An overview of methods for determining OWA weights

The ordered weighted aggregation (OWA) operator has received more and more attention since its appearance. One key point in the OWA operator is to determine its associated weights. In this article, I first briefly review existing main methods for determining the weights associated with the OWA operator, and then, motivated by the idea of normal distribution, I develop a novel practical method for obtaining the OWA weights, which is distinctly different from the existing ones. The method can relieve the influence of unfair arguments on the decision results by weighting these arguments with small values. Some of its desirable properties have also been investigated. © 2005 Wiley Periodicals, Inc. Int J Int Syst 20: 843–865, 2005.

[1]  Ronald R. Yager,et al.  Modeling prioritized multicriteria decision making , 2004, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[2]  Zeshui Xu,et al.  A method based on linguistic aggregation operators for group decision making with linguistic preference relations , 2004, Inf. Sci..

[3]  Z. S. Xu,et al.  The ordered weighted geometric averaging operators , 2002, Int. J. Intell. Syst..

[4]  Zeshui Xu,et al.  Induced uncertain linguistic OWA operators applied to group decision making , 2006, Inf. Fusion.

[5]  Z. S. Xu,et al.  An overview of operators for aggregating information , 2003, Int. J. Intell. Syst..

[6]  Francisco Herrera,et al.  Rationality of induced ordered weighted operators based on the reliability of the source of information in group decision-making , 2004, Kybernetika.

[7]  Ching-Lai Hwang,et al.  Fuzzy Multiple Attribute Decision Making - Methods and Applications , 1992, Lecture Notes in Economics and Mathematical Systems.

[8]  H. B. Mitchell,et al.  A generalized OWA operator , 1999 .

[9]  R. Yager,et al.  Learning OWA operator weights from data , 1994, Proceedings of 1994 IEEE 3rd International Fuzzy Systems Conference.

[10]  F. Herrera,et al.  An intelligent news recommender agent for filtering and categorizing large volumes of text corpus , 2004 .

[11]  Ronald R. Yager.  New modes of OWA information fusion , 1998, Int. J. Intell. Syst..

[12]  Janusz Kacprzyk,et al.  The Ordered Weighted Averaging Operators , 1997 .

[13]  Robert Fullér,et al.  An Analytic Approach for Obtaining Maximal Entropy Owa Operator Weights , 2001, Fuzzy Sets Syst..

[14]  Xu Ze-shui.  A Priority Method Based on Induced Ordered Weighted Averaging (IOWA) Operator for Fuzzy Linguistic Preference Matrices , 2003 .

[15]  Francisco Herrera,et al.  Direct approach processes in group decision making using linguistic OWA operators , 1996, Fuzzy Sets Syst..

[16]  J. Kacprzyk.  Group decision making with a fuzzy linguistic majority , 1986 .

[17]  Zeshui Xu,et al.  Uncertain linguistic aggregation operators based approach to multiple attribute group decision making under uncertain linguistic environment , 2004, Inf. Sci..

[18]  Ronald R. Yager,et al.  Including importances in OWA aggregations using fuzzy systems modeling , 1998, IEEE Trans. Fuzzy Syst..

[19]  R. Yager.  Solving mathematical programming problems with OWA operators as objective functions , 1995, Proceedings of 1995 IEEE International Conference on Fuzzy Systems..

[20]  R. Yager.  Quantifier guided aggregation using OWA operators , 1996, Int. J. Intell. Syst..

[21]  Ronald R. Yager,et al.  On the completion of qualitative possibility measures , 1993, IEEE Trans. Fuzzy Syst..

[22]  Kyung S. Park,et al.  Tools for interactive multiattribute decisionmaking with incompletely identified information , 1997 .

[23]  Vicenç Torra,et al.  OWA operators in data modeling and reidentification , 2004, IEEE Transactions on Fuzzy Systems.

[24]  Sung-Bae Cho,et al.  Fuzzy aggregation of modular neural networks with ordered weighted averaging operators , 1995, Int. J. Approx. Reason..

[25]  Francisco Herrera,et al.  Linguistic decision analysis: steps for solving decision problems under linguistic information , 2000, Fuzzy Sets Syst..

[26]  Ronald R. Yager,et al.  Heavy OWA Operators , 2002, Fuzzy Optim. Decis. Mak..

[27]  Soung Hie Kim,et al.  An interactive procedure for multiple attribute group decision making with incomplete information: Range-based approach , 1999, Eur. J. Oper. Res..

[28]  R. Brown,et al.  Smoothing, Forecasting, and Prediction of Discrete Time Series , 1965 .

[29]  R. Yager.  Families of OWA operators , 1993 .

[30]  Francisco Herrera,et al.  A note on the reciprocity in the aggregation of fuzzy preference relations using OWA operators , 2003, Fuzzy Sets Syst..

[31]  Ronald R. Yager,et al.  The induced fuzzy integral aggregation operator , 2002, Int. J. Intell. Syst..

[32]  Ronald R. Yager,et al.  An extension of the Analytical Hierarchy Process using OWA operators , 1999, J. Intell. Fuzzy Syst..

[33]  Lotfi A. Zadeh,et al.  A COMPUTATIONAL APPROACH TO FUZZY QUANTIFIERS IN NATURAL LANGUAGES , 1983 .

[34]  Francisco Herrera,et al.  Integrating multiplicative preference relations in a multipurpose decision-making model based on fuzzy preference relations , 2001, Fuzzy Sets Syst..

[35]  Gloria Bordogna,et al.  A linguistic modeling of consensus in group decision making based on OWA operators , 1997, IEEE Trans. Syst. Man Cybern. Part A.

[36]  Dimitar Filev,et al.  Induced ordered weighted averaging operators , 1999, IEEE Trans. Syst. Man Cybern. Part B.

[37]  Francisco Herrera,et al.  A rational consensus model in group decision making using linguistic assessments , 1997, Fuzzy Sets Syst..

[38]  Ronald R. Yager,et al.  Applications and Extensions of OWA Aggregations , 1992, Int. J. Man Mach. Stud..

[39]  Ronald R. Yager,et al.  On ordered weighted averaging aggregation operators in multicriteria decisionmaking , 1988, IEEE Trans. Syst. Man Cybern..

[40]  R. Mesiar,et al.  Aggregation operators: new trends and applications , 2002 .

[41]  J. Kacprzyk,et al.  The Ordered Weighted Averaging Operators: Theory and Applications , 1997 .

[42]  Ronald R. Yager,et al.  Induced aggregation operators , 2003, Fuzzy Sets Syst..

[43]  R. Yager,et al.  PARAMETERIZED AND-UKE AND OR-LIKE OWA OPERATORS , 1994 .

[44]  Vicenc Torra,et al.  Information Fusion in Data Mining , 2003 .

[45]  Ronald R. Yager,et al.  Nonmonotonic OWA operators , 1999, Soft Comput..

[46]  János C. Fodor,et al.  Characterization of the ordered weighted averaging operators , 1995, IEEE Trans. Fuzzy Syst..

[47]  Radko Mesiar,et al.  Quantitative weights and aggregation , 2004, IEEE Transactions on Fuzzy Systems.

[48]  Z. S. Xu,et al.  The uncertain OWA operator , 2002, Int. J. Intell. Syst..

[49]  Dimitar Filev,et al.  Analytic Properties of Maximum Entropy OWA Operators , 1995, Inf. Sci..

[50]  Dimitar Filev,et al.  On the issue of obtaining OWA operator weights , 1998, Fuzzy Sets Syst..

[51]  Ronald R. Yager,et al.  On ordered weighted averaging aggregation operators in multicriteria decision-making , 1988 .

[52]  Francisco Herrera,et al.  A study of the origin and uses of the ordered weighted geometric operator in multicriteria decision making , 2003, Int. J. Intell. Syst..

[53]  Soung Hie Kim,et al.  Interactive group decision making procedure under incomplete information , 1999, Eur. J. Oper. Res..

[54]  Francisco Herrera,et al.  Multiperson decision-making based on multiplicative preference relations , 2001, Eur. J. Oper. Res..

[55]  Francisco Herrera,et al.  Integrating three representation models in fuzzy multipurpose decision making based on fuzzy preference relations , 1998, Fuzzy Sets Syst..

[56]  Z. S. Xu,et al.  Eowa And Eowg Operators For Aggregating Linguistic Labels Based On Linguistic Preference Relations , 2004, Int. J. Uncertain. Fuzziness Knowl. Based Syst..

[57]  Ronald R. Yager,et al.  Decision making using minimization of regret , 2004, Int. J. Approx. Reason..

[58]  H. B. Mitchell,et al.  A Modified OWA Operator and its Use in Lossless DPCM Image Compression , 1997, Int. J. Uncertain. Fuzziness Knowl. Based Syst..

[59]  V. Torra.  The weighted OWA operator , 1997, International Journal of Intelligent Systems.

[60]  Ronald R. Yager,et al.  OWA aggregation over a continuous interval argument with applications to decision making , 2004, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[61]  M. O'Hagan,et al.  Aggregating Template Or Rule Antecedents In Real-time Expert Systems With Fuzzy Set Logic , 1988, Twenty-Second Asilomar Conference on Signals, Systems and Computers.

[62]  Francisco Herrera,et al.  A fusion approach for managing multi-granularity linguistic term sets in decision making , 2000, Fuzzy Sets Syst..