Abstract
The basic operations for combining real values are the weighted mean (WM) and the Ordered Weighted Averaging (OWA) operator. The weighted mean allows the system to compute an aggregate value from the ones coming from several sources, taking into account the reliability of each information source. Alternatively, the OWA operator allows the user to weight the values supplied in relation to their alternative ordering. The Weighted OWA operator (WOWA) allows the user to consider both aspects using two sets of weights. In this chapter we describe an extension of the WOWA operator to the continuous case after arguing its convenience. Then, we analyze the use of this operator for defuzzification.
This is a revised and expanded version of two previous papers of the same authors: “Averaging continuous distributions with the WOWA operator” in Proc. of EFDAN’97, Dortmund (Germany) pp. 10–19.; and “On defuzzification with continuous WOWA operators” in Proc. of ESTYLF’97, Tarragona (Spain), pp. 227–232.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
Abidi M.A. (1992) Fusion of Multi-dimensional Data Using Regulation, in M.A. Abidi, R.C. Gonzalez (eds.), Data Fusion In Robotics and Machine Intelligence, Academic Press, U.K., pp. 415–455.
Aczél J. (1984) On weighted synthesis of judgements, Aequationes Math., 27, 288–307.
Alsina C., Mayor G., Tomas M.S., Torrens J. (1993) A characterization of a class of aggregation functions, Fuzzy Sets and Systems, 53, pp. 33–38.
Calvo T., Kolesarova A., Komornikova M., Mesiar R. (2001) Aggregation operators: properties, classes and construction methods. Chapter in this monograph.
Chen J.E., Otto K.N. (1995) Constructing membership functions using interpolation and measurement theory, Fuzzy Sets and Systems, 73: 3, pp. 313–327.
Detyniecki M., Yager R. R. (2000) Ranking fuzzy numbers using a-weighted valuations, Int. J. of Unc., Fuzziness and Knowledge-Based Systems, 8: 5 573591.
Driankov D., Hellendoorn H., Reifrank M. (1993) An introduction to Fuzzy Control. Springer Verlag.
Dubois D., Fargier H., Prade H. (1996) Possibility theory in constraint satisfaction problems: Handling priority, preference and uncertainty. Applied Intelligence, 6, pp. 287–309.
Filev D., Yager R.R. (1991) A generalized defuzzification method under BADD distributions, Intl. Journal of Intelligent Systems 6, pp. 687–697.
Fodor J., Marichal J L, Roubens M. (1995) Characterization of Ordered Weighted Averaging Operators, IEEE Trans. of Fuzzy Systems, 3:2, pp. 236240.
Grabisch M. (1995) Fuzzy integral in multicriteria decision making, Fuzzy Sets and Systems, 69, pp. 279–298.
Genest C., Zidek J.V. (1986) Combining Probability Distributions: A Critique and An Annotated Bibliography, Statistical Science, 1: 1, pp. 114–148.
Klir G.J., Yuan B. (1995) Fuzzy Sets and Fuzzy Logic, Prentice-Hall PTR.
Lopez B., Alvarez S., Millân P., Puig D., Riano D., Torra V. (1994) Multistage vision system for road lane markings and obstacle detection, Proceedings of Euriscon ‘84, Malaga, pp. 489–497.
Luo R.C., Kay M.G. (1992) Data Fusion and Sensor Integration: State-of-the-art 1990s, in M.A. Abidi, R.C. Gonzalez (eds.), Data Fusion In Robotics and Machine Intelligence, Academic Press, U.K., pp. 7–135.
Nelsen R.B. (1999) An Introduction to Copulas, Lecture Notes in Statistics 139, Springer, New York, 1999.
Nishiwaki Y., Preyssl C., Schmid S. (1994) Decision Making under uncertainty: Application of fuzzy logic to risk assessment abd nabagement of space systems, Proceedings of the Third International Conference on Fuzzy Logic, Neural Networks and Soft Computing, lizuka (Japan), pp. 263–264.
Rondeau L., Ruedas R., Levrat L., Lamotte L. (1997) A defuzzification method respecting the fuzzification, Fuzzy Sets and Systems, 86, pp. 311–320.
Sandri S.A., Dubois D, Kalfsbeek H. (1995) Elicitation, Assesment, and Pooling of Expert Judgements Using Possibility Theory, IEEE Trans. on Fuzzy Systems, 3: 3, pp. 313–335.
Slany W. (1996) Scheduling as a fuzzy multiple criteria optimization problem, Fuzzy Sets and Systems, 78, pp. 197–222.
Torra V. (1996) Weighted OWA operators for synthesis of information, Proc. of Fifth IEEE Int. Conference on Fuzzy Systems (IEEE-FUZZ’96), pp. 966–971, New Orleans, USA.
Torra V. (1997) The Weighted OWA operator, Int. J. of Intel. Systems, 12, pp. 153–166.
Torra V. (1998) On some relationships between the WOWA operator and the Choquet integral, Proceedings of the Seventh Conference on Information Processing and Management of Uncertainty in Knowledge-Based Systems (IPMU’98), 818–824, Paris, France.
Torra, V. (2000) The WOWA operator and the interpolation function W*: Chen and Otto’s interpolation method revisited, Fuzzy Sets and Systems, 113: 3, pp. 389–396.
Valente de Oliveira J. (1995) A set-theoretical defuzzification method. Fuzzy sets and systems, 76, pp. 63–71.
Yager R.R. (1988) On ordered weighted averaging aggregation operators in multi-criteria decision making, IEEE Trans. on SMC, 18, pp. 183–190.
Yager R.R. (1993) Families of OWA operators, Fuzzy Sets and Systems, 59, pp. 125–148.
Yager R.R. (1996) Quantifier Guided Aggregation Using OWA operators, Int. J. of Intel. Systems, 11, pp. 49–73.
Yager R.R. (1996) Knowledge-based defuzzification. Fuzzy Sets and Systems, 80, pp. 177–185
Yager R.R., Filev D.P. (1993) On the issue of defuzzification and selection based on a fuzzy set. Fuzzy Sets and Systems, 55, pp. 255–271.
Yager R.R., Filev D.P. (1994) Essentials of fuzzy modeling and control, John Wiley.
Zadeh L.A. (1978) PRUF–A meaning representation language for natural language, Intl. Journal of Man-Machine Studies, 10, pp. 395–460.
Zimmermann H J. (1991) Fuzzy Set Theory - and Its Applications, Kluwer, Dordrecht, 2nd revised edition.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2002 Physica-Verlag Heidelberg
About this chapter
Cite this chapter
Torra, V., Godo, L. (2002). Continuous WOWA Operators with Application to Defuzzification. In: Calvo, T., Mayor, G., Mesiar, R. (eds) Aggregation Operators. Studies in Fuzziness and Soft Computing, vol 97. Physica, Heidelberg. https://doi.org/10.1007/978-3-7908-1787-4_4
Download citation
DOI: https://doi.org/10.1007/978-3-7908-1787-4_4
Publisher Name: Physica, Heidelberg
Print ISBN: 978-3-662-00319-0
Online ISBN: 978-3-7908-1787-4
eBook Packages: Springer Book Archive