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Sine Trigonometry Operational Laws for Complex Neutrosophic Sets and Their Aggregation Operators in Material Selection

D. Ajay1, J. Aldring1, G. Rajchakit2, P. Hammachukiattikul3, N. Boonsatit4,*
1 Sacred Heart College (Autonomous), Tamil Nadu, 635601, India
2 Maejo University, Chiang Mai, 50290, Thailand
3 Phuket Rajabhat University, Phuket, 83000, Thailand
4 Rajamangala University of Technology Suvarnabhumi, Nonthaburi, 11000, Thailand
* Corresponding Author:N. Boonsatit. Email:
(This article belongs to this Special Issue: Advances in Neutrosophic and Plithogenic Sets for Engineering and Sciences: Theory, Models, and Applications (ANPSESTMA))

Computer Modeling in Engineering & Sciences 2022, 130(2), 1033-1076.

Received 11 July 2021; Accepted 07 September 2021; Issue published 13 December 2021


In this paper, sine trigonometry operational laws (ST-OLs) have been extended to neutrosophic sets (NSs) and the operations and functionality of these laws are studied. Then, extending these ST-OLs to complex neutrosophic sets (CNSs) forms the core of this work. Some of the mathematical properties are proved based on ST-OLs. Fundamental operations and the distance measures between complex neutrosophic numbers (CNNs) based on the ST-OLs are discussed with numerical illustrations. Further the arithmetic and geometric aggregation operators are established and their properties are verified with numerical data. The general properties of the developed sine trigonometry weighted averaging/geometric aggregation operators for CNNs (ST-WAAO-CNN & ST-WGAO-CNN) are proved. A decision making technique based on these operators has been developed with the help of unsupervised criteria weighting approach called Entropy-ST-OLs-CNDM (complex neutrosophic decision making) method. A case study for material selection has been chosen to demonstrate the ST-OLs of CNDM method. To check the validity of the proposed method, entropy based complex neutrosophic CODAS approach with ST-OLs has been executed numerically and a comparative analysis with the discussion of their outcomes has been conducted. The proposed approach proves to be salient and effective for decision making with complex information.


Complex neutrosophic sets (CNSs); sine trigonometric operational laws (ST-OLs); aggregation operator; entropy; CODAS; material selection; decision making

Cite This Article

Ajay, D., Aldring, J., Rajchakit, G., Hammachukiattikul, P., Boonsatit, N. (2022). Sine Trigonometry Operational Laws for Complex Neutrosophic Sets and Their Aggregation Operators in Material Selection. CMES-Computer Modeling in Engineering & Sciences, 130(2), 1033–1076.

This work is licensed under a Creative Commons Attribution 4.0 International License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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