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Journal of Optical Technology

Journal of Optical Technology


  • Vol. 75, Iss. 4 — Apr. 1, 2008
  • pp: 242–246

Implementation of fuzzy logic with exclusions by the Fourier-holography method

A. M. Alekseev and A. V. Pavlov  »View Author Affiliations

Journal of Optical Technology, Vol. 75, Issue 4, pp. 242-246 (2008)

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In developing the biologically motivated approach proposed earlier to the implementation of logico-linguistic modeling by the method of Fourier holography, it was shown to be possible to implement logic with exclusions as a particular case of nonmonotonic logic. It was proposed to use one implication operator for both the premise and the exclusion by constructing linguistic scales for the premise and the exclusion with mutually inverse dependences of the value of the logical conclusion on the value of the input variable. Results are given for the numerical modelling of an example of the formation of a logical conclusion.

© 2008 Optical Society of America

A. M. Alekseev and A. V. Pavlov, "Implementation of fuzzy logic with exclusions by the Fourier-holography method," J. Opt. Technol. 75, 242-246 (2008)

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  1. K. Pribram, “Nonlocality and localization: The holographic hypothesis concerning the functioning of the brain in the process of perception and memory,” in Synergetics and Psychology, vol. 1, Metrological Questions (MGSU Soyuz, Moscow, 1997).
  2. K. V. Sudakov, “Holographic principle of systemic organization of the processes of vital activity,” Usp. Fiz. Nauk 28, 3 (1997).
  3. O. P. Kuznetsov, “Nonclassical paradigms in artificial intelligence,” Izv. Akad. Nauk Ser. Teoriya Sis. Uprav. No. 5, 3 (1995).
  4. H. Levesque, “All I Know: a study of autoepistemic logic,” Artif. Intell. 42, 263 (1990).
  5. L. Zade, “The concept of linguistic variable and its application to the making of approximate decisions,” Matematika. Novoe v zarubezhnoĭ Nauke 3 (1976).
  6. A. V. Pavlov, “Using the methods of Fourier holography to construct logic processors,” Opt. Zh. 69, No. 10, 42 (2002) A. V. Pavlov,[J. Opt. Technol. 69, 735 (2002)].
  7. A. V. Pavlov and Ya. Yu. Shevchenko, “Implementing a logical conclusion on linguistic scales by the method of Fourier holography,” Opt. Zh. 71, No. 7, 44 (2004) A. V. Pavlov and Ya. Yu. Shevchenko,[J. Opt. Technol. 71, 454 (2004)].
  8. A. M. Alekseev, A. M. Konstantinov, and A. V. Pavlov, “Using Fourier holography to model the principle of imagery of thought,” Opt. Zh. 73, No. 9, 77 (2006) A. M. Alekseev, A. M. Konstantinov, and A. V. Pavlov,[J. Opt. Technol. 73, 640 (2006)].
  9. G. Antoniou, Nonmonotonic Reasoning (MIT Press, Cambridge, Massachusetts, 1997).
  10. S. Benferhat, D. Dubois, and H. Prade, “Nonmonotonic reasoning, conditional objects and possibility theory,” Artif. Intell. 92, 259 (1997).
  11. T. Lukasiewicz, “Weak nonmonotonic probabilistic logics,” Artif. Intell. 168, 119 (2005). [CrossRef]
  12. “Eleventh international workshop on non-monotonic reasoning,” http://www.cs.ucl.ac.uk/staff/a.hunter/nmr/.
  13. M. M. Vin'kov and I. B. Fominykh, “Nonmonotonic reasoning in dynamic intelligent systems,” Novosti Iskusst. Intellekta No. 4, 12 (2005).
  14. S. V. Astanin and T. G. Kalashnikova, “Model of nonmonotonic reasoning based on fuzzy logic,” Izvestiya TrTU (Taganrog) No. 2, 81 (2000).
  15. S. Ishikawa, “Fuzzy inferences by algebraic method,” Fuzzy Sets and Systems 87, 181 (1997).
  16. S. Ishikawa, “A quantum mechanical approach to a fuzzy theory,” Fuzzy Sets and Systems 90, 277 (1997).
  17. S. Ishikawa, “Fuzzy logic in measurements,” Fuzzy Sets and Systems 100, 291 (1999).
  18. A. M. Kuleshov, S. A. Smaeva, and E. I. Shubnikov, “On optimality of a holographic matched filter,” Opt. Spektrosk. 60, 1273 (1986) A. M. Kuleshov, S. A. Smaeva, and E. I. Shubnikov,[Opt. Spectrosc. 60, 791 (1986)].

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