On the Relationship Between the Quantifier Threshold and OWA Operators

  • Luigi Troiano
  • Ronald R. Yager
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3885)


The OWA weighting vector and the fuzzy quantifiers are strictly related. An intuitive way for shaping a monotonic quantifier, is by means of the threshold that makes a separation between the regions of what is satisfactory and what is not. Therefore, the characteristics of a threshold can be directly related to the OWA weighting vector and to its metrics: the attitudinal character and the entropy (or dispersion). Generally these two metrics are supposed to be independent, although some limitations in their value come when they are considered jointly. In this paper we argue that these two metrics are strongly related by the definition of quantifier threshold, and we show how they can be used jointly to verify and validate a quantifier and its threshold.


Piecewise Linear Aggregation Operator Ordered Weight Average Ordered Weight Average Operator Ordered Weight Average 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Yager, R.R.: On ordered weighted averaging aggregation operators in multi-criteria decision making. IEEE Trans. on Systems, Man, and Cybernetics 18, 183–190 (1988)MathSciNetCrossRefzbMATHGoogle Scholar
  2. 2.
    Yager, R.R.: Measures of entropy and fuzziness related to aggregation operators. Information Sciences 82, 147–166 (1995)MathSciNetCrossRefzbMATHGoogle Scholar
  3. 3.
    O’Hagan, M.: Aggregating template rule antecedents in real-time expert systems with fuzzy set logic. In: 22th Annual IEEE Asilomar Conference on Signals, Systems and Computers, Pacific Grove, CA (1988)Google Scholar
  4. 4.
    Filev, D.P., Yager, R.R.: Analytic Properties of Maximum Entropy OWA Operators. Information Sciences, 11–27 (1995)Google Scholar
  5. 5.
    Fullér, R., Majlender, P.: An analytic approach for obtaining maximal entropy OWA operator weights. Fuzzy Sets and Systems 124, 53–57 (2001)MathSciNetCrossRefzbMATHGoogle Scholar
  6. 6.
    Troiano, L., Yager, R.R.: A meaure of dispersion for OWA operators. In: Liu, Y., Chen, G., Ying, M. (eds.) Proceedings of the Eleventh International Fuzzy systems Association World Congress, Beijing, China, pp. 82–87. Tsinghua University Press and Springer (2005) ISBN 7-302-11377-7Google Scholar
  7. 7.
    Yager, R.R.: Quantifier guided aggregation using OWA operators. International Journal of Intelligent Systems 11, 49–73 (1996)CrossRefGoogle Scholar
  8. 8.
    Yager, R.R.: Families of OWA operators. Fuzzy Sets and Systems 57, 125–148 (1993)MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Luigi Troiano
    • 1
  • Ronald R. Yager
    • 2
  1. 1.RCOSTUniversity of SannioBeneventoItaly
  2. 2.Machine Intelligence InstituteIONA CollegeNew RochelleUSA

Personalised recommendations