RENYI ENTROPY OF MAPS: APPLICATIONS TO FUZZY SETS. PATTERN RECOGNITION, AND CHAOTIC DYNAMICS

REFERENCES

• Aczel , J. , and Daroczy , Z. , On Measures of Information and their Characterizations , Academic Press , New York , 1975 .
   Google Scholar
• Campbell , L. L. A coding theorem and Renyi's entropy . Information and Control , Vol 8 , pp. 423 – 429 , 1965 .
   Google Scholar
• De Luca , A. , and Termini , S. , A definition of a nonprobabilistic entropy in the setting of fuzzy set theory . Information and Control , Vol 20 , pp. 301 – 312 , 1972 .
   Google Scholar
• Higashi , H. , and Klir , G. , Measures of uncertainty and information based on possibility distribution ; Int. J. General Systems , Vol 9 , pp. 43 – 58 , 1982 .
   Web of Science ®Google Scholar
• Hirota , K. , Ambiguity based on the concept of subjective entropy ; in Fuzzy Information and Decision Processes , et al. (eds), North-Holland , Amsterdam , pp. 29 – 40 , 1982 .
   Google Scholar
• Jumarie , G. , New results in the information theory of patterns and forms . J. Syst. Analysis, Modelling, Simulation , Vol 4 , No. 6 , pp. 483 – 521 , 1987 .
   Web of Science ®Google Scholar
• Jumarie , G. , Transinformation of order s and Shannon entropy of order s of R 2 → R maps. Two new applications of Renyi entropy ; in Cybernetics and Systems , R. Trappl (edt.), Reidel , Dordrecht , pp. 31 – 37 , 1988 .
   Google Scholar
• Jumarie , G. , Relative Information. Theories and Applications , Springer Verlag , New york , Berlin , ( in the press ), 1988 .
   Google Scholar
• Jumarie , G. , A Minkowskian thiery of observation. Applications to uncertainty and fuzziness . Fuzzy Sets and Systems , Vol 24 , No 2 , pp. 231 – 254 , 1987 .
   Web of Science ®Google Scholar
• Kullback , S. , Information Theory and Statistics . John Wiley , New York , 1959 .
   Google Scholar
• Renyi , A. , Probability Theory , North-Holland , Amsterdam , 1970 .
   Google Scholar
• Schuster , H. G. , Deterministic Chaos , Physik-Verlag GmbH , Weinheim , 1984 .
   Google Scholar
• Zadeh , L. A. , Probability measures of fuzzy events . J. Math. Anal. Applications , Vol 23 , pp. 421 – 427 , 1968 .
   Web of Science ®Google Scholar