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International Journal of Neutrosophic Science
Volume 21 , Issue 4, PP: 127-134 , 2023 | Cite this article as | XML | Html |PDF

Title

Algebraic Operations on Pythagorean neutrosophic sets (PNS): Extending Applicability and Decision-Making Capabilities

  Jamiatun Nadwa Ismail 1 * ,   Zahari Rodzi 2 ,   Faisal Al-Sharqi 3 ,   Ashraf Al-Quran 4 ,   Hazwani Hashim 5 ,   Nor Hashimah Sulaiman 6

1  College of Computing, Informatics and Media, UiTM Cawangan Negeri Sembilan, Kampus Seremban, 73000 Negeri Sembilan, Malaysia
    (ismail.nadwa@gmail.com)

2  College of Computing, Informatics and Media, UiTM Cawangan Negeri Sembilan, Kampus Seremban, 73000 Negeri Sembilan, Malaysia
    (zahari@uitm.edu.my)

3  Department of Mathematics, Faculty of Education for Pure Sciences, University Of Anbar, Ramadi, Anbar, Iraq
    (faisal.ghazi@uoanbar.edu.iq)

4  Basic Sciences Department, Preparatory Year Deanship, King Faisal University, Al-Ahsa 31982, Saudi Arabia
    (aalquran@kfu.edu.sa)

5  College of Computing, Informatics and Media, UiTM Cawangan Kelantan, Kampus Machang, 18500, Kelantan, Malaysia
    (hazwanihashim@uitm.edu.my)

6  College of Computing, Informatics and Media, UiTM Cawangan Selangor, Kampus Dengkil, 43800 Selangor, Malaysia
    (nhashima@tmsk.uitm.edu.my)

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Doi   :   https://doi.org/10.54216/IJNS.210412

Received: February 18, 2023 Revised: May 26, 2023 Accepted: July 21, 2023

Abstract :

Pythagorean neutrosophic sets (PNS) have been recognized as a highly effective mechanism for managing situations characterized by indeterminacy and inconsistency within decision-making procedures. This paper delves into the examination of algebraic operations performed on PNS, thereby expanding their scope of application, and enhancing their utility. In this study, we put forth a set of algebraic operations that can be applied to PNS. These operations encompass addition, multiplication, scalar multiplication, and power. These operations facilitate the efficient manipulation and combination of PNS, thereby enhancing decision-making in scenarios characterized by uncertainty and vagueness. To demonstrate the efficacy of these operations, we will present several illustrative examples accompanied by corroborating proofs. The introduction of algebraic operations enhances the capabilities of PNS, thereby creating opportunities for their practical application.

Keywords :

Pythagorean Neutrosophic Set; Algebraic Operations; decision making; addition; multiplication; scalar multiplication.

References :

[1] L. . Zadeh, “Fuzzy Sets,” Inf. Control, vol. 8, pp. 338–353, 1965, doi: https://doi.org/10.1016/S0019-9958(65)90241-X.

[2] L. A. Zadeh, “The concept of a linguistic variable and its application to approximate reasoning-I,” Inf. Sci. (Ny)., vol. 8, no. 3, pp. 199–249, 1975, doi: 10.1016/0020-0255(75)90036-5.

[3] M. Xue, X. Tang, and N. Feng, “An Extended VIKOR Method for Multiple Attribute Decision Analysis with Bidimensional Dual Hesitant Fuzzy Information,” Math. Probl. Eng., vol. 2016, 2016, doi: 10.1155/2016/4274690.

[4] K. Atanassov and G. Gargov, “interval-valued intuitionistic fuzzy sets,” Fuzzy Sets Syst., vol. 31, no. 3, pp. 343–349, 1989, doi: 10.1016/S0165-0114(98)00436-9.

[5] J. N. Ismail et al., “The Integrated Novel Framework : Linguistic Variables in Pythagorean Neutrosophic Set with DEMATEL for Enhanced,” Int. J. Neutrosophic Sci., vol. 21, no. 02, pp. 129–141, 2023.

[6] Z. Md Rodzi and N. Hassan, “A Hamming score distance of hesitant fuzzy sets,” J. Phys. Conf. Ser., vol. 1212, no. 1, pp. 1–8, 2019, doi: 10.1088/1742-6596/1212/1/012020.

[7] Z. Rodzi, A. G. Ahmad, N. Sa, and W. N. Mohamad, “Z-Score Functions of Dual Hesitant Fuzzy Set and Its Applications in Multi-Criteria Decision Making,” vol. 9, no. 3, pp. 225–232, 2021, doi: 10.13189/ms.2021.090303.

[8] C. Veeramani, R. Venugopal, and S. A. Edalatpanah, “Neutrosophic DEMATEL approach for financial ratio performance evaluation of the NASDAQ Exchange,” Neutrosophic Sets Syst., vol. 51, no. March 2023, pp. 766–782, 2022, doi: 10.5281/zenodo.7135415.

[9] Z. Rodzi and A. G. Ahmad, “Fuzzy Parameterized Dual Hesitant Fuzzy Soft Sets and Its Application in TOPSIS,” Math. Stat. 8, vol. 8, no. 1, pp. 32–41, 2020, doi: 10.13189/ms.2020.080104.

[10] F. Al-Sharqi, A. G. Ahmad, A. Al Quran, Mapping on interval complex neutrosophic soft sets, International Journal of Neutrosophic Science, vol.19(4), pp.77-85, 2022.

[11] T. Šmidovnik and P. Grošelj, “Inclusion of uncertainty with different types of fuzzy numbers into DEMATEL,” Serbian J. Manag., vol. 16, no. 1, pp. 49–59, 2021, doi: 10.5937/sjm16-30160.

[12] Z. M. Rodzi et al., “Uncovering Obstacles to HouseholdWaste Recycling in Seremban, Malaysia through Decision-Making Trial and Evaluation Laboratory (DEMATEL) Analysis,” Sci. Technol. Indones., vol. 8, no. 3, pp. 422–428, 2023.

[13] R. Radha, A. S. A. Mary, R. Prema, and S. Broumi, “Neutrosophic Pythagorean Sets with Dependent Neutrosophic Pythagorean Components and its Improved Correlation Coefficients,” Neutrosophic Sets Syst., vol. 46, no. I, pp. 77–86, 2021.

[14] R. Radha and A. Stanis Arul Mary, “Neutrosophic Pythagorean Soft Set With T and F as Dependent Neutrosophic Components,” Neutrosophic Sets Syst., vol. 42, no. August, pp. 65–78, 2021, doi: 10.5281/zenodo.4711505.

[15] F. Al-Sharqi, Y. Al-Qudah and N. Alotaibi, Decision-making techniques based on similarity measures of possibility neutrosophic soft expert sets. Neutrosophic Sets and Systems, 55(1) (2023), 358-382.

[16] A. Al-Quran, F. Al-Sharqi, K. Ullah, M. U. Romdhini, M. Balti and M. Alomai, Bipolar fuzzy hypersoft set and its application in decision making, International Journal of Neutrosophic Science, vol. 20, no. 4, pp. 65-77, 2023.

[17] A. Al Quran, A. G. Ahmad, F. Al-Sharqi, A. Lutfi, Q-Complex Neutrosophic Set, International Journal of Neutrosophic Science, vol. 20(2), pp.08-19, 2023.

[18] F. Al-Sharqi, M. U. Romdhini, A. Al-Quran, Group decision-making based on aggregation operator and score function of Q-neutrosophic soft matrix, Journal of Intelligent and Fuzzy Systems, vol. 45, pp.305–321, 2023. [19] F. Al-Sharqi, A.G. Ahmad, A. Al-Quran, Fuzzy parameterized-interval complex neutrosophic soft sets and their applications under uncertainty, Journal of Intelligent and Fuzzy Systems, vol. 44, pp.1453–1477, 2023.

[20] R. R. Yager, “Pythagorean membership grades in multicriteria decision making,” IEEE Trans. Fuzzy Syst., vol. 22, no. 4, pp. 958–965, 2014, doi: 10.1109/TFUZZ.2013.2278989.

[21] X. Zhang, “A Novel Approach Based on Similarity Measure for Pythagorean Fuzzy Multiple Criteria Group Decision Making,” Int. J. Intell. Syst., vol. 31, no. 6, pp. 593–611, 2016, doi: 10.1002/int.21796.

[22] K. Ullah, T. Mahmood, Z. Ali, and N. Jan, “On some distance measures of complex Pythagorean fuzzy sets and their applications in pattern recognition,” Complex Intell. Syst., vol. 6, no. 1, pp. 15–27, 2020, doi: 10.1007/s40747-019-0103-6.

Cite this Article as :
Style #
MLA Jamiatun Nadwa Ismail, Zahari Rodzi, Faisal Al-Sharqi, Ashraf Al-Quran, Hazwani Hashim, Nor Hashimah Sulaiman. "Algebraic Operations on Pythagorean neutrosophic sets (PNS): Extending Applicability and Decision-Making Capabilities." International Journal of Neutrosophic Science, Vol. 21, No. 4, 2023 ,PP. 127-134 (Doi   :  https://doi.org/10.54216/IJNS.210412)
APA Jamiatun Nadwa Ismail, Zahari Rodzi, Faisal Al-Sharqi, Ashraf Al-Quran, Hazwani Hashim, Nor Hashimah Sulaiman. (2023). Algebraic Operations on Pythagorean neutrosophic sets (PNS): Extending Applicability and Decision-Making Capabilities. Journal of International Journal of Neutrosophic Science, 21 ( 4 ), 127-134 (Doi   :  https://doi.org/10.54216/IJNS.210412)
Chicago Jamiatun Nadwa Ismail, Zahari Rodzi, Faisal Al-Sharqi, Ashraf Al-Quran, Hazwani Hashim, Nor Hashimah Sulaiman. "Algebraic Operations on Pythagorean neutrosophic sets (PNS): Extending Applicability and Decision-Making Capabilities." Journal of International Journal of Neutrosophic Science, 21 no. 4 (2023): 127-134 (Doi   :  https://doi.org/10.54216/IJNS.210412)
Harvard Jamiatun Nadwa Ismail, Zahari Rodzi, Faisal Al-Sharqi, Ashraf Al-Quran, Hazwani Hashim, Nor Hashimah Sulaiman. (2023). Algebraic Operations on Pythagorean neutrosophic sets (PNS): Extending Applicability and Decision-Making Capabilities. Journal of International Journal of Neutrosophic Science, 21 ( 4 ), 127-134 (Doi   :  https://doi.org/10.54216/IJNS.210412)
Vancouver Jamiatun Nadwa Ismail, Zahari Rodzi, Faisal Al-Sharqi, Ashraf Al-Quran, Hazwani Hashim, Nor Hashimah Sulaiman. Algebraic Operations on Pythagorean neutrosophic sets (PNS): Extending Applicability and Decision-Making Capabilities. Journal of International Journal of Neutrosophic Science, (2023); 21 ( 4 ): 127-134 (Doi   :  https://doi.org/10.54216/IJNS.210412)
IEEE Jamiatun Nadwa Ismail, Zahari Rodzi, Faisal Al-Sharqi, Ashraf Al-Quran, Hazwani Hashim, Nor Hashimah Sulaiman, Algebraic Operations on Pythagorean neutrosophic sets (PNS): Extending Applicability and Decision-Making Capabilities, Journal of International Journal of Neutrosophic Science, Vol. 21 , No. 4 , (2023) : 127-134 (Doi   :  https://doi.org/10.54216/IJNS.210412)
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