Multi-criteria group decision-making method based on generalized power harmonic aggregation operators with normal intuitionistic fuzzy numbers

Normal intuitionistic fuzzy number (NIFN), which is introduced based on intuitionistic fuzzy sets and normal fuzzy numbers, is a useful tool for presenting uncertain information under complicated situations. This study focuses on the development of an effective method by combining NIFNs with the power average and harmonic mean operators to address multi-criteria group decision-making (MCGDM) problems, wherein weight information is completely unknown. First, an effective ranking method for NIFNs is provided in view of defects of the existing comparison method of NIFNs. Subsequently, three normal intuitionistic generalized power harmonic aggregation operators are proposed based on the operations of NIFNs. Next, a new MCGDM method is developed. Finally, a numerical example concerning coal mine safety evaluation is provided for demonstration. The feasibility and validity of the proposed method are further verified by sensitivity analysis and comparison with other existing methods.

[1]  J. Harsanyi.  Cardinal Welfare, Individualistic Ethics, and Interpersonal Comparisons of Utility , 1955 .

[2]  XuZeshui,et al.  Hybrid aggregation operator and its application to multiple attribute decision making problems , 2003 .

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

[4]  Deng-Feng Li,et al.  A ratio ranking method of triangular intuitionistic fuzzy numbers and its application to MADM problems , 2010, Comput. Math. Appl..

[5]  Zeshui Xu,et al.  Fuzzy harmonic mean operators , 2009, Int. J. Intell. Syst..

[6]  Hong-yu Zhang,et al.  New operators on triangular intuitionistic fuzzy numbers and their applications in system fault analysis , 2013, Inf. Sci..

[7]  Mohammad Yazdi,et al.  Risk assessment based on novel intuitionistic fuzzy-hybrid-modified TOPSIS approach , 2018, Safety Science.

[8]  Peide Liu,et al.  Method for aggregating triangular fuzzy intuitionistic fuzzy information and its application to decision making , 2010 .

[9]  Shu-Ping Wan,et al.  The extended VIKOR method for multi-attribute group decision making with triangular intuitionistic fuzzy numbers , 2013, Knowl. Based Syst..

[10]  Ching-Hsue Cheng,et al.  Using intuitionistic fuzzy sets for fault-tree analysis on printed circuit board assembly , 2006, Microelectron. Reliab..

[11]  Xiaohong Chen,et al.  Value determination method based on multiple reference points under a trapezoidal intuitionistic fuzzy environment , 2018, Appl. Soft Comput..

[12]  Zeshui Xu,et al.  Some geometric aggregation operators based on intuitionistic fuzzy sets , 2006, Int. J. Gen. Syst..

[13]  Lin Li,et al.  An uncertain Z-number multicriteria group decision-making method with cloud models , 2019, Inf. Sci..

[14]  Jian-qiang Wang,et al.  Aggregation operators on intuitionistic trapezoidal fuzzy number and its application to multi-criteria decision making problems , 2009 .

[15]  LiDeyi,et al.  Study on the Universality of the Normal Cloud Model , 2005 .

[16]  Zhang-peng Tian,et al.  Multicriteria decision-making approach based on gray linguistic weighted Bonferroni mean operator , 2018, Int. Trans. Oper. Res..

[17]  Zeshui Xu,et al.  Generalized aggregation operators for intuitionistic fuzzy sets , 2010 .

[18]  Lin Li,et al.  Novel operations for linguistic neutrosophic sets on the basis of Archimedean copulas and co-copulas and their application in multi-criteria decision-making problems , 2019, J. Intell. Fuzzy Syst..

[19]  Shu-Ping Wan,et al.  Power Average of Trapezoidal Intuitionistic Fuzzy Numbers Using Strict t-Norms and t-Conorms , 2016, IEEE Transactions on Fuzzy Systems.

[20]  Miin-Shen Yang,et al.  On a class of fuzzy c-numbers clustering procedures for fuzzy data , 1996, Fuzzy Sets Syst..

[21]  Gagandeep Kaur,et al.  Extended TOPSIS method for multi-criteria group decision-making problems under cubic intuitionistic fuzzy environment , 2018, Scientia Iranica.

[22]  Xinyang Deng,et al.  D-DEMATEL: a new method to identify critical success factors in emergency management , 2017 .

[23]  Jian-qiang Wang,et al.  Cloud decision model for selecting sustainable energy crop based on linguistic intuitionistic information , 2017, Int. J. Syst. Sci..

[24]  Hossein Sayyadi Tooranloo,et al.  A model for failure mode and effects analysis based on intuitionistic fuzzy approach , 2016, Appl. Soft Comput..

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

[26]  Ping Li,et al.  Failure mode and effects analysis using intuitionistic fuzzy hybrid weighted Euclidean distance operator , 2014, Int. J. Syst. Sci..

[27]  Jian-qiang Wang,et al.  A Linguistic Neutrosophic Multi-criteria Group Decision-Making Approach with EDAS Method , 2018, Arabian Journal for Science and Engineering.

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

[29]  Zhou-Jing Wang,et al.  A note on "A group decision making model based on a generalized ordered weighted geometric average operator with interval preference matrices" , 2018, Fuzzy Sets Syst..

[30]  Dejian Yu,et al.  Prioritized Information Fusion Method for Triangular Intuitionistic Fuzzy Set and its Application to Teaching Quality Evaluation , 2013, Int. J. Intell. Syst..

[31]  Hong-yu Zhang,et al.  Multi-Criteria Decision-Making Method Based on induced Intuitionistic Normal Fuzzy Related Aggregation Operators , 2012, Int. J. Uncertain. Fuzziness Knowl. Based Syst..

[32]  Kannan Govindan,et al.  Supplier risk assessment based on trapezoidal intuitionistic fuzzy numbers and ELECTRE TRI-C: a case illustration involving service suppliers , 2016, J. Oper. Res. Soc..

[33]  Peng Zhou,et al.  Multi-criteria decision-making method based on normal intuitionistic fuzzy-induced generalized aggregation operator , 2014, TOP.

[34]  Guiwu Wei,et al.  Some Arithmetic Aggregation Operators with Intuitionistic Trapezoidal Fuzzy Numbers and Their Application to Group Decision Making , 2010, J. Comput..

[35]  H. Bizimana,et al.  Flood hazard risk evaluation using fuzzy logic and weightage based combination methods in Geographic Information System (GIS) , 2018, Scientia Iranica.

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

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

[38]  Jianqiang Wang,et al.  Weighted picture fuzzy aggregation operators and their applications to multi-criteria decision-making problems , 2019, Comput. Ind. Eng..

[39]  Huayou Chen,et al.  On the properties of the generalized OWHA operators and their application to group decision making , 2014, J. Intell. Fuzzy Syst..

[40]  Zhang-peng Tian,et al.  A multihesitant fuzzy linguistic multicriteria decision-making approach for logistics outsourcing with incomplete weight information , 2018, Int. Trans. Oper. Res..

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

[42]  Jizu Li,et al.  An intuitionistic fuzzy OWA-TOPSIS method for collaborative network formation considering matching characteristics , 2017 .

[43]  Qing-wei Cao,et al.  Same families of geometric aggregation operators with intuitionistic trapezoidal fuzzy numbers , 2013 .

[44]  Peide Liu,et al.  Multiple criteria decision making method based on normal interval-valued intuitionistic fuzzy generalized aggregation operator , 2016, Complex..

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

[46]  Xiaodong Liu,et al.  A spectral clustering method with semantic interpretation based on axiomatic fuzzy set theory , 2018, Appl. Soft Comput..

[47]  Soung Hie Kim,et al.  Interactive group decision making procedure under incomplete information , 1999, Eur. J. Oper. Res..

[48]  Zeshui Xu,et al.  Intuitionistic Fuzzy Aggregation Operators , 2007, IEEE Transactions on Fuzzy Systems.