The Energy of rough neutrosophic matrix and its application to MCDM problem for selecting the best building construction site

Authors

  • Jeni Seles Martina Donbosco Department of Mathematics, VIT University, Vellore, India
  • Deepa Ganesan Department of Mathematics, VIT University, Vellore, India

DOI:

https://doi.org/10.31181/dmame0305102022d

Keywords:

Rough set, rough neutrosophic set, rough neutrosophic matrix, energy of rough neutrosophic matrix, multi-criteria decision making

Abstract

An approach to data processing for relational databases is called a rough set theory. It is an interesting area of uncertainty mathematics that is mainly related to fuzzy theory. Rough set theory and neutrosophic set theory can be joined to create a powerful tool for dealing with indeterminacy. Neutrosophic matrices help decision-makers deal with multi-criteria decision-making by providing them with more useful and practical when we apply the concept of matrix energy. In this paper, we defined a Rough neutrosophic matrix and its energy. Some propositions, lower and upper limits of the rough neutrosophic matrix's energy were derived. The proposed energy of the rough neutrosophic matrix was applied in multi-criteria decision-making problems. The problem is to select the best place for constructing the school building. Applying the energy method to the MCDM problem became more relatable and produced good results.

Downloads

Download data is not yet available.

References

Alias, S., Mohamad, D., & Shuib, A. (2017). Rough neutrosophic multisets. Neutrosophic Sets Systems, 16, 80-88.

Arora, H. D., & Naithani, A. (2022). Significance of TOPSIS approach to MADM in computing exponential divergence measures for pythagorean fuzzy sets. Decision Making: Applications in Management and Engineering, 5(1), 246-263.

Bao, Z., Yang, S., & Zhao, J. (2014). Rough Fuzzy Set Model for Set-Valued Ordered Fuzzy Decision System. In International Conference on Rough Sets and Knowledge Technology (pp. 673-682). Springer, Cham.

Bo, C., Zhang, X., Shao, S., & Smarandache, F. (2018). New multigranulation neutrosophic rough set with applications. Symmetry, 10(11), 578.

Bravo, D., Cubria, F., & Rada, J. (2017). Energy of matrices. Applied Mathematics and Computation, 312, 149-157.

Broumi, S., Smarandache, & F., Dhar, M. (2014). Rough neutrosophic sets. Italian journal of pure and applied mathematics, 32, 493-502.

Broumi, S., & Smarandache, F. (2015). Interval neutrosophic rough set. Neutrosophic Sets and Systems, 7(1), 23-31.

Das, M., Mohanty, D., & Parida, K. C. (2021). On the neutrosophic soft set with rough set theory. Soft Computing, 25(21), 13365-13376.

Dhar, M., Broumi, S., & Smarandache, F. A (2014). note on square neutrosophic fuzzy matrices. Neutrosophic Sets and Systems 3, 37-41.

Gong, Z., Sun, B., & Chen, D. (2008). Rough set theory for the interval-valued fuzzy information systems. Information Sciences, 178(8), 1968-1985.

Gorcun, O. F., Senthil, S., & Kucukonder, H. (2021). Evaluation of tanker vehicle selection using a novel hybrid fuzzy MCDM technique. Decision Making: Applications in Management and Engineering, 4(2), 140-162.

Jin, Q., Hu, K., Bo, C., & Li, L. (2021). A New Single-Valued Neutrosophic Rough Sets and Related Topology. Journal of Mathematics, 2021, 1-14.

Kandasamy, W. V., & Smarandache, F. (2004). Fuzzy relational maps and neutrosophic relational maps (pp. 222-246). HEXIS Church Rock.

Kryszkiewicz, M. (1998). Rough set approach to incomplete information systems. Information sciences, 112(1-4), 39-49.

Mondal, K., & Pramanik, S. (2015). Rough neutrosophic multi-attribute decision-making based on grey relational analysis. Neutrosophic Sets and Systems, 7, 8-17.

Otay, I. (2022). Intuitive fuzzy multi-expert & multi-criteria decision-making methodology: An application in healthcare industry. Journal of the Faculty of Engineering and Architecture of Gazi University, 37(2), 1047-1062.

Pal, M., Khan, S. K., & Shyamal, A. K. (2002). Intuitionistic fuzzy matrices. Notes on Intuitionistic Fuzzy Sets, 8(2), 51-62.

Pawlak, Z. (1982). Rough Sets, International Journal of Computer and Information Sciences, 11, 341-356.

Pawlak, Z. (1985). Rough sets and fuzzy sets. Fuzzy sets and Systems, 17(1), 99-102.

Pramanik, S., Roy, R., Roy, T. K., & Smarandache, F. (2017). Multi criteria decision making using correlation coefficient under rough neutrosophic environment. 17, 29-36.

Rizvi, S., Naqvi, H. J., & Nadeem, D. (2002). Rough Intuitionistic Fuzzy Sets, Proceedings of the 6th Joint Conference on Information Science, 13, 101-104.

Samuel, A. E., & Narmadhagnanam, R. (2018). Rough Neutrosophic Sets in Medical Diagnosis. International Journal of Pure and Applied Mathematics, 120(8), 79-87.

Samuel, A. E., & Narmadhagnanam, R. (2019). Pi-distance of rough Neutrosophic sets for medical diagnosis. Neutrosophic Sets and Systems, 28, 51-57.

Sharma, H. K., Kumari, K., & Kar, S. (2018). Air passengers forecasting for Australian airline based on hybrid rough set approach. Journal of Applied Mathematics, Statistics and Informatics, 14(1), 5-18.

Sharma, H. K., Kumari, K., & Kar, S. (2021). Forecasting Sugarcane Yield of India based on rough set combination approach. Decision Making: Applications in Management and Engineering, 4(2), 163-177.

Sharma, H. K., Singh, A., Yadav, D., & Kar, S. (2022). Criteria selection and decision making of hotels using Dominance Based Rough Set Theory. Operational Research in Engineering Sciences: Theory and Applications, 5(1), 41-55.

Smarandache, F. (1998). Neutrosophy, Neutrosophic probability, set, and logic, ProQuest Information and Learning, 105, (pp. 118-123). Ann Arbor, Michigan, USA.

Thomason, M. G. (1977). Convergence of powers of a fuzzy matrix. Journal of mathematical analysis and applications, 57(2), 476-480.

Wang, J., & Zhang, X. (2022). A novel multi-criteria decision-making method based on rough sets and fuzzy measures. Axioms, 11(6), 275.

Wu, W. Z., Mi, J. S., & Zhang, W. X. (2003). Generalized fuzzy rough sets. Information sciences, 151, 263-282.

Yang, H. L., Zhang, C. L., Guo, Z. L., Liu, Y. L., & Liao, X. (2017). A hybrid model of single valued neutrosophic sets and rough sets: single valued neutrosophic rough set model. Soft Computing, 21(21), 6253-6267.

Zadeh, L. A. (1965). Fuzzy sets. Information and control, 8(3), 338-353.

Zhang, Z. (2012). On interval type-2 rough fuzzy sets. Knowledge-Based Systems, 35, 1-13.

Zhang, C., Li, D., Broumi, S., & Sangaiah, A. K. (2018). Medical diagnosis based on single-valued neutrosophic probabilistic rough multisets over two universes. Symmetry, 10(6), 213.

Downloads

Published

2022-10-05

How to Cite

Donbosco, J. S. M. ., & Ganesan, D. . (2022). The Energy of rough neutrosophic matrix and its application to MCDM problem for selecting the best building construction site. Decision Making: Applications in Management and Engineering, 5(2), 30–45. https://doi.org/10.31181/dmame0305102022d

Issue

Vol. 5 No. 2 (2022): Decision Making: Applications in Management and Engineering

Section

Regular articles

License

Copyright (c) 2022 Decision Making: Applications in Management and Engineering

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.