[go: up one dir, main page]
Skip to main content
Springer Nature Link
Log in

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

  • Contributed Papers
  • Published:
Journal of Optimization Theory and Applications Aims and scope Submit manuscript

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.

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

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Bellman, R., Kalaba, R., andZadeh, L.,Abstraction and Pattern Classification, Journal of Mathematical Analysis and Applications, Vol. 13, pp. 1–7, 1966.

    Google Scholar 

  2. Saaty, T. L.,A Scaling Method for Priorities in Hierarchical Structures, Journal of Mathematical Psychology, Vol. 15, No. 3, 1977.

  3. Saaty, T. L.,Modeling Unstructured Decision Problems. The Theory of Analytical Hierarchies, Proceedings of the First International Conference on Mathematical Modeling, Vol. 1, University of Missouri, Rolla, Missouri, 1977.

    Google Scholar 

  4. Kalaba, R., andSpingarn, K.,Numerical Approaches to the Eigenvalues of Saaty's Matrices for Fuzzy Sets, Computers and Mathematics with Applications (to appear).

  5. Chu, A. T. W.,Fuzzy Sets in Economics, MS Thesis, Department of Economics, University of Southern California, Los Angeles, California, 1978.

    Google Scholar 

  6. Ministry of Economic Affairs,Taiwan Exports, 1976–77 Foreign Trade Development of the Republic of China, Taiwan, Republic of China, 1977.

Download references

Author information

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
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. R. E. Kalaba
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. K. Spingarn
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

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

Rights and permissions

Reprints and permissions

About this article

Cite this article

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

Download citation

  • Issue Date:

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

Key Words