A generalization of the power aggregation operators for linguistic environment and its application in group decision making

We introduce a wide range of linguistic generalized power aggregation operators. First, we present the generalized power average (GPA) operator and the generalized power ordered weighted average (GPOWA) operator. Then we extend the GPA operator and the GPOWA operator to linguistic environment and propose the linguistic generalized power average (LGPA) operator, the weighted linguistic generalized power average (WLGPA) operator and the linguistic generalized power ordered weighted average (LGPOWA) operator, which are aggregation functions that use linguistic information and generalized mean in the power average (PA) operator. We give their particular cases such as the linguistic power ordered weighted average (LPOWA) operator, the linguistic power ordered weighted geometric average (LPOWGA) operator, the linguistic power ordered weighted harmonic average (LPOWHA) operator and the linguistic power ordered weighted quadratic average (LPOWQA) operator. Finally, we develop an application of the new approach in a multiple attribute group decision making problem concerning the evaluation of university faculty for tenure and promotion.

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

[2]  J. Merigó,et al.  Fuzzy Generalized Hybrid Aggregation Operators and its Application in Fuzzy Decision Making , 2010 .

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

[4]  Yejun Xu,et al.  Some properties of linguistic preference relation and its ranking in group decision making , 2010 .

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

[6]  W. Pedrycz,et al.  Generalized means as model of compensative connectives , 1984 .

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

[8]  Ronald R. Yager,et al.  The power average operator , 2001, IEEE Trans. Syst. Man Cybern. Part A.

[9]  Francisco Herrera,et al.  The ordered weighted Geometric operator: properties and application in MCDM problems , 2000 .

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

[11]  Zeshui Xu,et al.  Approaches to multiple attribute group decision making based on intuitionistic fuzzy power aggregation operators , 2011, Knowl. Based Syst..

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

[13]  Shady Aly,et al.  Fuzzy aggregation and averaging for group decision making: A generalization and survey , 2009, Knowl. Based Syst..

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

[15]  Ding-Hong Peng,et al.  Consolidating SWOT analysis with nonhomogeneous uncertain preference information , 2011, Knowl. Based Syst..

[16]  Zeshui Xu,et al.  An interactive method for fuzzy multiple attribute group decision making , 2007, Inf. Sci..

[17]  José M. Merigó,et al.  Induced and uncertain heavy OWA operators , 2011, Comput. Ind. Eng..

[18]  Zeshui Xu,et al.  An approach based on the uncertain LOWG and induced uncertain LOWG operators to group decision making with uncertain multiplicative linguistic preference relations , 2006, Decis. Support Syst..

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

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

[21]  Geert Wets,et al.  Road safety risk evaluation by means of ordered weighted averaging operators and expert knowledge , 2010, Knowl. Based Syst..

[22]  Zeshui Xu,et al.  Group decision making based on multiple types of linguistic preference relations , 2008, Inf. Sci..

[23]  Zeshui Xu,et al.  Induced generalized intuitionistic fuzzy operators , 2011, Knowl. Based Syst..

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

[25]  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..

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

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

[28]  Zeshui Xu,et al.  Power-Geometric Operators and Their Use in Group Decision Making , 2010, IEEE Transactions on Fuzzy Systems.

[29]  Huayou Chen,et al.  Continuous generalized OWA operator and its application to decision making , 2011, Fuzzy Sets Syst..

[30]  Cengiz Kahraman,et al.  Developing a group decision support system based on fuzzy information axiom , 2010, Knowl. Based Syst..

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

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

[33]  José M. Merigó,et al.  DECISION MAKING WITH DISTANCE MEASURES AND INDUCED AGGREGATION OPERATORS , 2008 .

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

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

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

[37]  A. M. M. Sharif Ullah,et al.  Algorithms for fuzzy multi expert multi criteria decision making (ME-MCDM) , 2011, Knowl. Based Syst..

[38]  Zeshui Xu,et al.  Dependent uncertain ordered weighted aggregation operators , 2008, Inf. Fusion.

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

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

[41]  Huayou Chen,et al.  Generalized ordered weighted logarithm aggregation operators and their applications to group decision making , 2010, Int. J. Intell. Syst..

[42]  Gui-Wu Wei,et al.  Some generalized aggregating operators with linguistic information and their application to multiple attribute group decision making , 2011, Comput. Ind. Eng..

[43]  Francisco Herrera,et al.  Aggregation operators for linguistic weighted information , 1997, IEEE Trans. Syst. Man Cybern. Part A.

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

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

[46]  Yejun Xu,et al.  Standard and mean deviation methods for linguistic group decision making and their applications , 2010, Expert Syst. Appl..

[47]  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..