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2017 | OriginalPaper | Chapter

A Method of Introducing Weights into OWA Operators and Other Symmetric Functions

Author : Gleb Beliakov

Published in: Uncertainty Modeling

Publisher: Springer International Publishing

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Abstract

This paper proposes a new way of introducing weights into OWA functions which are popular in fuzzy systems modelling. The proposed method is based on replicating the inputs of OWA the desired number of times (which reflect the importances of the inputs), and then using a pruned n-ary tree construction to calculate the weighted OWA. It is shown that this tree-based construction preserves many useful properties of the OWA, and in fact produces the discrete Choquet integral. A computationally efficient algorithm is provided. The tree-based construction is universal in its applicability to arbitrary symmetric idempotent n-ary functions such as OWA, and transparent in its handling the weighting vectors. It will be a valuable tool for decision making systems in the presence of uncertainty and for weighted compensative logic.

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Literature
1.
G. Beliakov. Shape preserving splines in constructing WOWA operators: Comment on paper by V. Torra in Fuzzy Sets and Systems 113 (2000) 389–396. Fuzzy Sets and Systems, 121:549–550, 2001.
2.
G. Beliakov and J.J. Dujmovic. Extension of bivariate means to weighted means of several arguments by using binary trees. Information Sciences 331:137–147, 2016.
3.
G. Beliakov, S. James, and G. Li. Learning Choquet-integral-based metrics for semisupervised clustering. IEEE Trans. on Fuzzy Systems, 19:562–574, 2011.CrossRef
4.
G. Beliakov, A. Pradera, and T. Calvo. Aggregation Functions: A Guide for Practitioners, volume 221 of Studies in Fuzziness and Soft Computing. Springer-Verlag, Berlin, 2007.
5.
6.
T. Calvo, R. Mesiar, and R.R. Yager. Quantitative weights and aggregation. IEEE Trans. on Fuzzy Systems, 12:62–69, 2004.CrossRef
7.
B. De Baets and J. Fodor. Van Melle’s combining function in MYCIN is a representable uninorm: An alternative proof. Fuzzy Sets and Systems, 104:133–136, 1999.MathSciNetCrossRefMATH
8.
J.J. Dujmovic. Continuous preference logic for system evaluation. IEEE Trans. on Fuzzy Systems, 15:1082–1099, 2007.CrossRef
9.
J.J. Dujmovic. An efficient algorithm for general weighted aggregation. In Proc. of the 8th AGOP Summer School, Katowice, Poland, 2015.
10.
J.J. Dujmovic. Weighted compensative logic with adjustable threshold andness and orness. IEEE Trans. on Fuzzy Systems, 23:270–290, 2015.CrossRef
11.
J.J. Dujmovic and G. Beliakov. Idempotent weighted aggregation based on binary aggregation trees. International Journal of Intelligent Systems, 32:31–50, 2017.
12.
J.J. Dujmovic and H.L. Larsen. Generalized conjunction/disjunction. Int. J. Approx. Reasoning, 46:423–446, 2007.CrossRef
13.
A. Emrouznejad and M. Marra. Ordered weighted averaging operators 1988-2014: A citation-based literature survey. Int. J. Intelligent Systems, 29:994–1014, 2014.CrossRef
14.
M. Grabisch, J.-L. Marichal, R. Mesiar, and E. Pap. Aggregation Functions. Encyclopedia of Mathematics and Its Foundations. Cambridge University Press, 2009.CrossRefMATH
15.
M. Grabisch, T. Murofushi, and M. Sugeno, editors. Fuzzy Measures and Integrals. Theory and Applications. Physica – Verlag, Heidelberg, 2000.MATH
16.
F. Herrera and E. Herrera-Viedma. A study of the origin and uses of the Ordered Weighted Geometric operator in multicriteria decision making. Int. J. Intelligent Systems, 18:689–707, 2003.CrossRefMATH
17.
18.
Y. Narukawa and V. Torra. Fuzzy measure and probability distributions: Distorted probabilities. IEEE Trans. on Fuzzy Systems, 13:617–629, 2005.CrossRef
19.
U. Thole, H.-J. Zimmermann, and P. Zysno. On the suitability of minimum and product operators for the intersection of fuzzy sets. Fuzzy Sets and Systems, 2:167–180, 1979.CrossRefMATH
20.
21.
V. Torra. The WOWA operator and the interpolation function W*: Chen and Otto’s interpolation revisited. Fuzzy Sets and Systems, 113:389–396, 2000.MathSciNetCrossRefMATH
22.
Z.S. Xu and Q.L. Da. The ordered weighted geometric averaging operator. Int. J. Intelligent Systems, 17:709–716, 2002.CrossRefMATH
23.
R. R. Yager. Norms induced from OWA operators. IEEE Trans. on Fuzzy Systems, 18(1):57–66, 2010.CrossRef
24.
R.R. Yager. On ordered weighted averaging aggregation operators in multicriteria decision making. IEEE Trans. on Systems, Man and Cybernetics, 18:183–190, 1988.
25.
R.R. Yager. Including importances in OWA aggregations using fuzzy systems modeling. IEEE Trans. on Fuzzy Systems, 6:286–294, 1998.CrossRef
26.
27.
28.
R.R. Yager and J. Kacprzyk, editors. The Ordered Weighted Averaging Operators. Theory and Applications. Kluwer, Boston, 1997.MATH
29.
R.R. Yager, J. Kacprzyk, and G. Beliakov, editors. Recent Developments in the Ordered Weighted Averaging Operators: Theory and Practice. Springer, Berlin, New York, 2011.
30.
31.
H.-J. Zimmermann and P. Zysno. Latent connectives in human decision making. Fuzzy Sets and Systems, 4:37–51, 1980.CrossRefMATH
Metadata
Title
A Method of Introducing Weights into OWA Operators and Other Symmetric Functions
Author
Gleb Beliakov
Copyright Year
2017
Book
Uncertainty Modeling

Print ISBN: 978-3-319-51051-4

Electronic ISBN: 978-3-319-51052-1

Copyright Year: 2017

DOI
https://doi.org/10.1007/978-3-319-51052-1_3

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