Asia pacific journal of information systems

  • 제16권1호
  • /
  • Pages.85-101
  • /
  • 2006
  • /
  • 2288-5404(pISSN)
  • /
  • 2288-6818(eISSN)
한국경영정보학회 (The Korea Society of Management Information Systems)
권호 표지

순위가 있는 가중치 평균 방법에서 일정한 수준의 결합력을 갖는 가중치 함수의 성질 및 다기준의사결정 문제에의 활용

The Ordered Weighted Averaging (OWA) Operator Weighting Functions with Constant Value of Orness and Application to the Multiple Criteria Decision Making Problems

  • 발행 : 2006.03.31
PDF 다운로드
⟨ 이전 논문 다음 논문 ⟩

초록

Actual type of aggregation performed by an ordered weighted averaging (OWA) operator heavily depends upon the weighting vector. A number of approaches have been suggested for obtaining the associated weights. In this paper, we present analytic forms of OWA operator weighting functions, each of which has such properties as rank-based weights and constant value of orness, irrespective of number of objectives aggregated. Specifically, we propose four analytic forms of OWA weighting functions that can be positioned at 0.25, 0.334, 0.667, and 0.75 on the orness scale. The merits for using these weights over other weighting schemes can be mentioned in a couple of ways. Firstiy, we can efficiently utilize the analytic forms of weighting functions without solving complicated mathematical programs once the degree of orness is specified a priori by decision maker. Secondly, combined with well-known OWA operator weights such as max, min, and average, any weighting vectors, having a desired value of orness and being independent of the number of objectives, can be generated. This can be accomplished by convex combinations of predetermined weighting functions having constant values of orness. Finally, in terms of a measure of dispersion, newly generated weighting vectors show just a few discrepancies with weights generated by maximum entropy OWA.

키워드

참고문헌

  1. Ahn, B.S., 'Extending Malakooti's Model for Ranking Multi-Criteria Alternatives with Preference Strength and Partial Information,'IEEE Transactions on Systems, Man and Cybernetics (Part A), Vol. 33, No. 3, 2003, pp. 281-287 https://doi.org/10.1109/TSMCA.2003.817049
  2. Ahn, B.S., 'Multiattribute Decision Aid with Extended ISMAUT,'to be published in IEEE Transactions on Systems, Man and Cybernetics (Part A), May 2006
  3. Yager, R.R., 'On Ordered Weighted Averaging Aggregation Operators in Multi-criteria Decision Making,'IEEE Transactions on Systems, Man and Cybernetics, Vol. 18, 1988, pp. 83-90
  4. von Winterfeldt, D. and Edwards, W., Decision Analysis and Behavioral Research, Cambridge University Press, England, 1986
  5. Keeney, R.L. and Raiffa, H., Decisions with Multiple Objectives: Preferences and Value Tradeoffs, Wiley, New York, 1976
  6. Hwang, C.L. and Lin, M.J., Group Decision Making under Multiple Criteria: Lecture Notes in Economics and Mathematical Systems, Springer-Verag, New York, 1986
  7. Yager, R.R., 'Fuzzy Aggregation of Modular Neural Networks with Ordered Weighted Averaging Operators,'International Journal of Approximate Reasoning, Vol. 13, 1995, pp. 359-375 https://doi.org/10.1016/0888-613X(95)00059-P
  8. Yager, R.R., 'On a Semantics for Neural Networks Based on Fuzzy Quantifiers,'International Journal of Intelligent Systems, Vol. 7, 1992, pp. 765-786 https://doi.org/10.1002/int.4550070805
  9. Yager, R.R., 'A Note on Weighted Queries in Information Retrieval Systems,'Journal of American Society for Information Science, Vol. 28, 1987, pp. 23-24
  10. Yager, R.R., 'Connectives and Quantifiers in Fuzzy Sets,'Fuzzy Sets and Systems, Vol. 40, 1991, pp. 39-75 https://doi.org/10.1016/0165-0114(91)90046-S
  11. Yager, R.R. and Filev, D.P., 'Fuzzy Logic Controllers with Flexible Structures,'in Proceeding of Second International Conference on Fuzzy Sets and Neural Networks, Tizuka, 1992, pp. 317-320
  12. Herrera, F., Herrera-Viedma, E., and Verdegay, J.L., 'A Sequential Selection Process in Group Decision Making with a Linguistic Assessment Approach,'Information Sciences, Vol. 85, 1995, pp. 223-239 https://doi.org/10.1016/0020-0255(95)00025-K
  13. Herrera, F., Herrera-Viedma, E., and Verdegay, J.L., 'A Model of Consensus in Group Decision Making under Linguistic Assessments,'Fuzzy Sets and Systems, Vol. 78, 1996a, pp. 73-87 https://doi.org/10.1016/0165-0114(95)00107-7
  14. Herrera, F., Herrera-Viedma, E., and Verdegay, J.L., 'Direct Approach Processes in Group Decision Making under Linguistic OWA Operators,'Fuzzy Sets and Systems, Vol. 79, 1996b, pp. 175-190 https://doi.org/10.1016/0165-0114(95)00162-X
  15. Fernandez Salido, J.M. and Murakami, S., 'Extending Yager's Orness Concept for the OWA Aggregators to Other Mean Operators,'Fuzzy Sets and Systems, Vol. 139, 2003, pp. 515-542 https://doi.org/10.1016/S0165-0114(02)00369-X
  16. Xu, Z.S. and Da, Q.L., 'An Overview of Operators for Aggregating Information,'International Journal of Intelligent Systems, Vol. 18, 2003, pp. 953-969 https://doi.org/10.1002/int.10127
  17. Filev, D. and Yager, R.R., 'On the Issue of Obtaining OWA Operator Weights,'Fuzzy Sets and Systems, Vol. 94, 1998, pp. 157-169 https://doi.org/10.1016/S0165-0114(96)00254-0
  18. O'Hagan, M., 'Using Maximum Entropy-ordered Weighted Averaging to Construct a Fuzzy Neuron,'in Proceeding of IEEE 24th Annual Asilomar Conference on Signals, Systems and Computers, Pacific Grove, CA, 1990, pp. 618-623
  19. Filev, D. and Yager, R.R., 'Analytic Properties of Maximum Entropy OWA Operators,'Information Sciences, Vol. 85, 1995, pp. 11-27 https://doi.org/10.1016/0020-0255(94)00109-O
  20. Fuller, R. and Majlender, P., 'An Analytic Approach for Obtaining Maximal Entropy OWA Operator Weights,'Fuzzy Sets and Systems, Vol. 124, 2001, pp. 53-57 https://doi.org/10.1016/S0165-0114(01)00007-0
  21. Fuller, R. and Majlender, P., 'On Obtaining Minimal Variability OWA Operator Weights,'Fuzzy Sets and Systems, Vol. 136, 2003, pp. 203-215 https://doi.org/10.1016/S0165-0114(02)00267-1
  22. Yager, R.R., 'Including Importance in OWA Aggregations Using Fuzzy Systems Modeling,'IEEE Transactions on Fuzzy Systems, Vol. 6, 1998, pp. 286-294 https://doi.org/10.1109/91.669028
  23. Chernoff, H. and Moses, L.E., Elementary Decision Theory, Wiley, New York, 1959
  24. Stillwell, W.G., Seaver, D.A., and Edwards, W., 'A Comparison of Weight Approximation Techniques in Multiattribute Utility Decision Making,'Organizational Behavior and Human Decision Processes, Vol. 28, 1981, pp. 62-77
  25. Edwards, W. and Barron, F.H., 'Smarts and Smarter: Improved Simple Methods for Multiattribute Utility Measurement,'Organizational Behavior and Human Decision Processes, Vol. 60, 1994, pp. 306-325 https://doi.org/10.1006/obhd.1994.1087
  26. Barron, F.H. and Barret, B.E., 'Decision Quality Using Ranked Attribute Weights,'Management Science, Vol. 42, 1996, pp. 1515- 1523 https://doi.org/10.1287/mnsc.42.11.1515