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WRAO and OWA learning using Levenberg–Marquardt and genetic algorithms

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Abstract

The generalized Weighted Relevance Aggregation Operator (WRAO) is a non-additive aggregation function. The Ordered Weighted Aggregation Operator (OWA) (or its generalized form: Generalized Ordered Weighted Aggregation Operator (GOWA)) is more restricted with the additivity constraint in its weights. In addition, it has an extra weights reordering step making it hard to learn automatically from data. Our intension here is to compare the efficiency (or effectiveness) of learning these two types of aggregation functions from empirical data. We employed two methods to learn WRAO and GOWA: Levenberg–Marquardt (LM) and a Genetic Algorithm (GA) based method. We use UCI (University of California Irvine) benchmark data to compare the aggregation performance of non-additive WRAO and additive GOWA. We found that the non-constrained aggregation function WRAO was learnt well automatically and produced consistent results, while GOWA was learnt less well and quite inconsistently.

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References

  1. Asuncion A, Newman D (2007) UCI machine learning repository. http://www.ics.uci.edu/~mlearn/MLRepository.html

  2. Beliakov G (2005) Learning weights in the generalized owa operators. Fuzzy Optim Decision Making 4(2): 119–130

    Article  MATH  MathSciNet  Google Scholar 

  3. Beliakov G, Warren J (2001) Appropriate choice of aggregation operators in fuzzy decisionsupport systems. Fuzzy Syst IEEE Trans 9(6): 773–784

    Article  Google Scholar 

  4. Ben-Arieh D (2005) Sensitivity of multi-criteria decision making to linguistic quantifiers and aggregation means. Comput Indus Eng 48(2): 289–309

    Article  Google Scholar 

  5. Bordogna G, Pasi G (2005) Personalised indexing and retrieval of heterogeneous structured documents. Inform Retriev 8(2): 301–318

    Article  Google Scholar 

  6. Botzheim J, Kóczy LT, Ruano AE (2002) Extension of the levenberg–marquardt algorithm for the extractionof trapezoidal and general piecewise linear fuzzy rules. In: Fuzzy systems, 2002. FUZZ-IEEE’02. Proceedings of the 2002 IEEE international conference on, vol. 1

  7. Dennis J Jr, Gay D, Walsh R (1981) An adaptive nonlinear least-squares algorithm. ACM Trans Math Softw 7(3): 348–368

    Article  MATH  Google Scholar 

  8. Dubois D, Prade H (1986) Weighted minimum and maximum operations in fuzzy set theory. Info Sci 39(2): 205–210

    Article  MATH  MathSciNet  Google Scholar 

  9. Dyckhoff H, Pedrycz W (1984) Generalized means as model of compensative connectives. Fuzzy Sets Syst 14(2): 143–154

    Article  MATH  MathSciNet  Google Scholar 

  10. Filev D, Yager R (1998) On the issue of obtaining owa operator weights. Fuzzy Sets Syst 94(2): 157–169

    Article  MathSciNet  Google Scholar 

  11. Fletcher R (1987) Practical methods of optimization. Wiley, New York

    MATH  Google Scholar 

  12. Fodor J, Marichal J, Roubens M (1994) Characterization of some aggregation functions arising from mcdm problems. Proc IPMU 94: 1026–1031

    Google Scholar 

  13. Fodor J, Marichal J, Roubens M (1995) Characterization of the ordered weighted averaging operators. Fuzzy Syst IEEE Trans 3(2): 236–240

    Article  Google Scholar 

  14. Gill P, Murray W, Wright M (1981) Practical optimization. Academic Press, London

    MATH  Google Scholar 

  15. Goldberg D (1989) Genetic algorithms in search, optimization and machine learning. Addison-Wesley Longman Publishing Co., Reading

    MATH  Google Scholar 

  16. Haupt R, Haupt S (2004) Practical genetic algorithms. Wiley, London

    MATH  Google Scholar 

  17. Herrera F, López E, Mendaña C, Rodríguez M (2001) A linguistic decision model for personnel management solved with a linguistic biobjective genetic algorithm. Fuzzy Sets Syst 118(1): 47–64

    Article  Google Scholar 

  18. Holland J (1975) Adaptation in natural and artificial systems. University of Michigan Press, Ann Arbor

    Google Scholar 

  19. Kacprzyk J, Wilbik A, Zadrozny S (2007) Linguistic summaries of time series via an OWA operator based aggregation of partial trends. In: IEEE international fuzzy systems conference. FUZZ-IEEE 2007, pp 1–6

  20. Koza J (1992) Genetic programming: on the programming of computers by means of natural selection. MIT Press, Cambridge

    MATH  Google Scholar 

  21. Levenberg K (1944) A method for the solution of certain nonlinear problems in least squares. Q Appl Math 2: 164–168

    MATH  MathSciNet  Google Scholar 

  22. Manna S, Mendis BSU, Gedeon TD (AUG 2009) Hierarchical document signature: a specialized application of fuzzy signature for document computing. FUZZ-IEEE 2009 international conference on Fuzzy systems, pp 1–6

  23. Marquardt D (1963) An algorithm for least-squares estimation of nonlinear parameters. J Soc Indus Appl Math 11(2): 431–441

    Article  MATH  MathSciNet  Google Scholar 

  24. Mendis BSU (2008) Fuzzy signatures: Hierarchical fuzzy systems and alpplications. Ph.D. thesis, College of Engineering and Computer Science, The Australian National University, Australia

  25. Mendis BSU, Gedeon TD (2008) Aggregation selection for hierarchical fuzzy signatures: a comparison of hierarchical owa and wrao. In: International conference of information processing and management of uncertainty in knowledge based systems (IPMU), pp 1–8

  26. Mendis BSU, Gedeon TD (2008) A comparison: Fuzzy signatures and choquet integral. In: IEEE world congress on computational intelligence, WCCI, Hong Kong, pp 1464–1471

  27. Mendis BSU, Gedeon TD, Botzheim J, Kóczy LT (2006) Generalised weighted relevance aggregation operators for hierarchical fuzzy signatures. In: International conference on computational inteligence for modelling control and automation and international conference on intelligent agents web technologies and international commerce (CIMCA’06). Sydney, Australia, pp 198–203

  28. Mendis BSU, Gedeon TD, Kóczy LT (2006) Learning generalized weighted relevance aggregation operators using levenberg–marquardt method. In: Sixth international conference on hybrid intelligent systems (HIS’06) and 4th conference on neuro-computing and evolving intelligence (NCEI 06’). New Zealand, pp 1–6

  29. Meuth R, Lim M, Ong Y, Wunsch D (2009) A proposition on memes and meta-memes in computing for higher-order learning. Memetic Comput 1(2): 85–100

    Article  Google Scholar 

  30. Miller J, Potter W, Gandham R, Lapena C (1993) An evaluation of local improvement operators for genetic algorithms. IEEE Trans Syst Man Cybernet SMC 23: 1340–1340

    Article  Google Scholar 

  31. Mor J (1977) The levenberg–marquardt algorithm: implementation and theory. Lecture Notes Math 630: 105–116

    Article  Google Scholar 

  32. Srinivas M, Patnaik L (1994) Genetic algorithms: a survey. Computer 27(6): 17–26

    Article  Google Scholar 

  33. Torra V, Godo L (2002) Continuous WOWA operators with application to defuzzification. Aggregation operators: new trends and applications, p 159

  34. Wong K, Gedeon T, Kóczy L (2004) Construction of fuzzy signature from data: an example of sars pre-clinical diagnosis system. Fuzzy systems, 2004. In: Proceedings of 2004 IEEE international conference on, vol 3

  35. Yager R (1988) On ordered weighted averaging aggregation operators in multicriteria decisionmaking. IEEE Trans Syst Man Cybernet 18(1): 183–190

    Article  MATH  MathSciNet  Google Scholar 

  36. Yager R (2004) Generalized owa aggregation operators. Fuzzy Optim Decision Making 3(1): 93–107

    Article  MATH  MathSciNet  Google Scholar 

  37. Zhu D, Mendis BSU, Gedeon TD, Asthana A, Goecke R (2008) A hybrid fuzzy approach for human eye gaze pattern recognition. In: 15th international conference on neural information processing (ICONIP08), vols. 1–8. Auckland, New Zealand

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  1. School of Computer Science, The College of Engineering and Computer Science, The Australian National University, Acton, ACT, Australia

    B. S. U. Mendis & T. D. Gedeon

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  1. B. S. U. Mendis
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  2. T. D. Gedeon
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Correspondence to B. S. U. Mendis.

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Mendis, B.S.U., Gedeon, T.D. WRAO and OWA learning using Levenberg–Marquardt and genetic algorithms. Memetic Comp. 3, 101–110 (2011). https://doi.org/10.1007/s12293-010-0054-3

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