On the Relationship Between the Quantifier Threshold and OWA Operators
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.
KeywordsPiecewise Linear Aggregation Operator Ordered Weight Average Ordered Weight Average Operator Ordered Weight Average
Unable to display preview. Download preview PDF.
- 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.Filev, D.P., Yager, R.R.: Analytic Properties of Maximum Entropy OWA Operators. Information Sciences, 11–27 (1995)Google Scholar
- 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