Some picture fuzzy Bonferroni mean operators with their application to multicriteria decision making

In this paper, we extend the Bonferroni mean (BM) operator with the picture fuzzy numbers (PFNs) to propose novel picture fuzzy aggregation operators and demonstrate their application to multicriteria decision making (MCDM). On the basis of the algebraic operational rules of PFNs and BM, we introduce some aggregation operators: the picture fuzzy Bonferroni mean, the picture fuzzy normalized weighted Bonferroni mean, and the picture fuzzy ordered weighted Bonferroni mean. Then, a new picture fuzzy MCDM method is proposed with the help of the proposed operators. Lastly, a practical application of proposed model is given to verify the developed model and related results of the proposed model is compared with the results of the existing models to indicate its applicability.

[1]  Le Hoang Son.  Generalized picture distance measure and applications to picture fuzzy clustering , 2016, Appl. Soft Comput..

[2]  Le Hoang Son.  Measuring analogousness in picture fuzzy sets: from picture distance measures to picture association measures , 2017, Fuzzy Optim. Decis. Mak..

[3]  Madhumangal Pal,et al.  Picture fuzzy Dombi aggregation operators: Application to MADM process , 2019, Appl. Soft Comput..

[4]  Bui Cong Cuong,et al.  Picture fuzzy sets , 2015 .

[5]  Wei Zhou,et al.  Intuitionistic Fuzzy Normalized Weighted Bonferroni Mean and Its Application in Multicriteria Decision Making , 2012, J. Appl. Math..

[6]  Peide Liu,et al.  Interval-Valued Intuitionistic Fuzzy Power Bonferroni Aggregation Operators and Their Application to Group Decision Making , 2017, Cognitive Computation.

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

[8]  Yuan Li,et al.  A model for selecting an ERP system based on linguistic information processing , 2007, Inf. Syst..

[9]  Pushpinder Singh,et al.  Correlation coefficients for picture fuzzy sets , 2015, J. Intell. Fuzzy Syst..

[10]  Robert LIN,et al.  NOTE ON FUZZY SETS , 2014 .

[11]  Guiwu Wei,et al.  Picture Fuzzy Hamacher Aggregation Operators and their Application to Multiple Attribute Decision Making , 2018, Fundam. Informaticae.

[12]  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..

[13]  Xiaohong Chen,et al.  Alternative selection of end-of-life vehicle management in China: A group decision-making approach based on picture hesitant fuzzy measurements , 2019, Journal of Cleaner Production.

[14]  Guiwu Wei,et al.  Picture fuzzy aggregation operators and their application to multiple attribute decision making , 2017, J. Intell. Fuzzy Syst..

[15]  Harish Garg.  Some Picture Fuzzy Aggregation Operators and Their Applications to Multicriteria Decision-Making , 2017, Arabian Journal for Science and Engineering.

[16]  G. Choquet.  Theory of capacities , 1954 .

[17]  Dalia Streimikiene,et al.  Normalized Weighted Bonferroni Harmonic Mean-Based Intuitionistic Fuzzy Operators and Their Application to the Sustainable Selection of Search and Rescue Robots , 2019, Symmetry.

[18]  Carlo Bonferroni.  Sulle medie multiple di potenze , 1950 .

[19]  Zeshui Xu,et al.  Intuitionistic Fuzzy Bonferroni Means , 2011, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[20]  Jianqiang Wang,et al.  Location selection of offshore wind power station by consensus decision framework using picture fuzzy modelling , 2018, Journal of Cleaner Production.

[21]  Le Hoang Son,et al.  A New Approach to Multi-variable Fuzzy Forecasting Using Picture Fuzzy Clustering and Picture Fuzzy Rule Interpolation Method , 2014, KSE.

[22]  Harish Garg,et al.  Bonferroni mean aggregation operators under intuitionistic fuzzy soft set environment and their applications to decision-making , 2018, J. Oper. Res. Soc..

[23]  Le Hoang Son,et al.  THEORETICAL ANALYSIS OF PICTURE FUZZY CLUSTERING: CONVERGENCE AND PROPERTY , 2018, Journal of Computer Science and Cybernetics.

[24]  Kun She,et al.  Matroidal Structure of Rough Sets from the Viewpoint of Graph Theory , 2012, J. Appl. Math..

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

[26]  Le Hoang Son,et al.  HIFCF: An effective hybrid model between picture fuzzy clustering and intuitionistic fuzzy recommender systems for medical diagnosis , 2015, Expert Syst. Appl..

[27]  Huayou Chen,et al.  Intuitionistic Fuzzy Power Geometric Bonferroni Means and Their Application to Multiple Attribute Group Decision Making , 2015, Int. J. Uncertain. Fuzziness Knowl. Based Syst..

[28]  Zeshui Xu,et al.  Generalized intuitionistic fuzzy Bonferroni means , 2012, Int. J. Intell. Syst..

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

[30]  Vladik Kreinovich,et al.  Picture fuzzy sets - A new concept for computational intelligence problems , 2013, 2013 Third World Congress on Information and Communication Technologies (WICT 2013).

[31]  Runtong Zhang,et al.  Some Picture Fuzzy Dombi Heronian Mean Operators with Their Application to Multi-Attribute Decision-Making , 2018, Symmetry.

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

[33]  Le Hoang Son.  DPFCM: A novel distributed picture fuzzy clustering method on picture fuzzy sets , 2015, Expert Syst. Appl..

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

[35]  Shyi-Ming Chen,et al.  Handling multicriteria fuzzy decision-making problems based on vague set theory , 1994 .

[36]  Hamido Fujita,et al.  Interpolative picture fuzzy rules: A novel forecast method for weather nowcasting , 2016, 2016 IEEE International Conference on Fuzzy Systems (FUZZ-IEEE).

[37]  Runtong Zhang,et al.  Some q-Rung Picture Fuzzy Dombi Hamy Mean Operators with Their Application to Project Assessment , 2019, Mathematics.