Multiattribute decision making based on the binary connection number in set pair analysis under an interval-valued intuitionistic fuzzy set environment

A new multiattribute decision-making (MADM) methodology based on set pair analysis (SPA) for an interval-valued intuitionistic fuzzy set environment is developed in this paper. The connection number, which is known as a major component of SPA, provides a quantitative analysis to integrate the certainty and uncertainty as a combined system. First, we briefly review the concepts of interval-valued intuitionistic fuzzy sets (IVIFS) and the binary connection number (BCN). Then, the transformation method of interval-valued intuitionistic fuzzy numbers into BCNs is studied. Finally, we present a new MADM method where interval-valued intuitionistic fuzzy values are used to express evaluating values of alternatives on attributes, and weights are represented with real numbers or IVIFS. Some typical examples are presented to illustrate the feasibility and validity of the proposed approach.

[1]  Zeshui Xu,et al.  Entropy/cross entropy-based group decision making under intuitionistic fuzzy environment , 2012, Inf. Fusion.

[2]  Witold Pedrycz,et al.  Multi-attribute group decision making based on extended TOPSIS method under interval-valued intuitionistic fuzzy environment , 2018, Appl. Soft Comput..

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

[4]  Pei Wang,et al.  Entropy, similarity measure of interval-valued intuitionistic fuzzy sets and their applications , 2011, Inf. Sci..

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

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

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

[8]  Harish Garg,et al.  Generalized and group-based generalized intuitionistic fuzzy soft sets with applications in decision-making , 2017, Applied Intelligence.

[9]  Deng-Feng Li,et al.  TOPSIS-Based Nonlinear-Programming Methodology for Multiattribute Decision Making With Interval-Valued Intuitionistic Fuzzy Sets , 2010, IEEE Transactions on Fuzzy Systems.

[10]  Harish Garg,et al.  Generalized intuitionistic fuzzy interactive geometric interaction operators using Einstein t-norm and t-conorm and their application to decision making , 2016, Comput. Ind. Eng..

[11]  Harish Garg,et al.  TOPSIS method based on the connection number of set pair analysis under interval-valued intuitionistic fuzzy set environment , 2016, Computational and Applied Mathematics.

[12]  Jiang Yunliang,et al.  Quick attribute reduct algorithm for neighborhood rough set model , 2014 .

[13]  Harish Garg,et al.  Novel Single-Valued Neutrosophic Aggregated Operators Under Frank Norm Operation and Its Application to Decision-Making Process , 2017 .

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

[15]  Harish Garg,et al.  A Robust Ranking Method for Intuitionistic Multiplicative Sets Under Crisp, Interval Environments and Its Applications , 2017, IEEE Transactions on Emerging Topics in Computational Intelligence.

[16]  Zeshui Xu,et al.  Generalized point operators for aggregating intuitionistic fuzzy information , 2010 .

[17]  V. Lakshmana Gomathi Nayagam,et al.  An intuitionistic fuzzy multi-criteria decision-making method based on non-hesitance score for interval-valued intuitionistic fuzzy sets , 2017, Soft Comput..

[18]  Wang Zhongbin,et al.  Multi-Attribute Group Decision Making Based on Set Pair Analysis , 2012 .

[19]  Jin-Han Park,et al.  Correlation coefficient of interval-valued intuitionistic fuzzy sets and its application to multiple attribute group decision making problems , 2009, Math. Comput. Model..

[20]  Jian-qiang Wang,et al.  An approach to interval-valued intuitionistic stochastic multi-criteria decision-making using set pair analysis , 2018, Int. J. Mach. Learn. Cybern..

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

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

[23]  Harish Garg,et al.  Novel intuitionistic fuzzy decision making method based on an improved operation laws and its application , 2017, Eng. Appl. Artif. Intell..

[24]  Harish Garg,et al.  An advanced study on the similarity measures of intuitionistic fuzzy sets based on the set pair analysis theory and their application in decision making , 2018, Soft Computing.

[25]  Harish Garg,et al.  Connection number of set pair analysis based TOPSIS method on intuitionistic fuzzy sets and their application to decision making , 2017, Applied Intelligence.

[26]  Zeshui Xu,et al.  A method based on distance measure for interval-valued intuitionistic fuzzy group decision making , 2010, Inf. Sci..

[27]  GargHarish.  A New Generalized Pythagorean Fuzzy Information Aggregation Using Einstein Operations and Its Application to Decision Making , 2016 .

[28]  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.

[29]  Jun Ye,et al.  Multicriteria fuzzy decision-making method based on a novel accuracy function under interval-valued intuitionistic fuzzy environment , 2009, Expert Syst. Appl..

[30]  Yuan Yao,et al.  Systems information in set pair analysis and its applications , 2004, Proceedings of 2004 International Conference on Machine Learning and Cybernetics (IEEE Cat. No.04EX826).

[31]  Shyi-Ming Chen,et al.  Multiattribute Decision Making Based on Interval-Valued Intuitionistic Fuzzy Values and Linear Programming Methodology , 2016 .

[32]  Harish Garg,et al.  Distance measures for connection number sets based on set pair analysis and its applications to decision-making process , 2018, Applied Intelligence.

[33]  Cengiz Kahraman,et al.  Evaluation of research proposals for grant funding using interval-valued intuitionistic fuzzy sets , 2017, Soft Comput..

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

[35]  Junhua Hu,et al.  Dynamic stochastic multi-criteria decision making method based on cumulative prospect theory and set pair analysis , 2011 .

[36]  Miin-Shen Yang,et al.  Similarity measures of intuitionistic fuzzy sets based on Hausdorff distance , 2004, Pattern Recognit. Lett..

[37]  Yong Liu,et al.  Method and Applications for Multiple Attribute Decision-Making Based on Converting Triangular Fuzzy Numbers into Connection Numbers , 2017, Trans. Edutainment.

[38]  Manhua Liu,et al.  Fingerprint orientation field reconstruction by weighted discrete cosine transform , 2014, Inf. Sci..

[39]  D. Dubois,et al.  Hybrid Probabilistic-Possibilistic Mixtures and Utility Functions , 2000 .

[40]  Harish Garg,et al.  A New Generalized Pythagorean Fuzzy Information Aggregation Using Einstein Operations and Its Application to Decision Making , 2016, Int. J. Intell. Syst..

[41]  Tamalika Chaira,et al.  A novel intuitionistic fuzzy C means clustering algorithm and its application to medical images , 2011, Appl. Soft Comput..

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

[43]  Sha Fu,et al.  Triangular Fuzzy Number Multi-attribute Decision-making Method Based on Set-pair Analysis , 2016 .

[44]  Fan Jing,et al.  Quick attribute reduction with generalized indiscernibility models , 2017 .

[45]  Zeshui Xu,et al.  Induced generalized intuitionistic fuzzy operators , 2011, Knowl. Based Syst..

[46]  Zhenhua Xie,et al.  Fuzzy Multi-attribute Decision Making Methods Based on Improved Set Pair Analysis , 2013, 2013 Sixth International Symposium on Computational Intelligence and Design.

[47]  Zhang Su.  Method for Multiple Attribute Decision Making with Linguistic Assessment Information Based on Set Pair Analysis and Intuitionistic Fuzzy Set , 2008 .