Correlated aggregation operators for simplified neutrosophic set and their application in multi-attribute group decision making

The simplified neutrosophic set (SNS) is a generalization of the fuzzy set that is designed for some incomplete, uncertain and inconsistent situations in which each element has different truth membership, indeterminacy membership and falsity membership functions. In this paper, we propose the simplified neutrosophic correlated averaging (SNCA) operator and the simplified neutrosophic correlated geometric (SNCG) operator, and further study the properties of the operators. Then, an approach to multi-attribute group decision making (MAGDM) within the framework of SNS is developed by the proposed aggregation operators. Finally, a practical application of the developed approach to the problem of investment is given, and the result shows that our approach is reasonable and effective in dealing with uncertain decision making problems.

[1]  Hong-yu Zhang,et al.  Simplified neutrosophic sets and their applications in multi-criteria group decision-making problems , 2016, Int. J. Syst. Sci..

[2]  Xiaohong Su,et al.  Multiattribute Decision Making Based on Entropy under Interval-Valued Intuitionistic Fuzzy Environment , 2013 .

[3]  V. Torra,et al.  A framework for linguistic logic programming , 2010 .

[4]  G. Klir,et al.  Fuzzy Measure Theory , 1993 .

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

[6]  Guiwu Wei,et al.  Some induced correlated aggregating operators with intuitionistic fuzzy information and their application to multiple attribute group decision making , 2012, Expert Syst. Appl..

[7]  Ali Emrouznejad,et al.  Ordered Weighted Averaging Operators 1988–2014: A Citation‐Based Literature Survey , 2014, Int. J. Intell. Syst..

[8]  Lotfi A. Zadeh,et al.  Is there a need for fuzzy logic? , 2008, NAFIPS 2008 - 2008 Annual Meeting of the North American Fuzzy Information Processing Society.

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

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

[11]  Francisco Gallego Lupiáñez,et al.  Interval neutrosophic sets and topology , 2008, Kybernetes.

[12]  Ronald R. Yager,et al.  A framework for fuzzy recognition technology , 2000, IEEE Trans. Syst. Man Cybern. Part C.

[13]  Zeshui Xu,et al.  Choquet integrals of weighted intuitionistic fuzzy information , 2010, Inf. Sci..

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

[15]  Florentin Smarandache,et al.  Single valued neutrosophic trapezoid linguistic aggregation operators based multi-attribute decision making , 2014 .

[16]  Ronald R. Yager,et al.  Induced aggregation operators , 2003, Fuzzy Sets Syst..

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

[18]  Vicenc Torra,et al.  Information Fusion in Data Mining , 2003 .

[19]  Renato Pennacchi,et al.  Principles of an abstract theory of systems , 1972 .

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

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