . Prentice-Hall , Upper Saddle River , N.J .
   Google Scholar
• Krishnapuram , Raghu , James Keller [ 1993 ], “ Possibilistic Approach to Clustering .”' IEEE Trans, on Fuzzy Systems , 1 ( 2 ), pp. 98 – 110 .
   Google Scholar
• Pawlak , Zdzislaw [ 1991 ], Rough Sets Theoretical Aspects of Reasoning about Data . Kluwer , Boston .
   Google Scholar
• lsn , Robert [ 1985 ], Anticipatory Systems . Pergamon , Oxford .
   Google Scholar
• Shafer , Glen [ 1976 ], Mathematical Theory of Evidence . Princeton University Press , Princeton .
   Google Scholar
• Tanaka , Hideo and Hisao Ishibuchi [ 1993 ], “ Evidence Theory of Exponential Possibility Distribution .” Int. J. Approximate Reasoning , 8 , pp. 123 – 140 .
   Google Scholar
• Walley , P. [ 1990 ], Statistical Reasoning with Imprecise Probabilities . Chapman and Hall , New York .
   Google Scholar
• Wang , P. Z. and X. H. Liu [ 1984 ], “ Set-Valued Statistics .” J. Engineering Mathematics , 1 ( 1 ), pp. 43 – 54 .
   Google Scholar
• Wang , P. Z. , X. H. Liu and E. Sanchez [ 1986 ], “ Set-Valued Statistics and its Application to Earthquake Engineering .” Fuzzy Sets and Systems , 18 , pp. 347 – 356 .
   Google Scholar
• Wang , Zhenyuan and George Klir [ 1992 ], Fuzzy Measure Theory . Plenum Press , New York .
   Google Scholar
• Cliff Joslyn received his B.A. in Cognitive Science and Mathematics from Oberlin College in 1985, with High Honors in Systems Theory, and hi-; M.S. in 1989 and Ph.D. in 1994, both in Systems Science from the State University of New York at Binghamton. In his dissertation he developed the semantic and mathematical basis for possibilistic measurement and modeling. He is currently a Postdoctoral Scientist at the Los Alamos National Laboratory, where he pursues research on data mining and data fusion using possibilistic and fuzzy systems theory. His research interests include Systems Science, General Information Theory (GIT), qualitative modeling, Soft Methods for Discrete EVent Systems (DEVS) modeling, Computer-Aided Systems Theory (CAST), biological semiotics, cybernetic philosophy, and distributed hypertext development environments.
   Google Scholar