Multiple attribute group decision making using J-divergence and evidential reasoning theory under intuitionistic fuzzy environment

AbstractThe theory of intuitionistic fuzzy sets has been proved to be an effective and convenient tool in the construction of fuzzy multiple attribute group decision-making models to deal with the uncertainty in developing complex decision support systems. Concerning this topic, the current studies mainly focus on their attention on two aspects including aggregation operators on intuitionistic fuzzy sets and determining the weights of both decision makers and attributes. However, some challenges have not been fully considered including existing aggregation operators which may induce unreasonable results in some situations and how to objectively determine the weights of both attributes and decision makers to meet different decision-making demands. To overcome the challenges of existing decision-making models and to satisfy much more decision-making situations, a novel intuitionistic fuzzy multiple attribute group decision-making method via J-divergence and evidential reasoning theory is proposed in this paper as a supplement of conventional models. On the one hand, a weighted J-divergence of intuitionistic fuzzy sets and a J-divergence between two intuitionistic fuzzy matrices are introduced. Following the two concepts, two consensus-based approaches are proposed to determine the weights of both decision makers and attributes. The weights obtained from the proposed method can more accurately reflect the importance levels of both attributes and decision makers from the perspective of consensus by comparison with existing models. On the other hand, an evidential reasoning theory-based operator is established to replace conventional operators for aggregating intuitionistic fuzzy information. The fusion result via this operator is consistent with most of intuitionistic fuzzy numbers. With these works, the proposed method can provide more accurate and reasonable decision results than existing algorithms.

[1]  Ronald R. Yager,et al.  Intuitionistic fuzzy interpretations of multi-criteria multi-person and multi-measurement tool decision making , 2005, Int. J. Syst. Sci..

[2]  Ching-Lai Hwang,et al.  Multiple Attribute Decision Making: Methods and Applications - A State-of-the-Art Survey , 1981, Lecture Notes in Economics and Mathematical Systems.

[3]  Shyi-Ming Chen,et al.  Multiattribute Decision Making Based on Interval-Valued Intuitionistic Fuzzy Sets, PSO Techniques, and Evidential Reasoning Methodology , 2015, IEEE Transactions on Fuzzy Systems.

[4]  Jun Ye.  Generalized Dice measures for multiple attribute decision making under intuitionistic and interval-valued intuitionistic fuzzy environments , 2017, Neural Computing and Applications.

[5]  Huayou Chen,et al.  Intuitionistic Fuzzy Interaction Bonferroni Means and Its Application to Multiple Attribute Decision Making , 2015, IEEE Transactions on Cybernetics.

[6]  Peng Shi,et al.  High-order Intuitionistic Fuzzy Cognitive Map Based on Evidential Reasoning Theory , 2019, IEEE Transactions on Fuzzy Systems.

[7]  Dimitrios K. Iakovidis,et al.  Intuitionistic Fuzzy Cognitive Maps for Medical Decision Making , 2011, IEEE Transactions on Information Technology in Biomedicine.

[8]  Ting-Yu Chen,et al.  Determining objective weights with intuitionistic fuzzy entropy measures: A comparative analysis , 2010, Inf. Sci..

[9]  Janusz Kacprzyk,et al.  Distances between intuitionistic fuzzy sets , 2000, Fuzzy Sets Syst..

[10]  Wei Xing Zheng,et al.  Robust Cooperative Spectrum Sensing Based on Adaptive Reputation and Evidential Reasoning Theory in Cognitive Radio Network , 2018, Circuits Syst. Signal Process..

[11]  Shyi-Ming Chen,et al.  Fuzzy multiattribute decision making based on transformation techniques of intuitionistic fuzzy values and intuitionistic fuzzy geometric averaging operators , 2016, Inf. Sci..

[12]  Maryam Alimardani,et al.  Target market selection based on market segment evaluation: a multiple attribute decision making approach , 2015 .

[13]  Jun Ye,et al.  Multiple attribute group decision-making methods with unknown weights in intuitionistic fuzzy setting and interval-valued intuitionistic fuzzy setting , 2013, Int. J. Gen. Syst..

[14]  Nouman Azam,et al.  Evaluation functions and decision conditions of three-way decisions with game-theoretic rough sets , 2017, Eur. J. Oper. Res..

[15]  Wei Zhao,et al.  Intuitive distance for intuitionistic fuzzy sets with applications in pattern recognition , 2017, Applied Intelligence.

[16]  Zeshui Xu,et al.  Information fusion for intuitionistic fuzzy decision making: An overview , 2016, Information Fusion.

[17]  Miin-Shen Yang,et al.  On the J-divergence of intuitionistic fuzzy sets with its application to pattern recognition , 2008, Inf. Sci..

[18]  Javier Fernando Botía Valderrama,et al.  On LAMDA clustering method based on typicality degree and intuitionistic fuzzy sets , 2018, Expert Syst. Appl..

[19]  Dong-Ling Xu,et al.  Evidential reasoning rule for evidence combination , 2013, Artif. Intell..

[20]  Satish Kumar,et al.  A dissimilarity Jensen–Shannon divergence measure for intuitionistic fuzzy sets , 2018, Int. J. Intell. Syst..

[21]  Shyi-Ming Chen,et al.  Multiple attribute decision making based on interval-valued intuitionistic fuzzy sets, linear programming methodology, and the extended TOPSIS method , 2017, Inf. Sci..

[22]  Shu-Ping Wan,et al.  Atanassov's Intuitionistic Fuzzy Programming Method for Heterogeneous Multiattribute Group Decision Making With Atanassov's Intuitionistic Fuzzy Truth Degrees , 2014, IEEE Transactions on Fuzzy Systems.

[23]  Chang-Hua Hu,et al.  A New BRB-ER-Based Model for Assessing the Lives of Products Using Both Failure Data and Expert Knowledge , 2016, IEEE Transactions on Systems, Man, and Cybernetics: Systems.

[24]  Morteza Yazdani,et al.  A state-of the-art survey of TOPSIS applications , 2012, Expert Syst. Appl..

[25]  L. Kiemeney,et al.  Obesity, metabolic factors and risk of different histological types of lung cancer: A Mendelian randomization study , 2017, PloS one.

[26]  Sherali Zeadally,et al.  Multiple Attributes Decision Fusion for Wireless Sensor Networks Based on Intuitionistic Fuzzy Set , 2017, IEEE Access.

[27]  Peide Liu,et al.  Some Muirhead Mean Operators for Intuitionistic Fuzzy Numbers and Their Applications to Group Decision Making , 2017, PloS one.

[28]  Arthur P. Dempster,et al.  The Dempster-Shafer calculus for statisticians , 2008, Int. J. Approx. Reason..

[29]  Ying-Ming Wang,et al.  Evidence combination rule with contrary support in the evidential reasoning approach , 2017, Expert Syst. Appl..

[30]  Chunfang Liu,et al.  New aggregation operators of single-valued neutrosophic hesitant fuzzy set and their application in multi-attribute decision making , 2017, Pattern Analysis and Applications.

[31]  Zeshui Xu,et al.  Multi-person multi-attribute decision making models under intuitionistic fuzzy environment , 2007, Fuzzy Optim. Decis. Mak..

[32]  Qing Guo,et al.  Ensemble Interval-Valued Fuzzy Cognitive Maps , 2018, IEEE Access.

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

[34]  Peter Harremoës,et al.  Rényi Divergence and Kullback-Leibler Divergence , 2012, IEEE Transactions on Information Theory.

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

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

[37]  Adem Kiliçman,et al.  On the refinement of Jensen's inequality , 2015, Appl. Math. Comput..

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

[39]  Jian-Bo Yang,et al.  On the evidential reasoning algorithm for multiple attribute decision analysis under uncertainty , 2002, IEEE Trans. Syst. Man Cybern. Part A.

[40]  Shu Liu,et al.  Fractional programming methodology for multi-attribute group decision-making using IFS , 2009, Appl. Soft Comput..

[41]  Ming-yuan Chen,et al.  Some induced intuitionistic fuzzy aggregation operators applied to multi-attribute group decision making , 2011, Int. J. Gen. Syst..

[42]  Muhammad Akram,et al.  Novel intuitionistic fuzzy soft multiple-attribute decision-making methods , 2016, Neural Computing and Applications.

[43]  Shu-Ping Wan,et al.  A preference degree for intuitionistic fuzzy values and application to multi-attribute group decision making , 2016, Inf. Sci..

[44]  Jian-Bo Yang,et al.  The evidential reasoning approach for multi-attribute decision analysis under interval uncertainty , 2006, Eur. J. Oper. Res..

[45]  V. Lakshmana Gomathi Nayagam,et al.  An improved ranking method for comparing trapezoidal intuitionistic fuzzy numbers and its applications to multicriteria decision making , 2016, Neural Computing and Applications.

[46]  J. H. Park,et al.  Extension of the TOPSIS method for decision making problems under interval-valued intuitionistic fuzzy environment , 2011 .

[47]  Adamu I. Abubakar,et al.  A Review on Soft Set-Based Parameter Reduction and Decision Making , 2017, IEEE Access.

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

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

[50]  Jun Ye.  Multicriteria fuzzy decision-making method using entropy weights-based correlation coefficients of interval-valued intuitionistic fuzzy sets , 2010 .

[51]  Gülçin Büyüközkan,et al.  Application of a new combined intuitionistic fuzzy MCDM approach based on axiomatic design methodology for the supplier selection problem , 2017, Appl. Soft Comput..