Interval neutrosophic numbers Choquet integral operator for multi-criteria decision making

In this paper, the Choquet integral and the interval neutrosophic set theory are combined to make multi-criteria decision for problems under neutrosophic fuzzy environment. Firstly, a ranking index is proposed according to its geometrical structure, and an approach for comparing two interval neutrosophic numbers is given. Then, a ≤L implied operation-invariant total order which satisfies order-preserving condition is proposed. Secondly, an interval neutrosophic number Choquet integral (INNCI) operator is established and a detailed discussion on its aggregation properties is presented. In addition, the procedure of multi-criteria decision making based on INNCI operator is given. Finally, a practical example for selecting the third party logistics providers is provided to illustrate the feasibility of the developed approach.

[1]  Rajshekhar Sunderraman,et al.  Single Valued Neutrosophic Sets , 2010 .

[2]  Jun Ye,et al.  Similarity measures between interval neutrosophic sets and their applications in multicriteria decision-making , 2014, J. Intell. Fuzzy Syst..

[3]  Jun Ye,et al.  Multicriteria decision-making method using the correlation coefficient under single-valued neutrosophic environment , 2013, Int. J. Gen. Syst..

[4]  F. Smarandache.  A Unifying Field in Logics: Neutrosophic Logic. , 1999 .

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

[6]  Jean-Luc Marichal,et al.  Dependence between criteria and multiple criteria decision aid , 1998 .

[7]  Qiang Zhang,et al.  Intuitionistic fuzzy-valued Choquet integral and its application in multicriteria decision making , 2013, Inf. Sci..

[8]  菅野 道夫,et al.  Theory of fuzzy integrals and its applications , 1975 .

[9]  Hsiang-chuan Liu.  Liu's Generalized Intuitionistic Fuzzy Sets , 2010 .

[10]  Xiaohong Chen,et al.  Intuitionistic fuzzy Choquet integral operator for multi-criteria decision making , 2010, Expert Syst. Appl..

[11]  Christophe Labreuche,et al.  The Choquet integral for the aggregation of interval scales in multicriteria decision making , 2003, Fuzzy Sets Syst..

[12]  M. Sugeno,et al.  Fuzzy Measures and Integrals: Theory and Applications , 2000 .

[13]  Hsiang-Chuan Liu.  Choquet integral on Liu's generalized intuitionistic fuzzy numbers , 2010, 2010 International Conference on Machine Learning and Cybernetics.

[14]  Sunil Jacob John.  Generalized Intuitionistic Fuzzy Soft Sets and Its Applications , 2011 .

[15]  Michel Grabisch,et al.  Classification by fuzzy integral: performance and tests , 1994, CVPR 1994.

[16]  Jun Ye.  Single valued neutrosophic cross-entropy for multicriteria decision making problems , 2014 .

[17]  Michel Grabisch,et al.  A review of methods for capacity identification in Choquet integral based multi-attribute utility theory: Applications of the Kappalab R package , 2008, Eur. J. Oper. Res..

[18]  Hong-yu Zhang,et al.  Interval Neutrosophic Sets and Their Application in Multicriteria Decision Making Problems , 2014, TheScientificWorldJournal.

[19]  George J. Klir,et al.  Genetic algorithms for determining fuzzy measures from data , 1998, J. Intell. Fuzzy Syst..

[20]  Umberto Rivieccio,et al.  Neutrosophic logics: Prospects and problems , 2008, Fuzzy Sets Syst..

[21]  Peide Liu,et al.  An Extended TOPSIS Method for the Multiple Attribute Decision Making Problems Based on Interval Neutrosophic Set , 2014 .

[22]  Jean-Luc Marichal,et al.  An axiomatic approach of the discrete Choquet integral as a tool to aggregate interacting criteria , 2000, IEEE Trans. Fuzzy Syst..

[23]  Jean-Luc Marichal,et al.  An axiomatic approach to the definition of the entropy of a discrete Choquet capacity , 2005, Inf. Sci..

[24]  Michel Grabisch,et al.  The representation of importance and interaction of features by fuzzy measures , 1996, Pattern Recognit. Lett..

[25]  F. Smarandache,et al.  Correlation Coefficient of Interval Neutrosophic Set , 2013 .

[26]  Yanqing Zhang,et al.  Interval Neutrosophic Sets and Logic: Theory and Applications in Computing , 2005, ArXiv.

[27]  Michel Grabisch,et al.  A new algorithm for identifying fuzzy measures and its application to pattern recognition , 1995, Proceedings of 1995 IEEE International Conference on Fuzzy Systems..

[28]  Ranjit Biswas,et al.  Some operations on intuitionistic fuzzy sets , 2000, Fuzzy Sets Syst..

[29]  Hsiang-Chuan Liu.  An addition-invariant partial order of ordered addition monoids of intuitionistic fuzzy values , 2010, 2010 International Symposium on Computer, Communication, Control and Automation (3CA).

[30]  Michel Grabisch,et al.  K-order Additive Discrete Fuzzy Measures and Their Representation , 1997, Fuzzy Sets Syst..

[31]  Jun Ye,et al.  A multicriteria decision-making method using aggregation operators for simplified neutrosophic sets , 2014, J. Intell. Fuzzy Syst..

[32]  E. Pap.  Null-Additive Set Functions , 1995 .

[33]  M. Grabisch.  The application of fuzzy integrals in multicriteria decision making , 1996 .

[34]  Jun Ye.  Another Form of Correlation Coefficient between Single Valued Neutrosophic Sets and Its Multiple Attribute Decision- Making Method , 2013 .