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A comparison of two methods for determining the weights of belonging to fuzzy sets

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Abstract

Saaty has solved a basic problem in fuzzy set theory using an eigenvector method to determine the weights of belonging of each member to the set. In this paper, a weighted least-square method is utilized to obtain the weights. This method has the advantage that it involves the solution of a set of simultaneous linear algebraic equations and is thus conceptually easier to understand than the eigenvector method. Examples are given for estimating the relative wealth of nations and the relative amount of foreign trade of nations. Numerical solutions are obtained using both the eigenvector method and the weighted least-square method, and the results are compared.

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References

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Authors and Affiliations

  1. Department of Economics, University of Southern California, Los Angeles, California

    A. T. W. Chu (Graduate Student) & R. E. Kalaba (Professor of Economics and Biomedical Engineering)

  2. Space and Communications Group, Hughes Aircraft Company, Los Angeles, California

    K. Spingarn (Senior Staff Engineer)

Authors
  1. A. T. W. Chu
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  2. R. E. Kalaba
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  3. K. Spingarn
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Additional information

Partial support of this research was provided by NIH Grant No. GM-23732.

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Chu, A.T.W., Kalaba, R.E. & Spingarn, K. A comparison of two methods for determining the weights of belonging to fuzzy sets. J Optim Theory Appl 27, 531–538 (1979). https://doi.org/10.1007/BF00933438

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  • DOI: https://doi.org/10.1007/BF00933438

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