Linguistic group decision making with induced aggregation operators and probabilistic information

A new approach for linguistic multi-criteria group decision making.The induced linguistic probabilistic OWA operator.A generalization with moving averages and Bonferroni means.An application in the management of import strategies. A new approach for linguistic group decision making by using probabilistic information and induced aggregation operators is presented. It is based on the induced linguistic probabilistic ordered weighted average (ILPOWA). It is an aggregation operator that uses probabilities and OWA operators in the same formulation considering the degree of importance that each concept has in the formulation. It uses complex attitudinal characters that can be assessed by using order inducing variables. Furthermore, it deals with an uncertain environment where the information cannot be studied in a numerical scale but it is possible to use linguistic variables. Several extensions to this approach are presented by using moving averages and Bonferroni means. The applicability of this approach is also studied with a focus on multi-criteria group decision making by using multi-person aggregation operators in order to deal with the opinion of several experts in the analysis. An illustrative example regarding importation strategies in the administration of a country is developed.

[1]  José M. Merigó,et al.  The uncertain induced quasi‐arithmetic OWA operator , 2011, Int. J. Intell. Syst..

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

[3]  J. Merigó.  Fuzzy Multi-Person Decision Making with Fuzzy Probabilistic Aggregation Operators , 2011 .

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

[5]  Francisco Herrera,et al.  A 2-tuple fuzzy linguistic representation model for computing with words , 2000, IEEE Trans. Fuzzy Syst..

[6]  Lotfi A. Zadeh,et al.  The concept of a linguistic variable and its application to approximate reasoning-III , 1975, Inf. Sci..

[7]  Shyi-Ming Chen,et al.  A NEW METHOD FOR HANDLING MULTICRITERIA FUZZY DECISION-MAKING PROBLEMS USING FN-IOWA OPERATORS , 2003, Cybern. Syst..

[8]  Sang Joon Kim,et al.  A Mathematical Theory of Communication , 2006 .

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

[10]  José M. Merigó,et al.  A unified model between the weighted average and the induced OWA operator , 2011, Expert Syst. Appl..

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

[12]  Peide Liu,et al.  The multiple-attribute decision making method based on the TFLHOWA operator , 2010, Comput. Math. Appl..

[13]  Dimitar Filev,et al.  On the concept of immediate probabilities , 1995, Int. J. Intell. Syst..

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

[15]  Matthias Ehrgott,et al.  Multiple criteria decision analysis: state of the art surveys , 2005 .

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

[17]  Yejun Xu,et al.  The induced generalized aggregation operators for intuitionistic fuzzy sets and their application in group decision making , 2012, Appl. Soft Comput..

[18]  Henrik Legind Larsen,et al.  Importance weighting and andness control in De Morgan dual power means and OWA operators , 2012, Fuzzy Sets Syst..

[19]  J. Merigó,et al.  Linguistic power aggregation operators and their application to multiple attribute group decision making , 2012 .

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

[21]  Lotfi A. Zadeh,et al.  The Concepts of a Linguistic Variable and its Application to Approximate Reasoning , 1975 .

[22]  Su Weihua.  LINGUISTIC INDUCED GENERALIZED AGGREGATION DISTANCE OPERATORS AND THEIR APPLICATION TO DECISION MAKING , 2012 .

[23]  Radko Mesiar,et al.  Aggregation functions: Means , 2011, Inf. Sci..

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

[25]  Huayou Chen,et al.  Generalized power aggregation operators and their applications in group decision making , 2012, Comput. Ind. Eng..

[26]  J. Merigó,et al.  Induced and Linguistic Generalized Aggregation Operators and Their Application in Linguistic Group Decision Making , 2010, Group Decision and Negotiation.

[27]  Zeshui Xu,et al.  Identifying and eliminating dominated alternatives in multi-attribute decision making with intuitionistic fuzzy information , 2012, Appl. Soft Comput..

[28]  Ronald R. Yager,et al.  Generalized Bonferroni mean operators in multi-criteria aggregation , 2010, Fuzzy Sets Syst..

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

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

[31]  José M. Merigó,et al.  Fuzzy decision making with immediate probabilities , 2010, Comput. Ind. Eng..

[32]  José M. Merigó,et al.  Linguistic Aggregation Operators for Linguistic Decision Making Based on the Dempster-Shafer Theory of Evidence , 2010, Int. J. Uncertain. Fuzziness Knowl. Based Syst..

[33]  Zhiming Zhang,et al.  Hesitant fuzzy power aggregation operators and their application to multiple attribute group decision making , 2013, Inf. Sci..

[34]  J. Merigó,et al.  The connection between distortion risk measures and ordered weighted averaging operators , 2013 .

[35]  Guiwu Wei,et al.  Some induced geometric aggregation operators with intuitionistic fuzzy information and their application to group decision making , 2010, Appl. Soft Comput..

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

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

[38]  R. Yager,et al.  MODELLING DECISION MAKING USING IMMEDIATE PROBABILITIES , 1996 .

[39]  E. Zavadskas,et al.  Multiple criteria decision making (MCDM) methods in economics: an overview , 2011 .

[40]  Francisco Herrera,et al.  A Fuzzy Linguistic Methodology to Deal With Unbalanced Linguistic Term Sets , 2008, IEEE Transactions on Fuzzy Systems.

[41]  Shouzhen Zeng,et al.  Fuzzy Generalized Ordered Weighted Averaging Distance Operator and Its Application to Decision Making , 2012 .

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

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

[44]  José M. Merigó,et al.  Generalized Moving averages, Distance Measures and OWA Operators , 2013, Int. J. Uncertain. Fuzziness Knowl. Based Syst..

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

[46]  Yejun Xu,et al.  Approaches based on 2-tuple linguistic power aggregation operators for multiple attribute group decision making under linguistic environment , 2011, Appl. Soft Comput..

[47]  Yejun Xu,et al.  Power Geometric Operators for Group Decision Making under Multiplicative Linguistic Preference Relations , 2012, Int. J. Uncertain. Fuzziness Knowl. Based Syst..

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

[49]  Gui-Wu Wei,et al.  Uncertain Linguistic Hybrid Geometric Mean Operator and its Application to Group Decision Making under Uncertain Linguistic Environment , 2009, Int. J. Uncertain. Fuzziness Knowl. Based Syst..

[50]  José M. Merigó,et al.  Fuzzy induced generalized aggregation operators and its application in multi-person decision making , 2011, Expert Syst. Appl..

[51]  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..

[52]  Yejun Xu,et al.  An Interactive Approach Based on Alternative Achievement Scale and Alternative Comprehensive Scale for Multiple Attribute Decision Making under Linguistic Environment , 2013, Int. J. Comput. Intell. Syst..

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

[54]  José M. Merigó,et al.  Decision-making with distance measures and induced aggregation operators , 2011, Comput. Ind. Eng..