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On characterizing features of OWA aggregation operators

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Abstract

We introduce the ordered weighted averaging (OWA) operator and emphasize how the choice of the weights, the weighting vector, allows us to implement different types of aggregation. We describe two important characterizing features associated with OWA weights. The first of these is the attitudinal character and the second is measure of dispersion. We discuss some methods for generating the weights and the role that these characterizing features can play in the determination of the OWA weights. We note that while in many cases these two features can help provide a clear distinction between different types of OWA operators there are some important cases in which these two characterizing features do not distinguish between OWA aggregations. In an attempt to address this we introduce a third characterizing feature associated with an OWA aggregation called the focus. We look at the calculation of this feature in a number of different situations.

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References

  • Beliakov, G. (2005). Learning weights in the generalized OWA operators. Fuzzy Optimization and Decision Making, 4, 119–130.

    Article  MATH  MathSciNet  Google Scholar 

  • DeLuca, A., & Termini, S. (1972). A definition of a non-probabilistic entropy in the setting of fuzzy sets. Information and Control, 20, 301–312.

    Article  MathSciNet  Google Scholar 

  • Fuller, R., & Majlender, P. (2003). On obtaining minimal variability OWA weights. Fuzzy Sets and Systems, 136, 203–215.

    Article  MATH  MathSciNet  Google Scholar 

  • Majlender, P. (2005). OWA operators with maximal Renya entropy. Fuzzy Sets and Systems, 155, 340–360.

    Article  MATH  MathSciNet  Google Scholar 

  • Merigó, J. M., & Gil-Lafuente, A. M. (2009). The induced generalized OWA operator. Information Sciences, 179, 729–741.

    Article  MATH  MathSciNet  Google Scholar 

  • Mitchell, H. B., & Estrakh, D. D. (1997). A modified OWA operator and its use in lossless DPCM image compression. International Journal of Uncertainty, Fuzziness and Knowledge Based Systems, 5, 429–436.

    Google Scholar 

  • O’Hagan, M. (1990). Using maximum entropy-ordered weighted averaging to construct a fuzzy neuron. In: Proceedings 24th annual IEEE Asilomar conference on signals, systems and computers, Pacific Grove, CA, pp. 618–623.

  • Troiano, L., & Yager, R. R. (2005). Recursive and iterative OWA operators. International Journal of Fuzziness, Uncertainty and Knowledge-Based Systems, 13, 579–599.

    Article  MATH  MathSciNet  Google Scholar 

  • Wang, Y. M., & Parkan, C. (2005). Minimax disparity approach for obtaining OWA operator weights. Information Sciences, 175, 20–29.

    Article  MATH  MathSciNet  Google Scholar 

  • Xu, Z. (2005). An overview of methods for determining OWA weights. International Journal of Intelligent Systems, 20, 843–865.

    Article  MATH  Google Scholar 

  • Yager, R. R. (1979). On the measure of fuzziness and negation part I: Membership in the unit interval. International Journal of General Systems, 5, 221–229.

    Article  MATH  MathSciNet  Google Scholar 

  • Yager, R. R. (1980). On the measure of fuzziness and negation part II: Lattices. Information and Control, 44, 236–260.

    Article  MATH  MathSciNet  Google Scholar 

  • Yager, R. R. (1988). On ordered weighted averaging aggregation operators in multi-criteria decision making. IEEE Transactions on Systems, Man and Cybernetics, 18, 183–190.

    Article  MATH  MathSciNet  Google Scholar 

  • Yager, R. R. (1996). Quantifier guided aggregation using OWA operators. International Journal of Intelligent Systems, 11, 49–73.

    Article  Google Scholar 

  • Yager, R. R. (1997). On the inclusion of importances in OWA aggregations. In R. R. Yager & J. Kacprzyk (Eds.), The ordered weighted averaging operators: Theory and applications (pp. 41–59). Norwell, MA: Kluwer.

    Chapter  Google Scholar 

  • Yager, R. R. (2004). Generalized OWA aggregation operators. Fuzzy Optimization and Decision Making, 3, 93–107.

    Article  MATH  MathSciNet  Google Scholar 

  • Yager, R. R. (2007). Using stress functions to obtain OWA operators. IEEE Transactions on Fuzzy Systems, 15, 1122–1129.

    Article  Google Scholar 

  • Yager, R. R. (2008). Time series smoothing and OWA aggregation. IEEE Transactions on Fuzzy Systems, 16, 994–1007.

    Article  Google Scholar 

  • Yager, R. R., & Kacprzyk, J. (1997). The ordered weighted averaging operators: Theory and applications. Norwell, MA: Kluwer.

    Book  Google Scholar 

  • Yager, R. R., & Filev, D. P. (1999). Induced ordered weighted averaging operators. IEEE Transaction on Systems, Man and Cybernetics, 29, 141–150.

    Article  Google Scholar 

  • Yager, R. R., Kacprzyk, J., & Beliakov, G. (2011). Recent developments in the ordered weighted averaging operators: Theory and practice. Berlin: Springer.

    Book  Google Scholar 

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Acknowledgments

This work has been supported by a Multidisciplinary University Research Initiative (MURI) Grant (Number W911NF-09-1-0392) US Army Research Office (ARO). This work has also been supported by an ONR Grant award. The authors would like to acknowledge the support from the Distinguished Scientist Fellowship Program at King Saud University.

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Authors and Affiliations

  1. Machine Intelligence Institute, Iona College, New Rochelle, NY, 10801, USA

    Ronald R. Yager

  2. Visiting Distinguished Scientist, King Saud University, Riyadh, Saudi Arabia

    Ronald R. Yager

  3. ALISR Laboratory, College of Computer and Information Sciences, King Saud University, P.O. Box 51178, Riyadh, 11543, Saudi Arabia

    Naif Alajlan

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  1. Ronald R. Yager
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  2. Naif Alajlan
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Correspondence to Ronald R. Yager.

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Yager, R.R., Alajlan, N. On characterizing features of OWA aggregation operators. Fuzzy Optim Decis Making 13, 1–32 (2014). https://doi.org/10.1007/s10700-013-9167-8

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  • DOI: https://doi.org/10.1007/s10700-013-9167-8

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