Group decision making with incomplete intuitionistic multiplicative preference relations

Abstract Intuitionistic multiplicative preference relations (IMPRs) have been widely applied in decision making for their ability to efficiently express the uncertainty of information. This paper investigates the decision making with incomplete IMPRs. First, a new consistency of incomplete IMPRs is defined. Then, we present some optimization models for estimating missing values by maximizing the consistency level. After that, the group IMPR is derived by using membership degrees in individual intuitionistic multiplicative judgments. Subsequently, a transformation method is offered to build a consistent IMPR through a normalized intuitionistic fuzzy priority weight vector. Moreover, a model is presented to get intuitionistic fuzzy priority weights. Finally, we propose a group decision making (GDM) method with incomplete IMPRs. A practical GDM problem on venue selection for communication drills is offered to indicate the specific application of main theoretical results.

[1]  Fanyong Meng,et al.  Heterogeneous group decision making in the setting of incomplete preference relations , 2019, Inf. Sci..

[2]  Zeshui Xu,et al.  Priority Weight Intervals Derived From Intuitionistic Multiplicative Preference Relations , 2013, IEEE Transactions on Fuzzy Systems.

[3]  Lei Li,et al.  Emergency decision-making combining cumulative prospect theory and group decision-making , 2019 .

[4]  Chonghui Guo,et al.  Deriving priority weights from intuitionistic multiplicative preference relations under group decision-making settings , 2017, J. Oper. Res. Soc..

[5]  T. L. Saaty.  A Scaling Method for Priorities in Hierarchical Structures , 1977 .

[6]  Shyi-Ming Chen,et al.  Group decision making systems using group recommendations based on interval fuzzy preference relations and consistency matrices , 2015, Inf. Sci..

[7]  Muhammad Sajjad Ali Khan,et al.  Hybrid aggregation operators based on Pythagorean hesitant fuzzy sets and their application to group decision making , 2018, Granular Computing.

[8]  Shyi-Ming Chen,et al.  Group decision making using incomplete fuzzy preference relations based on the additive consistency and the order consistency , 2014, Inf. Sci..

[9]  Shyi-Ming Chen,et al.  Multiattribute group decision making based on intuitionistic 2-tuple linguistic information , 2018, Inf. Sci..

[10]  Zeshui Xu,et al.  An intuitionistic fuzzy multiplicative best-worst method for multi-criteria group decision making , 2016, Inf. Sci..

[11]  Jun Liu,et al.  Multi-granularity unbalanced linguistic group decision-making with incomplete weight information based on VIKOR method , 2018 .

[12]  Shyi-Ming Chen,et al.  Group decision making with multiplicative interval linguistic hesitant fuzzy preference relations , 2019, Inf. Sci..

[13]  Zhiming Zhang,et al.  Approaches to group decision making based on interval-valued intuitionistic multiplicative preference relations , 2016, Neural Computing and Applications.

[14]  Zhiming Zhang,et al.  Logarithmic least squares approaches to deriving interval weights, rectifying inconsistency and estimating missing values for interval multiplicative preference relations , 2017, Soft Comput..

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

[16]  Zeshui Xu,et al.  Group decision making based on intuitionistic multiplicative aggregation operators , 2013 .

[17]  Huchang Liao,et al.  Intuitionistic multiplicative analytic hierarchy process in group decision making , 2016, Comput. Ind. Eng..

[18]  Zeshui Xu,et al.  Interval-valued intuitionistic multiplicative aggregation in group decision making , 2017, GRC 2017.

[19]  Shyi-Ming Chen,et al.  Some intuitionistic fuzzy Dombi Bonferroni mean operators and their application to multi-attribute group decision making , 2018, J. Oper. Res. Soc..

[20]  Zeshui Xu,et al.  Compatibility measures and consensus models for group decision making with intuitionistic multiplicative preference relations , 2013, Appl. Soft Comput..

[21]  Shyi-Ming Chen,et al.  Multiattribute decision making based on novel score function of intuitionistic fuzzy values and modified VIKOR method , 2019, Inf. Sci..

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

[23]  Zhou-Jing Wang,et al.  A multi-step goal programming approach for group decision making with incomplete interval additive reciprocal comparison matrices , 2015, Eur. J. Oper. Res..

[24]  Luis G. Vargas,et al.  Uncertainty and rank order in the analytic hierarchy process , 1987 .

[25]  Zeshui Xu,et al.  Managing multi-granularity linguistic information in qualitative group decision making: an overview , 2016 .

[26]  Tomoe Entani,et al.  Uncertainty index based interval assignment by Interval AHP , 2012, Eur. J. Oper. Res..

[27]  Zeshui Xu,et al.  Deriving priority weights from intuitionistic fuzzy multiplicative preference relations , 2019, Int. J. Intell. Syst..

[28]  Shyi-Ming Chen,et al.  A novel similarity measure between intuitionistic fuzzy sets based on the centroid points of transformed fuzzy numbers with applications to pattern recognition , 2016, Inf. Sci..

[29]  Dejian Yu,et al.  Group Decision Making Under Interval‐Valued Multiplicative Intuitionistic Fuzzy Environment Based on Archimedean t‐Conorm and t‐Norm , 2015, Int. J. Intell. Syst..

[30]  Zhou-Jing Wang.  Derivation of intuitionistic fuzzy weights based on intuitionistic fuzzy preference relations , 2013 .

[31]  Didier Dubois,et al.  Gradualness, uncertainty and bipolarity: Making sense of fuzzy sets , 2012, Fuzzy Sets Syst..

[32]  Shyi-Ming Chen,et al.  A consistency and consensus-based method for group decision making with hesitant fuzzy linguistic preference relations , 2019, Inf. Sci..

[33]  Peijun Guo,et al.  Decision-making with interval probabilities , 2008, 2008 IEEE International Conference on Systems, Man and Cybernetics.

[34]  J. Merigó,et al.  Interval-Valued Multiplicative Intuitionistic Fuzzy Preference Relations , 2013 .

[35]  Witold Pedrycz,et al.  Models of Mathematical Programming for Intuitionistic Multiplicative Preference Relations , 2017, IEEE Transactions on Fuzzy Systems.

[36]  Shyi-Ming Chen,et al.  Fuzzy multiple attributes group decision-making based on fuzzy preference relations , 2011, Expert Syst. Appl..

[37]  Fanyong Meng,et al.  Linguistic intuitionistic fuzzy Hamacher aggregation operators and their application to group decision making , 2018, Granular Computing.

[38]  A. S. Ranadive,et al.  Multi-granulation interval-valued fuzzy probabilistic rough sets and their corresponding three-way decisions based on interval-valued fuzzy preference relations , 2018, Granular Computing.

[39]  Zeshui Xu,et al.  Preference Relations Based on Intuitionistic Multiplicative Information , 2013, IEEE Transactions on Fuzzy Systems.

[40]  Zhiming Zhang,et al.  A Framework of Group Decision Making with Hesitant Fuzzy Preference Relations Based on Multiplicative Consistency , 2017, Int. J. Fuzzy Syst..

[41]  Zeshui Xu,et al.  Group decision making based on incomplete intuitionistic multiplicative preference relations , 2015, Inf. Sci..

[42]  Harish Garg.  DISTANCE AND SIMILARITY MEASURES FOR INTUITIONISTIC MULTIPLICATIVE PREFERENCE RELATION AND ITS APPLICATIONS , 2017 .

[43]  Zeshui Xu,et al.  Interval-Valued Intuitionistic Multiplicative Sets , 2014, Int. J. Uncertain. Fuzziness Knowl. Based Syst..

[44]  Muhammad Sajjad Ali Khan,et al.  Pythagorean fuzzy prioritized aggregation operators and their application to multi-attribute group decision making , 2018, Granular Computing.

[45]  Witold Pedrycz,et al.  Goal Programming Approaches to Managing Consistency and Consensus for Intuitionistic Multiplicative Preference Relations in Group Decision Making , 2018, IEEE Transactions on Fuzzy Systems.

[46]  Shyi-Ming Chen,et al.  Group decision making based on multiplicative consistency and consensus of fuzzy linguistic preference relations , 2020, Inf. Sci..

[47]  K. Rahman,et al.  Generalized interval-valued Pythagorean fuzzy aggregation operators and their application to group decision-making , 2019 .