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Some Weighted Aggregation Operators of Trapezoidal Neutrosophic Numbers and Their Multiple Attribute Decision Making Method
Volume 28, Issue 2 (2017), pp. 387–402
Pub. online: 1 January 2017      Type: Research Article      Open accessOpen Access
Received
1 January 2015
Accepted
1 January 2016
Published
1 January 2017

Abstract

This paper proposes the concepts of a neutrosophic number and a trapezoidal neutrosophic number (TNN), the basic operational relations of TNNs, and the score function of TNN. Then, we develop a trapezoidal neutrosophic weighted arithmetic averaging (TNWAA) operator and a trapezoidal neutrosophic weighted geometric averaging (TNWGA) operator to aggregate TNN information and investigate their properties. Furthermore, a multiple attribute decision making method based on the TNWAA and TNWGA operators and the score function of TNN is established under a TNN environment. Finally, an illustrative example of investment alternatives is given to demonstrate the application and effectiveness of the developed approach.

References

 
Atanassov, K. (1986). Intuitionistic fuzzy sets. Fuzzy Sets and Systems, 20, 87–96.
 
Atanassov, K., Gargov, G. (1989). Interval valued intuitionistic fuzzy sets. Fuzzy Sets and Systems, 31, 343–349.
 
Biswas, P., Pramanik, S., Giri, B.C. (2014). A new methodology for neutrosophic multi-attribute decision-making with unknown weight information. Neutrosophic Sets and Systems, 3, 42–50.
 
Broumi, S., Smarandache, F. (2014). Cosine similarity measure of interval valued neutrosophic sets. Neutrosophic Sets and Systems, 5, 15–20.
 
Broumi, S., Smarandache, F. (2015). New operations on interval neutrosophic sets. Journal of New Theory, 1, 24–37.
 
Chi, P.P., Liu, P.D. (2013). An extended TOPSIS method for the multiple attribute decision making problems based on interval neutrosophic sets. Neutrosophic Sets and Systems, 1, 63–70.
 
Liu, P., Yu, X. (2013). Density aggregation operators based on the intuitionistic trapezoidal fuzzy numbers for multiple attribute decision making. Technological and Economic Development of Economy, 19(sup1), S454–S470.
 
Liu, P.D., Chu, Y.C., Li, Y.W., Chen, Y.B. (2014). Some generalized neutrosophic number Hamacher aggregation operators and their application to group decision making. International Journal of Fuzzy Systems, 16(2), 242–255.
 
Meng, F., Chen, X. (2014). An approach to interval-valued hesitant fuzzy multi-attribute decision making with incomplete weight information based on hybrid Shapley operators. Informatica, 25(4), 617–642.
 
Smarandache, F. (1999). A Unifying Field in Logics. Neutrosophy: Neutrosophic Probability, Set and Logic. American Research Press, Rehoboth.
 
Turksen, I. (1986). Interval valued fuzzy sets based on normal forms. Fuzzy Sets and Systems, 20, 191–210.
 
Wan, S., Dong, J. (2014). Multi-attribute group decision making with trapezoidal intuitionistic fuzzy numbers and application to stock selection. Informatica, 25(4), 663–697.
 
Wang, W., Liu, X. (2014). Some hesitant fuzzy geometric operators and their application to multiple attribute group decision making. Technological and Economic Development of Economy, 20(3), 371–390.
 
Wang, J.Q., Zhang, Z. (2009). Aggregation operators on intuitionistic trapezoidal fuzzy number and its application to multi-criteria decision making problems. Systems Engineering and Electronics, 20(2), 321–326.
 
Wang, H., Smarandache, F., Zhang, Y.Q., Sunderraman, R. (2005). Interval Neutrosophic Sets and Logic: Theory and Applications in Computing. Hexis, Phoenix, AZ.
 
Wang, H., Smarandache, F., Zhang, Y.Q., Sunderraman, R. (2010). Single valued neutrosophic sets. Multispace and Multistructure, 4, 410–413.
 
Ye, J. (2013). Multicriteria decision-making method using the correlation coefficient under single-valued neutrosophic environment. International Journal of General Systems, 42(4), 386–394.
 
Ye, J. (2014a). Similarity measures between interval neutrosophic sets and their applications in multicriteria decision-making. Journal of Intelligent and Fuzzy Systems, 26, 165–172.
 
Ye, J. (2014b). Single valued neutrosophic cross-entropy for multicriteria decision making problems. Applied Mathematical Modelling, 38, 1170–1175.
 
Ye, J. (2014c). A multicriteria decision-making method using aggregation operators for simplified neutrosophic sets. Journal of Intelligent and Fuzzy Systems, 26, 2459–2466.
 
Ye, J. (2014d). Vector similarity measures of simplified neutrosophic sets and their application in multicriteria decision making. International Journal of Fuzzy Systems, 16(2), 204–211.
 
Ye, J. (2014e). Some aggregation operators of interval neutrosophic linguistic numbers for multiple attribute decision making. Journal of Intelligent and Fuzzy Systems, 27(5), 2231–2241.
 
Zadeh, L.A. (1965). Fuzzy sets. Information and Control, 8(5), 338–353.
 
Zhang, Z., Wu, C. (2014). A novel method for single valued neutrosophic multi-criteria decision making with incomplete weight information. Neutrosophic Sets and Systems, 4, 35–49.
 
Zhang, H.Y., Wang, J.Q., Chen, X.H. (2014). Interval neutrosophic sets and their application in multicriteria decision making problems. The Scientific World Journal, 2014.
 
Zhou, W., He, J.M. (2014). Interval-valued intuitionistic fuzzy ordered precise weighted aggregation operator and its application in group decision making. Technological and Economic Development of Economy, 20(4), 648–672.

Biographies

Ye Jun
yehjun@aliyun.com

J. Ye graduated and received his MS degree in automation and robotics from the Technical University of Koszalin, Poland in 1997. From February 2012 to August 2012, he was a visiting scholar in the School of Engineering of Southern Polytechnic State University in USA. Now, he is a professor in the Department of Electrical and Information Engineering, Shaoxing University, China. He has more than 30 years of experience in teaching and research. His research interests include soft computing, fuzzy decision-making, pattern recognitions, fault diagnosis, robotics, and intelligent control. He has published more than one hundred papers in journals. He has written a few books related to his research work. He has finished a few projects sponsored by government of China.


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Open access article under the CC BY license.

Keywords
trapezoidal neutrosophic number score function trapezoidal neutrosophic weighted arithmetic averaging (TNWAA) operator trapezoidal neutrosophic weighted geometric averaging (TNWGA) operator multiple attribute decision making

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