1
Department of Mathematics, Faculty of Arts and Science, Amman Arab University, Amman, Jordan
(Y.alqudah@aau.edu.jo)
2
Department of Mathematics, Faculty of Education for Pure Sciences, University Of Anbar, Ramadi, Anbar, Iraq
(faisal.ghazi@uoanbar.edu.iq)
Abstract :
hand the idea of interval-valued neutrosophic soft sets (IVNSSs) is a new generalization of the neutrosophic soft sets to the neutrosophic sets when the authors combine the critical features of IVNS and soft sets (SSs) in one model. Accordingly, this model worked to provide decision-makers with more flexibility in the process of interpreting uncertain information. From a scientific point of view, the process of evaluating this highperformance IVNSS disappears. Therefore, in this paper, we initiated a new approach known as possibility interval-valued neutrosophic soft sets (PIVNSSs) as a new development in a fuzzy soft computing environment. We investigate some fundamental operations on PIVNSSs along with their basic properties. Also, we investigate AND and OR operations between two PIVNSSs as well as several numerical examples to clarify the above fundamental operations. Finally, we have given similarity measure (SM) between two PIVNSSs to construct a new algorithm that is used to demonstrate the effectiveness of the method in handling some real-life applications.
Keywords :
Neutrosophic sets; neutrosophic soft sets; interval-valued neutrosophic soft sets; possibility intervalvalued neutrosophic soft sets.
References :
[1] L.A. Zadeh,Fuzzy sets, Information and Control, vol 8, pp. 338–353.1965.
[2] F. Smarandache, Neutrosophic probability, set, and logic, American Research Press: Rehoboth, IL, USA, 1998.
[3] K. Atanassov, Intuitionistic fuzzy sets, Fuzzy Sets and Systems, vol 20, no.1, pp. 87–96, 1986.
[4] H.Wang, F.Smarandache, Y.Q.Zhang, R.Sunderraman, Interval Neutrosophic Sets and Logic: Theory and Applicationsin Computing, Hexis; Neutrosophic book series, No:5, 2005.
[5] F. Al-Sharqi, A.G. Ahmad, A. Al-Quran, Interval complex neutrosophic soft relations and their application in decision-making, Journal of Intelligent and Fuzzy Systems, vol. 43 , pp. 745-771, 2022.
[6] F. Al-Sharqi, A.G. Ahmad, A. Al-Quran, Interval-valued neutrosophic soft expert set from real space to complex space, Computer Modeling in Engineering and Sciences, vol. 132(1), pp. 267–293, 2022.
[7] Al-Quran, A. (2021). A new multi attribute decision making method based on the T-spherical hesitant fuzzy sets. IEEE Access, 9, 156200-156210.
[8] 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.
[9] Al-Quran, A., Hashim, H., & Abdullah, L. (2020). A hybrid approach of interval neutrosophic vague sets and DEMATEL with new linguistic variable. Symmetry, 12(2), 275.
[10] Z. bin M. Rodzi et al., “Integrated Single-Valued Neutrosophic Normalized Weighted Bonferroni Mean (SVNNWBM)-DEMATEL for Analyzing the Key Barriers to Halal Certification Adoption in Malaysia,” Int. J. Neutrosophic Sci., vol. 21, no. 3, pp. 106–114, 2023.
[11] D. Molodtsov, Soft set theory, first results, Computers and Mathematics with Applications, vol. 37, no. 4-5, pp. 19-31, 1999.
[12] Saqlain, M., Jafar, M. N., & Riaz, M. (2020). A new approach of neutrosophic soft set with generalized fuzzy TOPSIS in application of smart phone selection. Neutrosophic Sets and Systems, 32, 306.
[13] Al-Qudah, Y.; Hassan, N. Complex multi-fuzzy soft set: Its entropy and similarity measure. IEEE Access 2018, 6, 65002-65017.
[14] G. Shanmugam, M. Palanikumar, K. Arulmozhi, Aiyared Iampan, Said Broumi. (2022). Agriculture Production Decision Making using Generalized q-Rung Neutrosophic Soft Set Method. International Journal of Neutrosophic Science, 19 ( 1 ), 166-176.
[15] M. M. Abed, F. G. Al-Sharqi, and A. A. Mhassin, “Study fractional ideals over some domains,” in AIP Conference Proceedings, 2019, vol. 2138, no. 1, p. 30001.
[16] M. M. Abed, F. Al-Sharqi, and S. H. Zail, “A Certain Conditions on Some Rings Give PP Ring,” in Journal of Physics: Conference Series, 2021, vol. 1818, no. 1, p. 12068.
[17] Deli, I. (2017). Interval-valued neutrosophic soft sets and its decision making. International Journal of Machine Learning and Cybernetics, 8, 665-676.
[18] S¸ ahin, R., and K¨uc¸ ¨uk, A. (2014). On similarity and entropy of neutrosophic soft sets. Journal of intelligent and fuzzy systems, 27(5), 2417-2430.
[19] 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.
[20] 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.
[21] Quek, S. G., Garg, H., Selvachandran, G., Palanikumar, M., Arulmozhi, K., & Smarandache, F. (2023). VIKOR and TOPSIS framework with a truthful-distance measure for the (t, s)-regulated interval-valued neutrosophic soft set. Soft Computing, 1-27.
[22] Broumi, S., Sahin, R., & Smarandache, F. (2014). Generalized interval neutrosophic soft set and its decision making problem. Journal of new results in science, 3(7), 29-47.
[23] 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.
[24] 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.
[25] Al-Qudah, Y., & Ganie, A. H. (2023). Bidirectional approximate reasoning and pattern analysis based on a novel Fermatean fuzzy similarity metric. Granular Computing, 1-16.
[26] Alhazaymeh, K., Al-Qudah, Y., Hassan, N., & Nasruddin, A. M. (2020). Cubic vague set and its application in decision making. Entropy, 22(9), 963.
[27] Al-Qudah, Y., Alhazaymeh, K., Hassan, N., Qoqazeh, H., Almousa, M., & Alaroud, M. (2022). Transitive Closure of Vague Soft Set Relations and its Operators. International Journal of Fuzzy Logic and Intelligent Systems, 22(1), 59-68.
[28] Al-Qudah, Y., Hassan, M., & Hassan, N. (2019). Fuzzy parameterized complex multi-fuzzy soft expert set theory and its application in decision-making. Symmetry, 11(3), 358.
[29] M Palanikumar, N Kausar, H Garg, S Kadry, J Kim, Robotic sensor based on score and accuracy values in q-rung complex diophatine neutrosophic normal set with an aggregation operation, Alexandria Engineering Journal 77, 149-164, 2023.
[30] SG Quek, H Garg, G Selvachandran,MPalanikumar, K Arulmozhi,VIKOR and TOPSIS framework with a truthful-distance measure for the (t, s)-regulated interval-valued neutrosophic soft set, Soft Computing, 1-27, 2023.
[31] MPalanikumar, K Arulmozhi, C Jana,MPal, Multiple-attribute decision-making spherical vague normal operators and their applications for the selection of farmers, Expert Systems 40 (3), e13188, 2023.
[32] M Palanikumar, K Arulmozhi, A Iampan, S Broumi, Medical diagnosis decision making using type- II generalized Pythagorean neutrosophic interval valued soft sets.International Journal of Neutrosophic Science (IJNS) 20 (1), 2023.
[33] M Palanikumar, K Arulmozhi, A Iampan, MULTI CRITERIA GROUP DECISION MAKING BAS1ED ON VIKOR AND TOPSIS METHODS FOR FERMATEAN FUZZY SOFT WITH AGGREGATION OPERATORS, ICIC Express Letters 16 (10), 1129–1138, 2022.
[34] M Palanikumar, K Arulmozhi, MCGDM based on TOPSIS and VIKOR using Pythagorean neutrosophic soft with aggregation operators, Neutrosophic Sets and Systems,, 538-555, 2022.
[35] M Palanikumar, S Broumi, Square root Diophantine neutrosophic normal interval-valued sets and their aggregated operators in application to multiple attribute decision making, International Journal of Neutrosophic Science, 4, 2022.
[36] M Palanikumar, N Kausar, SF Ahmed, SA Edalatpanah, E Ozbilge,New applications of various distance techniques to multi-criteria decision-making challenges for ranking vague sets, AIMS Mathematics 8 (5), 11397-11424, 2023
[37] M Palanikumar, N Kausar, H Garg, SF Ahmed, C Samaniego, Robot sensors process based on generalized Fermatean normal different aggregation operators framework, AIMS Mathematics 8 (7), 16252- 16277, 2023.
[38] Al-Qudah, Y., Hassan, M., & Hassan, N. (2019). Fuzzy parameterized complex multi-fuzzy soft expert set theory and its application in decision-making. Symmetry, 11(3), 358.
[39] M Palanikumar, K Arulmozhi, A Iampan, LJ Manavalan, NOVEL POSSIBILITY PYTHAGOREAN CUBIC FUZZY SOFT SETS AND THEIR APPLICATIONS, International Journal of Innovative Computing, Information and Control,19(2), 2023, 325-337
[40] Chinnadurai, V., & Bobin, A. (2021). Interval valued intuitionistic neutrosophic soft set and its application on diagnosing psychiatric disorder by using similarity measure. Neutrosophic Sets and Systems, 41, 215-245.
[41] Alkhazaleh, S., Salleh, A. R., & Hassan, N. (2011). Possibility fuzzy soft set. Advances in Decision Sciences, 2011.
[42] Zhang, H. D., & Shu, L. (2014). Possibility multi-fuzzy soft set and its application in decision making. Journal of Intelligent & Fuzzy Systems, 27(4), 2115-2125.
[43] Al-Quran, A., & Hassan, N. (2021). Possibility Neutrosophic Vague Soft Set for Medical Diagnosis Decision under Uncertainty. Thai Journal of Mathematics, 19(4), 1425-1438.
[44] 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.
[45] M Palanikumar, K Arulmozhi, C Jana, M Pal, Multiple attribute decision-making Pythagorean vague normal operators and their applications for the medical robots process on surgical system, Computational and Applied Mathematics 42 (6), 287, 2023.
[46] Karaaslan, F. (2017). Possibility neutrosophic soft sets and PNS-decision making method. Applied Soft Computing, 54, 403-414.
[47] Al-Sharqi, F. G., Abed, M. M., Mhassin, A. A. On Polish Groups and their Applications. J. Eng. Appl. Sci., 2018, 13(18), 7533-7536.
[48] Al-Jumaili, A. F.; Abed, M.M.; Al-Sharqi, F. Other new types of Mappings with Strongly Closed Graphs in Topological spaces via e-θ and δ − β − θ-open sets. Journal of Physics: Conference Series, 2019, 1234(1), 012101.
[49] Mohammed Abed, M., Hassan, N., & Al-Sharqi, F. (2022). On Neutrosophic Multiplication Module. Neutrosophic Sets and Systems, 49(1), 12
[50] F. Al-Sharqi, A. Al-Quran, A. G. Ahmad, and S. Broumi, “Interval-valued complex neutrosophic soft set and its applications in decision-making,” Neutrosophic Sets and Systems, vol. 40, pp. 149-168, 2021.
[51] Al-qudah, Y., Alaroud, M., Qoqazeh, H., Jaradat, A., Alhazmi, S. E., & Al-Omari, S. (2022). Approximate analytic–numeric fuzzy solutions of fuzzy fractional equations using a residual power series approach. Symmetry, 14(4), 804.
[52] F. Al-Sharqi, A. Al-Quran, M. U. Romdhini, Decision-making techniques based on similarity measures of possibility interval fuzzy soft environment, Iraqi Journal for Computer Science and Mathematics, vol. 4, pp.18–29, 2023.
[53] Ashraf Al-Quran, Faisal Al-Sharqi, Zahari Md. Rodzi, Mona Aladil, Rawan A. shlaka, Mamika Ujianita Romdhini, Mohammad K. Tahat, Obadah Said Solaiman. (2023). The Algebraic Structures of QComplex Neutrosophic Soft Sets Associated with Groups and Subgroups. International Journal of Neutrosophic Science, 22 ( 1 ), 60-76.
[54] Zail, S. H., Abed, M. M., & Faisal, A. S. (2022). Neutrosophic BCK-algebra and -BCK-algebra. International Journal of Neutrosophic Science, 19(3), 8-15.
[55] M. M. Abed and F. G. Al-Sharqi, “Classical Artinian module and related topics,” in Journal of Physics: Conference Series, 2018, vol. 1003, no. 1, p. 12065.
| Style | # |
|---|---|
| MLA | Yousef Al-Qudah, Faisal Al-Sharqi. "Algorithm for decision-making based on similarity measures of possibility interval-valued neutrosophic soft setting settings." International Journal of Neutrosophic Science, Vol. 22, No. 3, 2023 ,PP. 69-83 (Doi : https://doi.org/10.54216/IJNS.220305) |
| APA | Yousef Al-Qudah, Faisal Al-Sharqi. (2023). Algorithm for decision-making based on similarity measures of possibility interval-valued neutrosophic soft setting settings. Journal of International Journal of Neutrosophic Science, 22 ( 3 ), 69-83 (Doi : https://doi.org/10.54216/IJNS.220305) |
| Chicago | Yousef Al-Qudah, Faisal Al-Sharqi. "Algorithm for decision-making based on similarity measures of possibility interval-valued neutrosophic soft setting settings." Journal of International Journal of Neutrosophic Science, 22 no. 3 (2023): 69-83 (Doi : https://doi.org/10.54216/IJNS.220305) |
| Harvard | Yousef Al-Qudah, Faisal Al-Sharqi. (2023). Algorithm for decision-making based on similarity measures of possibility interval-valued neutrosophic soft setting settings. Journal of International Journal of Neutrosophic Science, 22 ( 3 ), 69-83 (Doi : https://doi.org/10.54216/IJNS.220305) |
| Vancouver | Yousef Al-Qudah, Faisal Al-Sharqi. Algorithm for decision-making based on similarity measures of possibility interval-valued neutrosophic soft setting settings. Journal of International Journal of Neutrosophic Science, (2023); 22 ( 3 ): 69-83 (Doi : https://doi.org/10.54216/IJNS.220305) |
| IEEE | Yousef Al-Qudah, Faisal Al-Sharqi, Algorithm for decision-making based on similarity measures of possibility interval-valued neutrosophic soft setting settings, Journal of International Journal of Neutrosophic Science, Vol. 22 , No. 3 , (2023) : 69-83 (Doi : https://doi.org/10.54216/IJNS.220305) |