Determination of Ordered Weighted Averaging Operator Weights Based on the M‐Entropy Measures

In this paper, based upon the M‐Entropy measures, two new models for obtaining the ordered weighted averaging (OWA) operators are propoosed. In these models, it is assumed, according to available information, that the OWA weights are in a decreasing or increasing order. Some properties of the models are analyzed, and the method of Lagrange multipliers is used to provide a direct way to find these weights. The models are solved with a specific level of orness comparing the results with some other related models. The results demonstrate the efficiency of the M‐Entropy models in generating the OWA operator weights.

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

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

[3]  Ronald R. Yager,et al.  Measures of Entropy and Fuzziness Related to Aggregation Operators , 1995, Inf. Sci..

[4]  Enrique Herrera-Viedma,et al.  A model of an information retrieval system with unbalanced fuzzy linguistic information: Research Articles , 2007 .

[5]  Enrique Herrera-Viedma,et al.  Evaluating the informative quality of documents in SGML format from judgements by means of fuzzy linguistic techniques based on computing with words , 2003, Inf. Process. Manag..

[6]  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).

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

[8]  Enrique Herrera-Viedma,et al.  A model of an information retrieval system with unbalanced fuzzy linguistic information , 2007, Int. J. Intell. Syst..

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

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

[11]  José M. Merigó,et al.  THE FUZZY GENERALIZED OWA OPERATOR AND ITS APPLICATION IN STRATEGIC DECISION MAKING , 2010, Cybern. Syst..

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

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

[14]  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..

[15]  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.

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

[17]  Ronald R. Yager,et al.  Weighted Maximum Entropy OWA Aggregation With Applications to Decision Making Under Risk , 2009, IEEE Transactions on Systems, Man, and Cybernetics - Part A: Systems and Humans.

[18]  Frank Klawonn,et al.  Neural fuzzy logic programming , 1992, IEEE Trans. Neural Networks.

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

[20]  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.

[21]  E. Herrera‐Viedma,et al.  Evaluating the Informative Quality of Documents in SGML Format Using Fuzzy Linguistic Techniques Based on Computing with Words , 2001 .