Elliptical distribution‐based weight‐determining method for ordered weighted averaging operators

The ordered weighted averaging (OWA) operators play a crucial role in aggregating multiple criteria evaluations into an overall assessment supporting the decision makers’ choice. One key point steps is to determine the associated weights. In this paper, we first briefly review some main methods for determining the weights by using distribution functions. Then we propose a new approach for determining OWA weights by using the regular increasing monotone quantifier. Motivated by the idea of normal distribution‐based method to determine the OWA weights, we develop a method based on elliptical distributions for determining the OWA weights, and some of its desirable properties have been investigated.

[1]  José M. Merigó,et al.  The probabilistic weighted average and its application in multiperson decision making , 2012, Int. J. Intell. Syst..

[2]  Ronald R. Yager,et al.  Generalized OWA Aggregation Operators , 2004, Fuzzy Optim. Decis. Mak..

[3]  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..

[4]  Naif Alajlan,et al.  Multi-criteria formulations with uncertain satisfactions , 2018, Eng. Appl. Artif. Intell..

[5]  XU Ze-shui A New Method of Giving OWA Weights , 2008 .

[6]  Jian Wang,et al.  On some characteristics and related properties for OWF and RIM quantifier , 2018, Int. J. Intell. Syst..

[7]  LeSheng Jin,et al.  OWA Generation Function and Some Adjustment Methods for OWA Operators With Application , 2016, IEEE Transactions on Fuzzy Systems.

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

[9]  José M. Merigó,et al.  Decision Making in Reinsurance with Induced OWA Operators and Minkowski Distances , 2016, Cybern. Syst..

[10]  Radko Mesiar,et al.  Aggregation of OWA Operators , 2018, IEEE Transactions on Fuzzy Systems.

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

[12]  Bonifacio Llamazares Rodríguez SUOWA operators: Constructing semi-uninorms And analyzing specific cases , 2016 .

[13]  LeSheng Jin,et al.  Some properties and representation methods for Ordered Weighted Averaging operators , 2015, Fuzzy Sets Syst..

[14]  Rudolf Vetschera,et al.  How well does the OWA operator represent real preferences? , 2017, Eur. J. Oper. Res..

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

[16]  R. Yager On generalized measures of realization in uncertain environments , 1992 .

[17]  Vicenç Torra,et al.  The weighted OWA operator , 1997, Int. J. Intell. Syst..

[18]  Janusz Kacprzyk,et al.  Recent Developments in the Ordered Weighted Averaging Operators: Theory and Practice , 2011, Studies in Fuzziness and Soft Computing.

[19]  José M. Merigó,et al.  Probabilities in the OWA operator , 2012, Expert Syst. Appl..

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

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

[22]  Radko Mesiar,et al.  Generalizations of OWA Operators , 2015, IEEE Transactions on Fuzzy Systems.

[23]  Bonifacio Llamazares,et al.  Construction of Choquet integrals through unimodal weighting vectors , 2018, Int. J. Intell. Syst..

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

[25]  Bonifacio Llamazares,et al.  SUOWA operators: Constructing semi-uninorms and analyzing specific cases , 2016, Fuzzy Sets Syst..

[26]  Naif Alajlan,et al.  Some issues on the OWA aggregation with importance weighted arguments , 2016, Knowl. Based Syst..

[27]  Maxime Lenormand Generating OWA weights using truncated distributions , 2018, Int. J. Intell. Syst..

[28]  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..

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

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

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

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

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

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

[35]  Ronald R. Yager,et al.  Quantifier guided aggregation using OWA operators , 1996, Int. J. Intell. Syst..

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

[37]  Emiliano A. Valdez,et al.  Tail Conditional Expectations for Elliptical Distributions , 2003 .

[38]  Luis Martínez-López,et al.  A dynamic multi-criteria decision making model with bipolar linguistic term sets , 2018, Expert Syst. Appl..

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

[40]  LeSheng Jin,et al.  On Obtaining Piled OWA Operators , 2015, Int. J. Intell. Syst..

[41]  Xinwang Liu,et al.  An analytic approach to obtain the least square deviation OWA operator weights , 2014, Fuzzy Sets Syst..

[42]  José M. Merigó,et al.  Probabilistic OWA distances applied to asset management , 2018, Soft Comput..

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

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

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

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

[47]  Zeshui Xu,et al.  Probability distribution based weights for weighted arithmetic aggregation operators , 2016, Fuzzy Optim. Decis. Mak..

[48]  Jozo J. Dujmovic,et al.  LSP method and its use for evaluation of Java IDEs , 2006, Int. J. Approx. Reason..

[49]  Ronald R. Yager,et al.  OWA aggregation of multi-criteria with mixed uncertain satisfactions , 2017, Inf. Sci..

[50]  Francisco Herrera,et al.  A Sequential Selection Process in Group Decision Making with a Linguistic Assessment Approach , 1995, Inf. Sci..