Linguistic Intuitionistic Fuzzy Group Decision Making Based on Aggregation Operators

This paper researches decision making with linguistic intuitionistic fuzzy variables. Several linguistic intuitionistic fuzzy operations are first defined. Then, several linguistic intuitionistic fuzzy aggregation operators are provided, including the linguistic intuitionistic fuzzy hybrid weighted arithmetical averaging operator, and the linguistic intuitionistic fuzzy hybrid weighted geometric mean operator. Considering the interactive characteristics between the weights of elements in a set, several linguistic intuitionistic fuzzy Shapley aggregation operators are presented, including the linguistic intuitionistic fuzzy hybrid Shapley arithmetical averaging operator, and the linguistic intuitionistic fuzzy hybrid Shapley geometric mean operator. To ensure the application reasonably, several desirable properties are discussed. When the weighting information is incompletely known, models for the optimal fuzzy and additive measures are constructed. After that, an approach to multi-criteria group decision making with linguistic intuitionistic fuzzy information is performed. Finally, a practical example about evaluating different types of engines is provided to illustrate the developed procedure.

[1]  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..

[2]  Zeshui Xu,et al.  Choquet integrals of weighted intuitionistic fuzzy information , 2010, Inf. Sci..

[3]  Fanyong Meng,et al.  Correlation Coefficient of Interval-Valued Intuitionistic Uncertain Linguistic Sets and Its Application , 2017, Cybern. Syst..

[4]  Humberto Bustince,et al.  Entropy on intuitionistic fuzzy sets and on interval-valued fuzzy sets , 1996, Fuzzy Sets Syst..

[5]  K. Atanassov,et al.  Interval-Valued Intuitionistic Fuzzy Sets , 2019, Studies in Fuzziness and Soft Computing.

[6]  Li Dengfeng,et al.  New similarity measures of intuitionistic fuzzy sets and application to pattern recognitions , 2002, Pattern Recognit. Lett..

[7]  L. Shapley.  A Value for n-person Games , 1988 .

[8]  Huayou Chen,et al.  Linguistic continuous ordered weighted distance measure and its application to multiple attributes group decision making , 2014, Appl. Soft Comput..

[9]  Fanyong Meng,et al.  Several Generalized Interval-Valued 2-Tuple Linguistic Weighted Distance Measures and their Application , 2017, Int. J. Fuzzy Syst..

[10]  Hong-yu Zhang,et al.  An extended outranking approach for multi-criteria decision-making problems with linguistic intuitionistic fuzzy numbers , 2017, Appl. Soft Comput..

[11]  Zeshui Xu,et al.  A thermodynamic method of intuitionistic fuzzy MCDM to assist the hierarchical medical system in China , 2017, Inf. Sci..

[12]  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..

[13]  K. S. Ravichandran,et al.  A new extension to PROMETHEE under intuitionistic fuzzy environment for solving supplier selection problem with linguistic preferences , 2017, Appl. Soft Comput..

[14]  Iain MacLeod,et al.  Situation Awareness and campaign assessments , 2017, J. Oper. Res. Soc..

[15]  Tiantian Bao,et al.  MADM method based on prospect theory and evidential reasoning approach with unknown attribute weights under intuitionistic fuzzy environment , 2017, Expert Syst. Appl..

[16]  Fanyong Meng,et al.  Uncertain linguistic hesitant fuzzy sets and their application in multi‐attribute decision making , 2018, Int. J. Intell. Syst..

[17]  Francisco Herrera,et al.  Hesitant Fuzzy Linguistic Term Sets for Decision Making , 2012, IEEE Transactions on Fuzzy Systems.

[18]  Glin Bykzkan,et al.  Application of a new combined intuitionistic fuzzy MCDM approach based on axiomatic design methodology for the supplier selection problem , 2017 .

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

[20]  Ze Tang,et al.  Novel approaches to pin cluster synchronization on complex dynamical networks in Lur'e forms , 2018, Commun. Nonlinear Sci. Numer. Simul..

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

[22]  Janusz Kacprzyk,et al.  Entropy for intuitionistic fuzzy sets , 2001, Fuzzy Sets Syst..

[23]  Peide Liu,et al.  Multiple attribute group decision making method based on interval-valued intuitionistic fuzzy power Heronian aggregation operators , 2017, Comput. Ind. Eng..

[24]  Krassimir T. Atanassov,et al.  Intuitionistic fuzzy sets , 1986 .

[25]  Shyi-Ming Chen,et al.  Multiple attribute group decision making based on intuitionistic fuzzy interaction partitioned Bonferroni mean operators , 2017, Inf. Sci..

[26]  Harish Garg,et al.  Correction to: Some Aggregation Operators for Linguistic Intuitionistic Fuzzy Set and its Application to Group Decision-Making Process Using the Set Pair Analysis , 2018, Arabian Journal for Science and Engineering.

[27]  T. R. Gulati,et al.  Application of intuitionistic fuzzy optimization technique in transportation models , 2016 .

[28]  Zheng Pei,et al.  An approach to multiple attribute group decision making based on linguistic intuitionistic fuzzy numbers , 2015, Int. J. Comput. Intell. Syst..

[29]  Ze Tang,et al.  Distributed impulsive synchronization of Lur'e dynamical networks via parameter variation methods , 2018 .

[30]  Sidong Xian,et al.  Interval-valued intuitionistic fuzzy combined weighted averaging operator for group decision making , 2017, J. Oper. Res. Soc..

[31]  Peide Liu,et al.  Some Generalized Einstein Aggregation Operators Based on the Interval-Valued Intuitionistic Fuzzy Numbers and Their Application to Group Decision Making , 2015 .

[32]  Lotfi A. Zadeh,et al.  Fuzzy Sets , 1996, Inf. Control..

[33]  J. Merigó,et al.  The uncertain probabilistic OWA distance operator and its application in group decision making , 2013 .

[34]  Fanyong Meng,et al.  A Method for Multi-Attribute Group Decision Making Based on Generalized Interval-Valued Intuitionistic Fuzzy Choquet Integral Operators , 2017, Int. J. Uncertain. Fuzziness Knowl. Based Syst..

[35]  Zhiming Zhang,et al.  Interval-valued intuitionistic fuzzy Frank aggregation operators and their applications to multiple attribute group decision making , 2017, Neural Computing and Applications.

[36]  Pengfei Shi,et al.  Similarity measures on intuitionistic fuzzy sets , 2003, Pattern Recognit. Lett..

[37]  Fanyong Meng,et al.  Interval‐Valued Intuitionistic Fuzzy Multiattribute Group Decision Making Based on Cross Entropy Measure and Choquet Integral , 2013, Int. J. Intell. Syst..

[38]  Peide Liu.  Some geometric aggregation operators based on interval intuitionistic uncertain linguistic variables and their application to group decision making , 2013 .

[39]  Qiang Zhang,et al.  Multi-attribute decision analysis under a linguistic hesitant fuzzy environment , 2014, Inf. Sci..

[40]  Zeshui Xu,et al.  Exploiting the priority weights from interval linguistic fuzzy preference relations , 2019, Soft Comput..

[41]  Yin-Feng Xu,et al.  The OWA-based consensus operator under linguistic representation models using position indexes , 2010, Eur. J. Oper. Res..

[42]  Zhiming Zhang,et al.  Multi-criteria group decision-making methods based on new intuitionistic fuzzy Einstein hybrid weighted aggregation operators , 2016, Neural Computing and Applications.

[43]  Xiaohong Chen,et al.  Several Generalized Interval-Valued 2-Tuple Linguistic Interval Distance Measures and Their Application , 2017, Int. J. Uncertain. Fuzziness Knowl. Based Syst..

[44]  Peide Liu,et al.  Scaled Prioritized Operators Based on the Linguistic Intuitionistic Fuzzy Numbers and Their Applications to Multi-Attribute Decision Making , 2018, Int. J. Fuzzy Syst..