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Simplification of fuzzy switching functions

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Abstract

This paper is concerned with the study of simplification of fuzzy switching functions. A novel algorithm for generating all fuzzy prime implicants is introduced, followed by a new method of simplification of fuzzy switching functions. This algorithm is then reduced to a simple algorithm that produces only those fuzzy prime implicants that are essential. There areonly two other valid techniques for the minimization of fuzzy switching functions in the literature,(1,2) and those methods are not very suitable for computerized application. Thus, the principal advantages of this technique are the new concept of direct simplification via essential fuzzy prime implicants (without generation of all of the fuzzy prime implicants), and the fact that the algorithm is the first one to be suitable for efficient computer implementation.

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References

  1. F. P. Preparata and R. T. Yeh, “Continuously valued logic,”J. Comput. Syst. Sci. 6(5): 397–418 (1972).

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  2. A. Kandel, “On minimization of fuzzy functions,”IEEE Trans. Comput. C-22(9):826–832 (1973).

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  3. L. A. Zadeh, “Fuzzy sets,”Inf. Control 8:338–353 (1965).

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  4. A. Kandel, “A note on the simplification of fuzzy switching functions,”CSR 139, Computer Science Department, New Mexico Institute of Mining and Technology, Socorro, New Mexico (1975).

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Author notes

  1. Thomas P. Neff

    Present address: Computer Science Department, Cornell University, Ithaca, New York

Authors and Affiliations

  1. Computer Science Department, New Mexico Institute of Mining and Technology, Socorro, New Mexico

    Thomas P. Neff

  2. Electrical Engineering Department, Ben-Gurion University of the Negev, Beer-Sheva, Israel

    Abraham Kandel

Authors
  1. Thomas P. Neff
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  2. Abraham Kandel
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Additional information

On leave from the Computer Science Department, New Mexico Institute of Mining and Technology, Socorro, New Mexico.

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Neff, T.P., Kandel, A. Simplification of fuzzy switching functions. International Journal of Computer and Information Sciences 6, 55–70 (1977). https://doi.org/10.1007/BF00991483

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  • DOI: https://doi.org/10.1007/BF00991483

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