A Review of the OWA Determination Methods: Classification and Some Extensions

The OWA operator determination is an important prerequisite step for OWA operator applications. With the application of OWA operator in various areas, the OWA operator determination becomes an active topic in recent years. Based on recent developments, the paper give a summary on the OWA determination methods in classification way: the optimization criteria methods, the sample learning methods, the function based methods, the argument dependent methods and the preference methods. Some relationships between the methods in the same kind and the relationships between different kinds are provided. An uniform framework to connect these OWA determination methods together is also attempted. Some extensions, problems and future research directions are given with discussions.

[1]  Debjani Chakraborty,et al.  A decision scheme based on OWA operator for an evaluation programme: an approximate reasoning approach , 2004, Appl. Soft Comput..

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

[3]  Itsuo Hatono,et al.  Linguistic labels for expressing fuzzy preference relations in fuzzy group decision making , 1998, IEEE Trans. Syst. Man Cybern. Part B.

[4]  Xinwang Liu,et al.  The solution equivalence of minimax disparity and minimum variance problems for OWA operators , 2007, Int. J. Approx. Reason..

[5]  Oscar Cordón,et al.  A model of fuzzy linguistic IRS based on multi-granular linguistic information , 2003, Int. J. Approx. Reason..

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

[7]  Changyong Liang,et al.  A linear programming model for determining ordered weighted averaging operator weights with maximal Yager's entropy , 2009, Comput. Ind. Eng..

[8]  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.

[9]  Zhongsheng Hua,et al.  Aggregating preference rankings using OWA operator weights , 2007, Inf. Sci..

[10]  Ying-Ming Wang,et al.  A minimax disparity approach for obtaining OWA operator weights , 2005, Inf. Sci..

[11]  Ali Emrouznejad,et al.  MP-OWA: The most preferred OWA operator , 2008, Knowl. Based Syst..

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

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

[14]  Qingli Da,et al.  On the properties of regular increasing monotone (RIM) quantifiers with maximum entropy† , 2008, Int. J. Gen. Syst..

[15]  Zeshui Xu,et al.  Dependent OWA Operators , 2006, MDAI.

[16]  Xinwang Liu,et al.  On the properties of equidifferent OWA operator , 2006, International Journal of Approximate Reasoning.

[17]  Solomon Tesfamariam,et al.  Probability density functions based weights for ordered weighted averaging (OWA) operators: An example of water quality indices , 2007, Eur. J. Oper. Res..

[18]  Ronald R. Yager,et al.  An extension of the naive Bayesian classifier , 2006, Inf. Sci..

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

[20]  Ying-Ming Wang,et al.  A preemptive goal programming method for aggregating OWA operator weights in group decision making , 2007, Inf. Sci..

[21]  Yong Fang,et al.  The relationships between two kinds of OWA operator determination methods , 2008, 2008 IEEE International Conference on Fuzzy Systems (IEEE World Congress on Computational Intelligence).

[22]  Ying Luo,et al.  Two new models for determining OWA operator weights , 2007, Comput. Ind. Eng..

[23]  R. Yager On the analytic representation of the Leximin ordering and its application to flexible constraint propagation , 1997 .

[24]  Byeong Seok Ahn,et al.  Preference relation approach for obtaining OWA operators weights , 2008, Int. J. Approx. Reason..

[25]  Xinwang Liu,et al.  Parameterized additive neat OWA operators with different orness levels , 2006, Int. J. Intell. Syst..

[26]  Robert Fullér,et al.  On Obtaining Minimal Variability Owa Operator Weights , 2002, Fuzzy Sets Syst..

[27]  Gleb Beliakov,et al.  How to build aggregation operators from data , 2003, Int. J. Intell. Syst..

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

[29]  Bonifacio Llamazares,et al.  Choosing OWA operator weights in the field of Social Choice , 2007, Inf. Sci..

[30]  Péter Majlender,et al.  OWA operators with maximal Rényi entropy , 2005, Fuzzy Sets Syst..

[31]  Xinwang Liu,et al.  The Relationships between Two Variability and orness Optimization Problems for OWA Operator with Rim Quantifier Extensions , 2010, Int. J. Uncertain. Fuzziness Knowl. Based Syst..

[32]  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..

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

[34]  Christian Fonteix,et al.  Weights determination of OWA operators by parametric identification , 2008, Math. Comput. Simul..

[35]  José Ignacio Peláez,et al.  Analysis of OWA operators in decision making for modelling the majority concept , 2007, Appl. Math. Comput..

[36]  Xinwang Liu,et al.  Orness and parameterized RIM quantifier aggregation with OWA operators: A summary , 2008, Int. J. Approx. Reason..

[37]  Zeshui Xu,et al.  An overview of methods for determining OWA weights , 2005, Int. J. Intell. Syst..

[38]  Thierry Marchant Maximal orness Weights with a Fixed Variability for OWA Operators , 2006, Int. J. Uncertain. Fuzziness Knowl. Based Syst..

[39]  Ronald R. Yager,et al.  On the valuation of alternatives for decision‐making under uncertainty , 2002, Int. J. Intell. Syst..

[40]  Ronald R. Yager,et al.  Time Series Smoothing and OWA Aggregation , 2008, IEEE Transactions on Fuzzy Systems.

[41]  Gleb Beliakov,et al.  Learning Weights in the Generalized OWA Operators , 2005, Fuzzy Optim. Decis. Mak..

[42]  Ronald R. Yager,et al.  Toward a language for specifying summarizing statistics , 2003, IEEE Trans. Syst. Man Cybern. Part B.

[43]  V. Torra Learning weights for weighted OWA operators , 2000, 2000 26th Annual Conference of the IEEE Industrial Electronics Society. IECON 2000. 2000 IEEE International Conference on Industrial Electronics, Control and Instrumentation. 21st Century Technologies.

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

[45]  Ching-Hsue Cheng,et al.  Flexible fuzzy OWA querying method for hemodialysis database , 2006, Soft Comput..

[46]  G. Mayor,et al.  On a class of monotonic extended OWA operators , 1997, Proceedings of 6th International Fuzzy Systems Conference.

[47]  J. Merigó,et al.  The Induced Generalized OWA Operator , 2009, EUSFLAT Conf..

[48]  Gholam R. Amin Notes on properties of the OWA weights determination model , 2007, Comput. Ind. Eng..

[49]  José Ignacio Peláez,et al.  Majority additive–ordered weighting averaging: A new neat ordered weighting averaging operator based on the majority process , 2003, Int. J. Intell. Syst..

[50]  Gleb Beliakov Methods of construction of OWA operators from data , 2001, 10th IEEE International Conference on Fuzzy Systems. (Cat. No.01CH37297).

[51]  Francisco Herrera,et al.  Fuzzy Sets and Their Extensions: Representation, Aggregation and Models , 2008 .

[52]  José Ignacio Peláez,et al.  A majority model in group decision making using QMA–OWA operators , 2006, Int. J. Intell. Syst..

[53]  Xinwang Liu,et al.  On the properties of equidifferent RIM quantifier with generating function , 2005, Int. J. Gen. Syst..

[54]  Xinwang Liu,et al.  Some properties of the weighted OWA operator , 2006, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

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

[56]  Xinwang Liu,et al.  On the properties of parametric geometric OWA operator , 2004, Int. J. Approx. Reason..

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

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

[59]  Tossapon Boongoen,et al.  Clus-DOWA: A new dependent OWA operator , 2008, 2008 IEEE International Conference on Fuzzy Systems (IEEE World Congress on Computational Intelligence).

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

[61]  Ronald R. Yager,et al.  Using Stress Functions to Obtain OWA Operators , 2007, IEEE Transactions on Fuzzy Systems.

[62]  Slawomir Zadrozny,et al.  On Group Decision Making, Consensus Reaching, Voting and Voting Paradoxes under Fuzzy Preferences and a Fuzzy Majority: A Survey and some Perspectives , 2008, Fuzzy Sets and Their Extensions: Representation, Aggregation and Models.

[63]  Byeong Seok Ahn,et al.  Least‐squared ordered weighted averaging operator weights , 2008, Int. J. Intell. Syst..

[64]  Itsuo Hatono,et al.  Hierarchical semi-numeric method for pairwise fuzzy group decision making , 2002, IEEE Trans. Syst. Man Cybern. Part B.

[65]  Slawomir Zadrozny,et al.  On Tuning OWA Operators in a Flexible Querying Interface , 2006, FQAS.

[66]  Janusz Kacprzyk,et al.  Computing with words in intelligent database querying: standalone and Internet-based applications , 2001, Inf. Sci..

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

[68]  Ronald R. Yager A Hierarchical Document Retrieval Language , 2004, Information Retrieval.

[69]  Gholam R. Amin Note on "A preemptive goal programming method for aggregating OWA operator weights in group decision making" , 2007, Inf. Sci..

[70]  Ronald R. Yager,et al.  Centered OWA Operators , 2007, Soft Comput..

[71]  Vicenç Torra,et al.  Learning weights for the quasi-weighted means , 2002, IEEE Trans. Fuzzy Syst..

[72]  Ali Emrouznejad,et al.  An extended minimax disparity to determine the OWA operator weights , 2006, Comput. Ind. Eng..

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

[74]  Ronald R. Yager,et al.  Fuzzy modeling for intelligent decision making under uncertainty , 2000, IEEE Trans. Syst. Man Cybern. Part B.

[75]  Byeong Seok Ahn,et al.  An Efficient Pruning Method for Decision Alternatives of OWA Operators , 2008, IEEE Transactions on Fuzzy Systems.

[76]  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).

[77]  Changyong Liang,et al.  An argument‐dependent approach to determining OWA operator weights based on the rule of maximum entropy , 2007, Int. J. Intell. Syst..

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

[79]  Slawomir Zadrozny,et al.  Computing with words for text processing: An approach to the text categorization , 2006, Inf. Sci..

[80]  Ching-Hsue Cheng,et al.  Mcdm Aggregation Model Using Situational Me-OWA and Me-Owga Operators , 2006, Int. J. Uncertain. Fuzziness Knowl. Based Syst..

[81]  Gleb Beliakov,et al.  Aggregation Functions: A Guide for Practitioners , 2007, Studies in Fuzziness and Soft Computing.

[82]  Xinwang Liu,et al.  A general model of parameterized OWA aggregation with given orness level , 2008, Int. J. Approx. Reason..

[83]  Byeong Seok Ahn,et al.  On the properties of OWA operator weights functions with constant level of orness , 2006, IEEE Transactions on Fuzzy Systems.

[84]  Radko Mesiar,et al.  Fitting Generated Aggregation Operators To Empirical Data , 2004, Int. J. Uncertain. Fuzziness Knowl. Based Syst..

[85]  M. Sicilia,et al.  Empirical assessment of a collaborative filtering algorithm based on OWA operators , 2008 .