Symmetry Measures of Simplified Neutrosophic Sets for Multiple Attribute Decision-Making Problems

A simplified neutrosophic set (containing interval and single-valued neutrosophic sets) can be used for the expression and application in indeterminate decision-making problems because three elements in the simplified neutrosophic set (including interval and single valued neutrosophic sets) are characterized by its truth, falsity, and indeterminacy degrees. Under a simplified neutrosophic environment, therefore, this paper firstly defines simplified neutrosophic asymmetry measures. Then we propose a normalized symmetry measure and a weighted symmetry measure of simplified neutrosophic sets and develop a simplified neutrosophic multiple attribute decision-making method based on the weighted symmetry measure. All alternatives can be ranked through the weighted symmetry measure between the ideal solution/alternative and each alternative, and then the best one can be determined. Finally, an illustrative example on the selection of manufacturing schemes (alternatives) in the flexible manufacturing system demonstrates the applicability of the proposed method in a simplified (interval and single valued) neutrosophic setting, and then the decision-making method based on the proposed symmetry measure is in accord with the ranking order and best choice of existing projection and bidirectional projection-based decision-making methods and strengthens the resolution/discrimination in the decision-making process corresponding to the comparative example.

[1]  uan-juan Penga,et al.  An outranking approach for multi-criteria decision-making problems with simplified neutrosophic sets , 2014 .

[2]  Jun Ye Vector Similarity Measures of Simplified Neutrosophic Sets and Their Application in Multicriteria Decision Making , 2014 .

[3]  Hong-yu Zhang,et al.  An Improved Weighted Correlation Coefficient Based on Integrated Weight for Interval Neutrosophic Sets and its Application in Multi-criteria Decision-making Problems , 2015, Int. J. Comput. Intell. Syst..

[4]  Jun Ye,et al.  Projection and bidirectional projection measures of single-valued neutrosophic sets and their decision-making method for mechanical design schemes , 2017, J. Exp. Theor. Artif. Intell..

[5]  Hong-yu Zhang,et al.  An outranking approach for multi-criteria decision-making problems with interval-valued neutrosophic sets , 2015, Neural Computing and Applications.

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

[7]  Romualdas Bausys,et al.  Model for residential house element and material selection by neutrosophic MULTIMOORA method , 2017, Engineering applications of artificial intelligence.

[8]  Bijan Davvaz,et al.  Properties of single-valued neutrosophic graphs , 2018, Journal of Intelligent & Fuzzy Systems.

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

[10]  Guan Hongjun,et al.  Interval valued neutrosophic sets and multi-attribute decision-making based on generalized weighted aggregation operator , 2015 .

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

[12]  Peide Liu,et al.  Some Generalized Neutrosophic Number Hamacher Aggregation Operators and Their Application to Group Decision Making , 2014 .

[13]  Romualdas Bausys,et al.  Garage location selection for residential house by WASPAS-SVNS method , 2017 .

[14]  Yao Ouyang,et al.  Interval neutrosophic numbers Choquet integral operator for multi-criteria decision making , 2015, J. Intell. Fuzzy Syst..

[15]  Elyas Shivanian,et al.  AN EXTENDED METHOD USING TOPSIS AND VIKOR FOR MULTIPLE ATTRIBUTE DECISION MAKING WITH MULTIPLE DECISION MAKERS AND SINGLE VALUED NEUTROSOPHIC NUMBERS , 2017 .

[16]  Peide Liu,et al.  Interval neutrosophic prioritized OWA operator and its application to multiple attribute decision making , 2016, J. Syst. Sci. Complex..

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

[18]  Hong-yu Zhang,et al.  outranking approach for multi-criteria decision-making problems ith simplified neutrosophic sets uan - , 2014 .

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

[20]  Jun Ye,et al.  Another Form of Correlation Coefficient between Single Valued Neutrosophic Sets and Its Multiple Attribute Decision Making Method , 2019 .

[21]  Jun Ye,et al.  Simplified neutrosophic harmonic averaging projection-based method for multiple attribute decision-making problems , 2015, International Journal of Machine Learning and Cybernetics.

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

[23]  Peide Liu,et al.  Multiple attribute decision-making method based on single-valued neutrosophic normalized weighted Bonferroni mean , 2014, Neural Computing and Applications.

[24]  Surapati Pramanik,et al.  TOPSIS method for multi-attribute group decision-making under single-valued neutrosophic environment , 2014, Neural Computing and Applications.

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

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