Research Article
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Decision-making using the correlation coefficient measures of intuitionistic fuzzy rough graph

Year 2024, Volume: 53 Issue: 6, 1774 - 1797, 28.12.2024

Shaik Noorjahan , Sharief Basha Shaik

https://doi.org/10.15672/hujms.1486239

Abstract

The hybrid approach produced by combining mathematical representations of intuitionistic fuzzy sets and rough sets is called an intuitionistic fuzzy rough framework. This novel approach addresses vagueness and soft computation by using the lower and upper approximation spaces. The degree of connection between intuitionistic fuzzy rough preference relations is assessed in this study using the correlation coefficient method. An improved comprehension of the link between fuzzy elements is made possible by the superior features of the suggested correlation coefficient measure over the current one. An intuitionistic fuzzy rough environment in which attribute decision-making is based on integrated with the correlation coefficient measure. Additionally, a novel method for determining expert weights based on intuitionistic fuzzy rough preference relations uncertainty and the degree of each intuitionistic fuzzy rough preference relations's correlation coefficient is proposed in the paper. The correlation coefficient measurements between each option and the optimal choice are used in the study to calculate the ranking order of the alternatives. Finally, we introduce a cooperative decision-making method in a cotton seed; this concept may be developed in several advantageous cotton seedlings.

Keywords

Intuitionistic fuzzy rough graph correlation coefficient energy intuitionistic fuzzy rough preference relationship decision-making problem.

Ethical Statement

Nil

Supporting Institution

Vellore Institute of Technology

Project Number

Nil

Thanks

Vellore Institute of Technology

References

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  • [2] M. Akram and S. Zahid, Group decision-making method with Pythagorean fuzzy rough number for the evaluation of best design concept, Granular Comput. 8 (6), 1121-1148, 2023.
  • [3] N. K. Akula and S. B. Shaik, Correlation Coefficient Measure of Intuitionistic Fuzzy Graphs with Application in Money Investing Schemes, Comput. Inform. 42 (2), 436- 456, 2023.
  • [4] M. I. Ali, F. Feng, T. Mahmood, I. Mahmood and H. Faizan, SA graphical method for ranking Atanassovs intuitionistic fuzzy values using the uncertainty index and entropy, Int. J. Intell. Syst. 34 (10), 2692-2712, 2019.
  • [5] W. Ali, T. Shaheen, H. G. Toor, T. Alballa, A. Alburaikan and H. A. E. W. Khalifa, An Improved Intuitionistic Fuzzy Decision-Theoretic Rough Set Model and Its Application, Axioms. 12 (11), 1003, 2023.
  • [6] K. T. Atanassov, Intuitionistic fuzzy sets, Fuzzy sets syst. 20, 87-96, 1986.
  • [7] S. Ayub, M. Shabir, M. Riaz, W. Mahmood, D. Bozanic and D. Marinkovic, Linear Diophantine fuzzy rough sets: A new rough set approach with decision making, Symmetry. 14 (3), 525, 2022.
  • [8] J. Bajaj and S. Kumar, A new intuitionistic fuzzy correlation coefficient approach with applications in multi-criteria decision-making, Decis. Anal. J. 9, 100340, 2023.
  • [9] R. Balakrishnan, The energy of a graph, Linear Algebra its Appl. 387, 287-295, 2004.
  • [10] Z. Bashir, M. G. Abbas Malik, S. Asif and T. Rashid, The topological properties of intuitionistic fuzzy rough sets, J. Int. Fuzzy Syst. 38 (1), 795-807, 2020.
  • [11] P. Bhattacharya, Some remarks on fuzzy graphs, Pattern Recognit. Lett. 6 (5), 297- 302, 1987.
  • [12] D. Bozanic, I. Epler, A. Puska, S. Biswas, D. Marinkovic and S. Koprivica, Application of the DIBR II rough MABAC decision-making model for ranking methods and techniques of lean organization systems management in the process of technical maintenance, Facta Universitatis-Series Mech. Eng. 22 (1), 101-123, 2023
  • [13] R. Chinram, A. Hussain, T. Mahmood and M. I. Ali, EDAS method for multi-criteria group decision making based on intuitionistic fuzzy rough aggregation operators, IEEE. 9, 10199-10216, 2021.
  • [14] C. L. Chowdhary and D. P. Acharjya, A hybrid scheme for breast cancer detection using intuitionistic fuzzy rough set technique, Int. J. Healthcare Inf. Sys. Inf. 11 (2), 38-61, 2016.
  • [15] C. Cornelis, M. De Cock and E. E. Kerre, Intuitionistic fuzzy rough sets: At the crossroads of imperfect knowledge, Expert Syst. 20 (5), 260-270, 2003, 2019.
  • [16] C. Dhankhar and K. Kumar, Multi-attribute decision-making based on the advanced possibility degree measure of intuitionistic fuzzy numbers, Granular comput. 8 (3), 467-478, 2023.
  • [17] D. Dubois and H. Prade, Rough fuzzy sets and fuzzy rough sets, Int. J. Gen. Syst. 17 (2-3), 191-209, 1990.
  • [18] I. U. Haq, T. Shaheen, H. Toor, T. Senapati and S. Moslem, Incomplete Dominancebased Intuitionistic Fuzzy Rough Sets and their Application in Estimation of Inflation Rates in the Least Developed Countries, IEEE. 2023.
  • [19] Y. He, H. Chen, L. Zhou, J. Liu and Z. Tao, Intuitionistic fuzzy geometric interaction averaging operators and their application to multi-criteria decision making, Inf. Sci. 259, 142-159, 2014.
  • [20] G. R. Jahanshahloo, F. H. Lotfi and M. Izadikhah, Extension of the TOPSIS method for decision-making problems with fuzzy data, Appl. Math. Comput. 181 (2), 1544- 1551, 2006.
  • [21] T. Mahmood, J. Ahmmad, Z. Ali and M. S. Yang, Confidence level aggregation operators based on intuitionistic fuzzy rough sets with application in medical diagnosis, IEEE. 11, 8674-8688, 2023.
  • [22] T. Mahmood, J. Ahmmad, U. U. Rehman and M. B. Khan, Analysis and prioritization of the factors of the robotic industry with the assistance of EDAS technique based on intuitionistic fuzzy rough Yager aggregation operators, IEEE. 11, 50462-50479, 2023.
  • [23] H. M. Malik and M. Akram, A new approach based on intuitionistic fuzzy rough graphs for decision-making, J. Int. Fuzzy Syst. 34 (4), 2325-2342, 2018.
  • [24] F. A. Mazarbhuiya and M. Shenify, An Intuitionistic Fuzzy-Rough Set-Based Classification for Anomaly Detection, Appl. Sci. 13 (9), 5578, 2023.
  • [25] A. R. Mishra, P. Rani, F. Cavallaro and A. F. Alrasheedi, Assessment of sustainable wastewater treatment technologies using interval-valued intuitionistic fuzzy distance measure-based MAIRCA method, Facta Universitatis-Series: Mech. Eng. 21 (3), 359 -386, 2023.
  • [26] I. Nazeer, T. Rashid and A. Keikha, An application of product of intuitionistic fuzzy incidence graphs in textile industry, Complexity. 2021, 1-16, 2021.
  • [27] S. Noorjahan and S. Sharief Basha, Developing an intuitionistic fuzzy rough new correlation coefficient approach for enhancing robotic vacuum cleaner, Science Progress. 107 (3), 1-28, 2024.
  • [28] Z. Pawlak, Rough sets, Int. J. Computer & Inf. Sci. 11, 341-356, 1982.
  • [29] Z. Pawlak and A. Skowron, Rudiments of rough sets, Inf. Sci. 177 (1), 3-27, 2007.
  • [30] B. Praba, V. M. Chandrasekaran and G. Deepa, Energy of an intuitionistic fuzzy graph, Ital. J. Pure Appl Math. 32, 431-444, 2014.
  • [31] S. M. Qurashi and M. Shabir, Roughness in quantale modules, J. Int. Fuzzy Sys. 35 (2), 2359-2372, 2018.
  • [32] Y. Rao, Q. Zhou, M. Akhoundi, A. A. Talebi, S. Omidbakhsh Amiri and G. Muhiuddin, Novel concepts in rough Cayley fuzzy graphs with applications, J. Math. 2023, 1-11, 2023.
  • [33] N. R. Reddy, and S. S. Basha, The correlation coefficient of hesitancy fuzzy graphs in decision making, Comput. Syst. Sci. Eng. 46, 579- 596, 2023.
  • [34] B. Said, M. Lathamaheswari, P. K. Singh, A. A. Ouallane, A. Bakhouyi, A. Bakali and N. Deivanayagampillai, An intelligent traffic control system using neutrosophic sets, rough sets, graph theory, fuzzy sets and its extended approach: a literature review, Neutrosophic Sets Syst. 50, 10-26, 2022.
  • [35] M. Sarwar, M. Akram and F. Zafar, Decision making approach based on competition graphs and extended TOPSIS method under bipolar fuzzy environment, Math. Comput. Appl. 23, 117, 2018.
  • [36] M. R. Seikh and U. Mandal, Intuitionistic fuzzy Dombi aggregation operators and their application to multiple attribute decision-making, Granular Comput. 6, 473-488, 2021.
  • [37] M. A. Shumrani, S. Topal, F. Smarandache and C. Ozel, Covering-based rough fuzzy, intuitionistic fuzzy and neutrosophic nano topology and applications, IEEE. 7, 172839- 172846, 2019.
  • [38] S. Singh and T. Som, Intuitionistic Fuzzy Rough Sets: Theory to Practice, Math. Comput. Sci. and Eng. 91-133, 2022.
  • [39] P. Sivaprakasam and M. Angamuthu, Generalized Z-fuzzy soft - covering based rough matrices and its application to MAGDM problem based on AHP method, Decision Making: Appl. in Manage. Eng. 6 (1), 134152, 2023.
  • [40] A. K. Tiwari, A. Nath, R. K. Pandey and P. Maratha, A novel intuitionistic fuzzy rough instance selection and attribute reduction with kernelized intuitionistic fuzzy Cmeans clustering to handle imbalanced datasets, Expert Sys. with Appli. 251, 124087, 2024.
  • [41] A. K. Tiwari, R. Saini, A. Nath, P. Singh and M. A. Shah, Hybrid similarity relation based mutual information for feature selection in intuitionistic fuzzy rough framework and its applications, Scientific Reports. 14 (1), 5958, 2024.
  • [42] D. K. Tripathi, S. K. Nigam, P. Rani and A. R. Shah, New intuitionistic fuzzy parametric divergence measures and score function-based CoCoSo method for decisionmaking problems, Decision Making: Appl. in Manage. Eng. 6 (1), 535563, 2023.
  • [43] Y. H. Wang, Z. F. Shan and L. Huang, The extension of TOPSIS method for multi-attribute decision-making with q-rung orthopair hesitant fuzzy sets, IEEE. 8, 165151165167, 2020.
  • [44] J. Wang and X. Zhang, Two types of intuitionistic fuzzy covering rough sets and an application to multiple criteria group decision making, Symmetry. 10 (10), 462, 2018.
  • [45] F. Xiao, A distance measure for intuitionistic fuzzy sets and its application to pattern classification problems, IEEE Trans. Syst. Man, and Cybernetics: Syst. 51 (6), 3980- 3992, 2019.
  • [46] Z. Xu, Intuitionistic fuzzy aggregation, IEEE Trans. Fuzzy Systs. 15 (6), 1179-1187, 2007.
  • [47] W. Xu, Y. Liu and W. Sun, Intuitionistic fuzzy rough sets model based on (, ),- operators, 2012 9th International Conference on Fuzzy Systems, Knowledge Discovery, IEEE. 234-238, 2012.
  • [48] Z. Xu and R. R. Yager, Some geometric aggregation operators based on intuitionistic fuzzy sets, Int. J. General Sys. 35 (4), 417-433, 2006.
  • [49] L. Yang and H. Mao, Intuitionistic fuzzy threshold graphs, J. Int. Fuzzy Syst. 36 (6), 6641-6651, 2019.
  • [50] L. A. Zadeh, Fuzzy sets, Inf. Control. 8 (3), 338- 353, 1965.
  • [51] J. Zhan, H. Masood Malik and M. Akram, Novel decision-making algorithms based on intuitionistic fuzzy rough environment, Int. J. Machine Learning and Cybernetics. 10, 1459-1485, 2019.
  • [52] R. M. Zulqarnain, X. L. Xin, M. Saqlain and W. A. Khan, TOPSIS Method Based on the Correlation Coefficient of IntervalValued Intuitionistic Fuzzy Soft Sets and Aggregation Operators with Their Application in DecisionMaking, J. Math. 2021 (1), 6656858, 2021.

Year 2024, Volume: 53 Issue: 6, 1774 - 1797, 28.12.2024

Shaik Noorjahan , Sharief Basha Shaik

https://doi.org/10.15672/hujms.1486239

Abstract

Project Number

Nil

References

  • [1] U. Ahmad and I. Nawaz, Directed rough fuzzy graph with application to trade networking, Comput. Appl. Math. 41 (8), 366, 2022.
  • [2] M. Akram and S. Zahid, Group decision-making method with Pythagorean fuzzy rough number for the evaluation of best design concept, Granular Comput. 8 (6), 1121-1148, 2023.
  • [3] N. K. Akula and S. B. Shaik, Correlation Coefficient Measure of Intuitionistic Fuzzy Graphs with Application in Money Investing Schemes, Comput. Inform. 42 (2), 436- 456, 2023.
  • [4] M. I. Ali, F. Feng, T. Mahmood, I. Mahmood and H. Faizan, SA graphical method for ranking Atanassovs intuitionistic fuzzy values using the uncertainty index and entropy, Int. J. Intell. Syst. 34 (10), 2692-2712, 2019.
  • [5] W. Ali, T. Shaheen, H. G. Toor, T. Alballa, A. Alburaikan and H. A. E. W. Khalifa, An Improved Intuitionistic Fuzzy Decision-Theoretic Rough Set Model and Its Application, Axioms. 12 (11), 1003, 2023.
  • [6] K. T. Atanassov, Intuitionistic fuzzy sets, Fuzzy sets syst. 20, 87-96, 1986.
  • [7] S. Ayub, M. Shabir, M. Riaz, W. Mahmood, D. Bozanic and D. Marinkovic, Linear Diophantine fuzzy rough sets: A new rough set approach with decision making, Symmetry. 14 (3), 525, 2022.
  • [8] J. Bajaj and S. Kumar, A new intuitionistic fuzzy correlation coefficient approach with applications in multi-criteria decision-making, Decis. Anal. J. 9, 100340, 2023.
  • [9] R. Balakrishnan, The energy of a graph, Linear Algebra its Appl. 387, 287-295, 2004.
  • [10] Z. Bashir, M. G. Abbas Malik, S. Asif and T. Rashid, The topological properties of intuitionistic fuzzy rough sets, J. Int. Fuzzy Syst. 38 (1), 795-807, 2020.
  • [11] P. Bhattacharya, Some remarks on fuzzy graphs, Pattern Recognit. Lett. 6 (5), 297- 302, 1987.
  • [12] D. Bozanic, I. Epler, A. Puska, S. Biswas, D. Marinkovic and S. Koprivica, Application of the DIBR II rough MABAC decision-making model for ranking methods and techniques of lean organization systems management in the process of technical maintenance, Facta Universitatis-Series Mech. Eng. 22 (1), 101-123, 2023
  • [13] R. Chinram, A. Hussain, T. Mahmood and M. I. Ali, EDAS method for multi-criteria group decision making based on intuitionistic fuzzy rough aggregation operators, IEEE. 9, 10199-10216, 2021.
  • [14] C. L. Chowdhary and D. P. Acharjya, A hybrid scheme for breast cancer detection using intuitionistic fuzzy rough set technique, Int. J. Healthcare Inf. Sys. Inf. 11 (2), 38-61, 2016.
  • [15] C. Cornelis, M. De Cock and E. E. Kerre, Intuitionistic fuzzy rough sets: At the crossroads of imperfect knowledge, Expert Syst. 20 (5), 260-270, 2003, 2019.
  • [16] C. Dhankhar and K. Kumar, Multi-attribute decision-making based on the advanced possibility degree measure of intuitionistic fuzzy numbers, Granular comput. 8 (3), 467-478, 2023.
  • [17] D. Dubois and H. Prade, Rough fuzzy sets and fuzzy rough sets, Int. J. Gen. Syst. 17 (2-3), 191-209, 1990.
  • [18] I. U. Haq, T. Shaheen, H. Toor, T. Senapati and S. Moslem, Incomplete Dominancebased Intuitionistic Fuzzy Rough Sets and their Application in Estimation of Inflation Rates in the Least Developed Countries, IEEE. 2023.
  • [19] Y. He, H. Chen, L. Zhou, J. Liu and Z. Tao, Intuitionistic fuzzy geometric interaction averaging operators and their application to multi-criteria decision making, Inf. Sci. 259, 142-159, 2014.
  • [20] G. R. Jahanshahloo, F. H. Lotfi and M. Izadikhah, Extension of the TOPSIS method for decision-making problems with fuzzy data, Appl. Math. Comput. 181 (2), 1544- 1551, 2006.
  • [21] T. Mahmood, J. Ahmmad, Z. Ali and M. S. Yang, Confidence level aggregation operators based on intuitionistic fuzzy rough sets with application in medical diagnosis, IEEE. 11, 8674-8688, 2023.
  • [22] T. Mahmood, J. Ahmmad, U. U. Rehman and M. B. Khan, Analysis and prioritization of the factors of the robotic industry with the assistance of EDAS technique based on intuitionistic fuzzy rough Yager aggregation operators, IEEE. 11, 50462-50479, 2023.
  • [23] H. M. Malik and M. Akram, A new approach based on intuitionistic fuzzy rough graphs for decision-making, J. Int. Fuzzy Syst. 34 (4), 2325-2342, 2018.
  • [24] F. A. Mazarbhuiya and M. Shenify, An Intuitionistic Fuzzy-Rough Set-Based Classification for Anomaly Detection, Appl. Sci. 13 (9), 5578, 2023.
  • [25] A. R. Mishra, P. Rani, F. Cavallaro and A. F. Alrasheedi, Assessment of sustainable wastewater treatment technologies using interval-valued intuitionistic fuzzy distance measure-based MAIRCA method, Facta Universitatis-Series: Mech. Eng. 21 (3), 359 -386, 2023.
  • [26] I. Nazeer, T. Rashid and A. Keikha, An application of product of intuitionistic fuzzy incidence graphs in textile industry, Complexity. 2021, 1-16, 2021.
  • [27] S. Noorjahan and S. Sharief Basha, Developing an intuitionistic fuzzy rough new correlation coefficient approach for enhancing robotic vacuum cleaner, Science Progress. 107 (3), 1-28, 2024.
  • [28] Z. Pawlak, Rough sets, Int. J. Computer & Inf. Sci. 11, 341-356, 1982.
  • [29] Z. Pawlak and A. Skowron, Rudiments of rough sets, Inf. Sci. 177 (1), 3-27, 2007.
  • [30] B. Praba, V. M. Chandrasekaran and G. Deepa, Energy of an intuitionistic fuzzy graph, Ital. J. Pure Appl Math. 32, 431-444, 2014.
  • [31] S. M. Qurashi and M. Shabir, Roughness in quantale modules, J. Int. Fuzzy Sys. 35 (2), 2359-2372, 2018.
  • [32] Y. Rao, Q. Zhou, M. Akhoundi, A. A. Talebi, S. Omidbakhsh Amiri and G. Muhiuddin, Novel concepts in rough Cayley fuzzy graphs with applications, J. Math. 2023, 1-11, 2023.
  • [33] N. R. Reddy, and S. S. Basha, The correlation coefficient of hesitancy fuzzy graphs in decision making, Comput. Syst. Sci. Eng. 46, 579- 596, 2023.
  • [34] B. Said, M. Lathamaheswari, P. K. Singh, A. A. Ouallane, A. Bakhouyi, A. Bakali and N. Deivanayagampillai, An intelligent traffic control system using neutrosophic sets, rough sets, graph theory, fuzzy sets and its extended approach: a literature review, Neutrosophic Sets Syst. 50, 10-26, 2022.
  • [35] M. Sarwar, M. Akram and F. Zafar, Decision making approach based on competition graphs and extended TOPSIS method under bipolar fuzzy environment, Math. Comput. Appl. 23, 117, 2018.
  • [36] M. R. Seikh and U. Mandal, Intuitionistic fuzzy Dombi aggregation operators and their application to multiple attribute decision-making, Granular Comput. 6, 473-488, 2021.
  • [37] M. A. Shumrani, S. Topal, F. Smarandache and C. Ozel, Covering-based rough fuzzy, intuitionistic fuzzy and neutrosophic nano topology and applications, IEEE. 7, 172839- 172846, 2019.
  • [38] S. Singh and T. Som, Intuitionistic Fuzzy Rough Sets: Theory to Practice, Math. Comput. Sci. and Eng. 91-133, 2022.
  • [39] P. Sivaprakasam and M. Angamuthu, Generalized Z-fuzzy soft - covering based rough matrices and its application to MAGDM problem based on AHP method, Decision Making: Appl. in Manage. Eng. 6 (1), 134152, 2023.
  • [40] A. K. Tiwari, A. Nath, R. K. Pandey and P. Maratha, A novel intuitionistic fuzzy rough instance selection and attribute reduction with kernelized intuitionistic fuzzy Cmeans clustering to handle imbalanced datasets, Expert Sys. with Appli. 251, 124087, 2024.
  • [41] A. K. Tiwari, R. Saini, A. Nath, P. Singh and M. A. Shah, Hybrid similarity relation based mutual information for feature selection in intuitionistic fuzzy rough framework and its applications, Scientific Reports. 14 (1), 5958, 2024.
  • [42] D. K. Tripathi, S. K. Nigam, P. Rani and A. R. Shah, New intuitionistic fuzzy parametric divergence measures and score function-based CoCoSo method for decisionmaking problems, Decision Making: Appl. in Manage. Eng. 6 (1), 535563, 2023.
  • [43] Y. H. Wang, Z. F. Shan and L. Huang, The extension of TOPSIS method for multi-attribute decision-making with q-rung orthopair hesitant fuzzy sets, IEEE. 8, 165151165167, 2020.
  • [44] J. Wang and X. Zhang, Two types of intuitionistic fuzzy covering rough sets and an application to multiple criteria group decision making, Symmetry. 10 (10), 462, 2018.
  • [45] F. Xiao, A distance measure for intuitionistic fuzzy sets and its application to pattern classification problems, IEEE Trans. Syst. Man, and Cybernetics: Syst. 51 (6), 3980- 3992, 2019.
  • [46] Z. Xu, Intuitionistic fuzzy aggregation, IEEE Trans. Fuzzy Systs. 15 (6), 1179-1187, 2007.
  • [47] W. Xu, Y. Liu and W. Sun, Intuitionistic fuzzy rough sets model based on (, ),- operators, 2012 9th International Conference on Fuzzy Systems, Knowledge Discovery, IEEE. 234-238, 2012.
  • [48] Z. Xu and R. R. Yager, Some geometric aggregation operators based on intuitionistic fuzzy sets, Int. J. General Sys. 35 (4), 417-433, 2006.
  • [49] L. Yang and H. Mao, Intuitionistic fuzzy threshold graphs, J. Int. Fuzzy Syst. 36 (6), 6641-6651, 2019.
  • [50] L. A. Zadeh, Fuzzy sets, Inf. Control. 8 (3), 338- 353, 1965.
  • [51] J. Zhan, H. Masood Malik and M. Akram, Novel decision-making algorithms based on intuitionistic fuzzy rough environment, Int. J. Machine Learning and Cybernetics. 10, 1459-1485, 2019.
  • [52] R. M. Zulqarnain, X. L. Xin, M. Saqlain and W. A. Khan, TOPSIS Method Based on the Correlation Coefficient of IntervalValued Intuitionistic Fuzzy Soft Sets and Aggregation Operators with Their Application in DecisionMaking, J. Math. 2021 (1), 6656858, 2021.
There are 52 citations in total.

Details

Primary Language English
Subjects Statistical Analysis
Journal Section Statistics
Authors

Shaik Noorjahan 0009-0001-3303-4544

Sharief Basha Shaik 0000-0002-3866-246X

Project Number Nil
Early Pub Date November 25, 2024
Publication Date December 28, 2024
Submission Date May 18, 2024
Acceptance Date November 9, 2024
Published in Issue Year 2024 Volume: 53 Issue: 6

Cite

APA Noorjahan, S., & Shaik, S. B. (2024). Decision-making using the correlation coefficient measures of intuitionistic fuzzy rough graph. Hacettepe Journal of Mathematics and Statistics, 53(6), 1774-1797. https://doi.org/10.15672/hujms.1486239
AMA Noorjahan S, Shaik SB. Decision-making using the correlation coefficient measures of intuitionistic fuzzy rough graph. Hacettepe Journal of Mathematics and Statistics. December 2024;53(6):1774-1797. doi:10.15672/hujms.1486239
Chicago Noorjahan, Shaik, and Sharief Basha Shaik. “Decision-Making Using the Correlation Coefficient Measures of Intuitionistic Fuzzy Rough Graph”. Hacettepe Journal of Mathematics and Statistics 53, no. 6 (December 2024): 1774-97. https://doi.org/10.15672/hujms.1486239.
EndNote Noorjahan S, Shaik SB (December 1, 2024) Decision-making using the correlation coefficient measures of intuitionistic fuzzy rough graph. Hacettepe Journal of Mathematics and Statistics 53 6 1774–1797.
IEEE S. Noorjahan and S. B. Shaik, “Decision-making using the correlation coefficient measures of intuitionistic fuzzy rough graph”, Hacettepe Journal of Mathematics and Statistics, vol. 53, no. 6, pp. 1774–1797, 2024, doi: 10.15672/hujms.1486239.
ISNAD Noorjahan, Shaik - Shaik, Sharief Basha. “Decision-Making Using the Correlation Coefficient Measures of Intuitionistic Fuzzy Rough Graph”. Hacettepe Journal of Mathematics and Statistics 53/6 (December 2024), 1774-1797. https://doi.org/10.15672/hujms.1486239.
JAMA Noorjahan S, Shaik SB. Decision-making using the correlation coefficient measures of intuitionistic fuzzy rough graph. Hacettepe Journal of Mathematics and Statistics. 2024;53:1774–1797.
MLA Noorjahan, Shaik and Sharief Basha Shaik. “Decision-Making Using the Correlation Coefficient Measures of Intuitionistic Fuzzy Rough Graph”. Hacettepe Journal of Mathematics and Statistics, vol. 53, no. 6, 2024, pp. 1774-97, doi:10.15672/hujms.1486239.
Vancouver Noorjahan S, Shaik SB. Decision-making using the correlation coefficient measures of intuitionistic fuzzy rough graph. Hacettepe Journal of Mathematics and Statistics. 2024;53(6):1774-97.

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