Skip to main content
SpringerLink
Log in

A Survey of Some Quantitative Approaches to the Notion of Information

  • Chapter
  • First Online:
Formal and Natural Computing

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2300))

Abstract

We survey some formalizations of the intuitive notion of information which have been formulated in different mathematical and conceptual frames. The existence of different formalizations reflects the different aspects of the notion of information which are strongly related to the mechanisms of information processing of the receiver. Finally, some considerations and remarks on information in Physics and Biology are made.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Alsina, C., Trillas, E.: Sur les mesures du degré de flou. Stocastica 3 (1979) 81–84

    MATH  MathSciNet  Google Scholar 

  2. Backer, E.: A Non Statistical Type of Uncertainty in Fuzzy Events, in: Topics in Information Theory, Colloquia Mathematica Societatis Janos Bolyai, vol. 16, pp. 53–73. Amsterdam: North-Holland 1977

    Google Scholar 

  3. Bedrosian, S.D., Xie, W.X.: An Information Measure for Fuzzy Sets. IEEE Transactions on Systems, Man, and Cybernetics 14 (1984) 151–156

    MathSciNet  Google Scholar 

  4. Blum, M.: A Machine Independent Theory of the Complexity of Recursive Functions. J. of ACM 14 (1967) 322–336

    Article  MATH  MathSciNet  Google Scholar 

  5. Boltzmann, L.: Vorlesungen über Gas Theorie, vol.1. J. A. Barth Leipzig, 1896, English Transl. Lectures on Gas Theory. Berkeley Calif. 1964

    Google Scholar 

  6. Brillouin, L.: La Science et La Théorie de l’Information. Paris: Masson 1959

    Google Scholar 

  7. Capocelli, R., de Luca, A.: Fuzzy Sets and Decision Theory. Information and Control 23 (1973) 446–473

    Article  MathSciNet  MATH  Google Scholar 

  8. Carnap, R., Bar-Hillel, Y.: An Outline of a Theory of Semantic Information. Tech. Rep. 247, M.I.T., Research Laboratory of Electronics, 1952, Reprinted in Bar-Hillel, Y.: Language and Information. Reading, MA: Addison Wesley 1962

    Google Scholar 

  9. Carpi, A., de Luca, A.: Words and Special Factors. Theoretical Computer Science 259 (2001) 145–182

    Article  MATH  MathSciNet  Google Scholar 

  10. Carpi, A., de Luca, A.: Words and Repeated Factors. Séminaire Lotharingien de Combinatoire B42l (1998) 24 pp. and in: Foata, D., Han, G. (Eds.) Andrews Festschrift, pp. 231–251. Berlin: Springer 2001

    Google Scholar 

  11. Carpi, A., de Luca, A.: Repetitions and Boxes in Words and Pictures, in: Karhumäki, J., Maurer, H., Păun, G., Rozenberg, G. (Eds.) Jewels Are Forever, pp. 295–306. Berlin: Springer 1999

    Google Scholar 

  12. Carpi, A., de Luca, A.: Special Factors, Periodicity, and an Application to Sturmian Words. Acta Informatica 36 (2000) 983–1006

    Article  MATH  MathSciNet  Google Scholar 

  13. Carpi, A., de Luca, A.: Periodic-like Words, Periodicity, and Boxes. Acta Informatica 37 (2001) 597–618

    Article  MATH  MathSciNet  Google Scholar 

  14. Carpi, A., de Luca, A., Varricchio, S.: Special Factors and Uniqueness Conditions in Rational Trees. Theory of Computing Systems (to appear)

    Google Scholar 

  15. Carpi, A., de Luca, A., Varricchio, S.: Words, Univalent Factors, and Boxes. Preprint 41/2000, Dipartimento di Matematica dell’Università di Roma ‘La Sapienza’, 2000

    Google Scholar 

  16. Chaitin, G.J.: On the Length of Programs for Computing Finite Binary Sequences. J. of ACM 13 (1966) 547–569

    Article  MATH  MathSciNet  Google Scholar 

  17. Chaitin, G.J.: Information-Theoretic Computational Complexity. IEEE Trans. on Information Theory 20 (1974) 10–15

    Article  MATH  MathSciNet  Google Scholar 

  18. Colosimo, A., de Luca, A.: Special Factors in Biological Strings. J. Theor. Biol. 204 (2000) 29–46

    Article  Google Scholar 

  19. Davis, M.: Computability and Unsolvability. New York: McGraw Hill 1958

    MATH  Google Scholar 

  20. de Luca, A.: Complexity and Information Theory, in: Longo, G. (Ed.) Coding and Complexity, CISM Courses and Lectures No. 216, pp. 207–270. Wien: Springer 1975

    Google Scholar 

  21. de Luca, A.: On the Entropy of a Formal Languages, Lecture Notes in Computer Science, vol. 33, pp. 103–109. Berlin: Springer 1975

    Google Scholar 

  22. de Luca, A.: The Mind as a Mechanism of the Brain. (1982) (manuscript)

    Google Scholar 

  23. de Luca, A.: Dispersion Measures of Fuzzy Sets, in: Gupta, M.M., Kandel, A., Bandler, W., Kiszka, J.B. (Eds.) Approximate Reasoning in Expert Systems, pp. 199–216. Amsterdam: North-Holland 1985

    Google Scholar 

  24. de Luca, A.: On the Combinatorics of FiniteWords. Theoretical Computer Science 218 (1999) 13–39

    Article  MATH  MathSciNet  Google Scholar 

  25. de Luca, A., Fischetti, E.: Outline of a New Logical Approach to Information Theory, in Caianiello, E.R. (Ed.) New Concepts and Technologies in Parallel Processing, Nato Advanced Study Institutes Series, Series E: Applied Sciences-No.9, pp. 359–380. Leyden: Noordho. International Publ. 1975

    Google Scholar 

  26. de Luca, A., Termini, S.: A Definition of a Non-probabilistic Entropy in the Setting of Fuzzy Sets Theory. Information and Control 20 (1972) 301–312

    Article  MathSciNet  MATH  Google Scholar 

  27. de Luca, A., Termini, S.: Algebraic Properties of Fuzzy Sets. J. Math. Anal. Appl. 40 (1972) 373–386

    Article  MathSciNet  Google Scholar 

  28. de Luca, A., Termini, S.: Entropy of L-fuzzy Sets. Information and Control 24 (1974) 55–73

    Article  MathSciNet  MATH  Google Scholar 

  29. de Luca, A., Termini, S.: Entropy and Energy Measures of a Fuzzy Set, in: Gupta, M.M., Ragade, R.K., Yager, R.R. (Eds.) Advances in Fuzzy Set Theory and Applications, pp. 321–338. Amsterdam: North-Holland 1979

    Google Scholar 

  30. de Luca, A., Termini, S.: Superposition Sets and Their Entropies, Proc. s IEEE Int. Conf. on Systems, Man and Cybernetics, Delhi/Bombay, India, pp. 493–497. New York: IEEE 1983

    Google Scholar 

  31. de Luca, A., Termini, S.: Entropy Measures in the Theory of Fuzzy Sets, in Singh, M.G. (Ed.) Encyclopedia of Systems and Control, pp. 1467–1473. Oxford: Pergamon-Press 1983

    Google Scholar 

  32. Ebanks, B.R.: On Measures of Fuzziness and Their Representations. J. Math. Anal. Appl. 94 (1983) 24–37

    Article  MATH  MathSciNet  Google Scholar 

  33. Hartley, R.V.L.: Transmission of Information. Bell Syst. Tech. J. 7 (1928) 535–563

    Google Scholar 

  34. Khinchin, A.I.: Mathematical Foundations of Information Theory. New York: Dover Publ. 1957

    MATH  Google Scholar 

  35. Klir, G.J. (Ed.): Measures of Uncertainty. Fuzzy Sets and Systems (Special Issue) 24 (1987) n.2

    Google Scholar 

  36. Knopfmacher, J.: On Measures of Fuzziness. J. Math. Anal. Appl. 49 (1975) 529–534

    Article  MATH  MathSciNet  Google Scholar 

  37. Kolmogorov, A.N.: Three Approaches to the Quantitative Definition of Information. Problemi Peredachi Informatsii 1 (1965) 3–11

    MathSciNet  MATH  Google Scholar 

  38. Li, M., Vitanyi, P.: An Introduction to Kolmogorov Complexity and Its Applications. Berlin: Springer 1993

    MATH  Google Scholar 

  39. Lothaire, M.: Combinatorics on Words. Reading, MA: Addison-Wesley 1983

    MATH  Google Scholar 

  40. Lothaire, M.: Algebraic Combinatorics on Words. Cambridge: Cambridge University Press (to appear)

    Google Scholar 

  41. Martin-Löf, P.: The Definition of Random Sequences. Information and Control 9 (1966) 602–619

    Article  MathSciNet  Google Scholar 

  42. Nyquist, H.: Certain Factors Affecting Telegraph Speed. Bell Syst. Tech. J. 3 (1924) 324

    Google Scholar 

  43. Pal, S.K.: A Note on the Quantitative Measure of Image Enhancement Through Fuzziness. IEEE Trans. on Pattern Analysis and Machine Intelligence 4 (1982) 204–208

    Article  MATH  Google Scholar 

  44. Papadimitriou, C.H.: Computational Complexity. Reading MA: Addison-Wesley 1994

    MATH  Google Scholar 

  45. Shannon, C.E.: A Mathematical Theory of Communication. Bell Syst. Tech. J. 27 (1948) 379–423, 623–656

    MathSciNet  MATH  Google Scholar 

  46. Shannon C.E., Weaver, W.: The Mathematical Theory of Communication. Urbana ILL: University of Illinois Press 1949

    MATH  Google Scholar 

  47. Shimizu, A.: Approximate Reasoning Based on Fuzzy Entropy’s Theory, in: Piera Carreté, N., Singh, M.G. (Eds.) Qualitative Reasoning and Decision Technologies, pp. 662–671. Barcelona: CIMNE 1983

    Google Scholar 

  48. Solomonov, R.J.: A Formal Theory of Inductive Inference. Part I. Information and Control 7 (1964) 1–22

    Article  MathSciNet  Google Scholar 

  49. Szilard, L.: Über die Entropieverminderung in einem thermodynamischen System bei Eingriffen intelligenter Wesen. Zeitschrift f. Physik 53 (1929) 840–856, Reprinted: On Decrease of Entropy in Thermodynamic System by the Intervention of Intelligent Beings. Behavioral Science 9 (1964) 301–310

    Article  Google Scholar 

  50. Taneja, I.J.: On Generalized Entropies with Applications, in Ricciardi, L.M. (Ed.) Lectures in Applied Mathematics and Informatics, pp. 107–169. Manchester: Manchester University Press 1990

    Google Scholar 

  51. Trillas, E., Riera, T.: Entropies in Finite Fuzzy Sets. Information Sciences 15 (1978) 159–168

    Article  MATH  MathSciNet  Google Scholar 

  52. Wiener, N.: The Extrapolation, Interpolation and Smoothing of Stationary Time Series. New York: J. Wiley and Sons 1949

    Google Scholar 

  53. Zadeh, L.A.: Fuzzy Sets. Information and Control 8 (1965) 338–353

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Dipartimento di Matematica dell’Università di Roma “La Sapienza”, Piazzale A. Moro 2, 00185, Roma, Italy

    Aldo de Luca

  2. Centro Interdisciplinare ‘B. Segre’, Accademia dei Lincei, via della Lungara 10, 00100, Roma, Italy

    Aldo de Luca

Authors
  1. Aldo de Luca
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Computer Science Department, Technical University of Munich, Arcisstraße 21, 80333, Munich, Germany

    Wilfried Brauer

  2. Computer Science Department, Technical University of Berlin, Franklinstraße 28/29, 10587, Berlin, Germany

    Hartmut Ehrig

  3. Department of Mathematics, University of Turku, 20014, Turku, Finland

    Juhani Karhumäki

  4. Turku Centre for Computer Science, Lemminkäisenkatu 14A, 20520, Turku, Finland

    Arto Salomaa

Rights and permissions

Reprints and permissions

Copyright information

© 2002 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

de Luca, A. (2002). A Survey of Some Quantitative Approaches to the Notion of Information. In: Brauer, W., Ehrig, H., Karhumäki, J., Salomaa, A. (eds) Formal and Natural Computing. Lecture Notes in Computer Science, vol 2300. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45711-9_6

Download citation

  • DOI: https://doi.org/10.1007/3-540-45711-9_6

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-43190-9

  • Online ISBN: 978-3-540-45711-4

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation