Document Type : Research Paper


Department of Mathematics, College of Science and Arts, Qassim University, Ar Rass 52571, Saudi Arabia.


This study introduces an approach for Multiple Attribute Decision-Making (MADM) that deals with the complexity of Single-Valued Neutrosophic Uncertain Linguistic Variables (SVNULVs). This method is engineered to grasp the interconnectedness of multiple inputs and to meet the diverse requirements for semantic transformations. Due to the shortcomings of existing operational rules in terms of closeness and flexibility, this paper proposes a novel set of operational rules and a ranking process for SVNULVs, integrating the concept of a Linguistic Scale Function (LSF). We propose an innovative operator along with its weighted counterpart to amalgamate SVNULVs, thereby characterizing the dynamics among various inputs through these new operations. Concurrently, we scrutinize and discuss the unique cases and favorable properties of these proposed operators. Building upon this new operator, the paper also unveils a fresh MADM methodology leveraging SVNULVs. To validate the effectiveness of this proposed methodology, an illustrative example is employed, demonstrating the precision of the method and its advantages over existing MADM techniques.


Main Subjects

[1]     Shariatmadari Serkani, E. (2015). Using DEMATEL--ANP hybrid algorithm approach to select the most effective dimensions of CRM on innovation capabilities. Journal of applied research on industrial engineering, 2(2), 120–138.
[2]     Biswas, T. K., Akash, S. M., & Saha, S. (2018). A fuzzy-AHP method for selection best apparel item to start-up with new garment factory: a case study in Bangladesh. International journal of research in industrial engineering, 7(1), 32–50.
[3]     Adabavazeh, N., Amindoust, A., & Nikbakht, M. (2022). A fuzzy BWM approach to prioritize distribution network enablers. International journal of research in industrial engineering, 11(4), 349–365.
[4]     El-Araby, A. (2023). The utilization of MARCOS method for different engineering applications: a comparative study. International journal of research in industrial engineering, 12(2), 155–164.
[5]     Afzali Behbahani, N., Khodadadi-Karimvand, M., & Ahmadi, A. (2022). Environmental risk assessment using FMEA and entropy based on TOPSIS method: a case study oil wells drilling. Big data and computing visions, 2(1), 31–39.
[6]     Li, P., Edalatpanah, S. A., Sorourkhah, A., Yaman, S., & Kausar, N. (2023). An integrated fuzzy structured methodology for performance evaluation of high schools in a group decision-making problem. Systems, 11(3), 159.
[7]     Palanikumar, M., Kausar, N., Ahmed, S. F., Edalatpanah, S. A., Ozbilge, E., & Bulut, A. (2023). New applications of various distance techniques to multi-criteria decision-making challenges for ranking vague sets. AIMS mathematics, 8(5), 11397–11424.
[8]     Zadeh, L. A. (1975). The concept of a linguistic variable and its application to approximate reasoning—I. Information sciences, 8(3), 199–249.
[9]     Riera, J. V., Massanet, S., Herrera-Viedma, E., & Torrens, J. (2015). Some interesting properties of the fuzzy linguistic model based on discrete fuzzy numbers to manage hesitant fuzzy linguistic information. Applied soft computing, 36, 383–391.
[10]   Edalatpanah, S. A. (2020). Neutrosophic structured element. Expert systems, 37(5), e12542.
[11]   Liu, P., & Jin, F. (2012). Methods for aggregating intuitionistic uncertain linguistic variables and their application to group decision making. Information sciences, 205, 58–71.
[12]   Tang, L., Pan, C., & Wang, W. (2002). Surplus energy index for analysing rock burst proneness. Journal of central south university of technology(china), 33(2), 129–132.
[13]   Zhong, J. (2021). BWM-TODIM supplier evaluation and selection based on interval-valued intuitionistic uncertain linguistic sets. Frontiers in economics and management, 2(12), 315–324.
[14]   Garg, H. (2018). Linguistic Pythagorean fuzzy sets and its applications in multiattribute decision-making process. International journal of intelligent systems, 33(6), 1234–1263.
[15]   Villa Silva, A. J., Perez-Dominguez, L., Martinez Gomez, E., Luviano-Cruz, D., & Valles-Rosales, D. (2021). Dimensional analysis under linguistic Pythagorean fuzzy set. Symmetry, 13(3), 440.
[16]   Qiyas, M., Abdullah, S., Al-Otaibi, Y. D., & Aslam, M. (2021). Generalized interval-valued picture fuzzy linguistic induced hybrid operator and TOPSIS method for linguistic group decision-making. Soft computing, 25, 5037–5054.
[17]   Xian, S., Cheng, Y., & Liu, Z. (2021). A novel picture fuzzy linguistic Muirhead Mean aggregation operators and their application to multiple attribute decision making. Soft computing, 25(23), 14741–14756.
[18]   Akram, M., Naz, S., Edalatpanah, S. A., & Mehreen, R. (2021). Group decision-making framework under linguistic q-rung orthopair fuzzy Einstein models. Soft computing, 25(15), 10309–10334.
[19]   Wu, Z., & Xu, J. (2015). Possibility distribution-based approach for MAGDM with hesitant fuzzy linguistic information. IEEE transactions on cybernetics, 46(3), 694–705.
[20]   Rodriguez, R. M., Martinez, L., & Herrera, F. (2011). Hesitant fuzzy linguistic term sets for decision making. IEEE transactions on fuzzy systems, 20(1), 109–119.
[21]   Morente-Molinera, J. A., Pérez, I. J., Ureña, M. R., & Herrera-Viedma, E. (2015). On multi-granular fuzzy linguistic modeling in group decision making problems: A systematic review and future trends. Knowledge-based systems, 74, 49–60.
[22]   Zhang, Z., Yu, W., Martinez, L., & Gao, Y. (2019). Managing multigranular unbalanced hesitant fuzzy linguistic information in multiattribute large-scale group decision making: A linguistic distribution-based approach. IEEE transactions on fuzzy systems, 28(11), 2875–2889.
[23]   Herrera, F., & Martinez, L. (2000). A 2-tuple fuzzy linguistic representation model for computing with words. IEEE transactions on fuzzy systems, 8(6), 746–752. DOI: 10.1109/91.890332.
[24]   Giráldez-Cru, J., Chica, M., Cordón, O., & Herrera, F. (2020). Modeling agent-based consumers decision-making with 2-tuple fuzzy linguistic perceptions. International journal of intelligent systems, 35(2), 283–299.
[25]   Dehghani Filabadi, A., & Hesamian, G. (2021). Development of a multi-period multi-attribute group decision-making method using type-2 fuzzy set of linguistic variables. International journal of research in industrial engineering, 10(2), 138–154.
[26]   Sajjad, M., Sałabun, W., Faizi, S., Ismail, M., & Wątróbski, J. (2022). Statistical and analytical approach of multi-criteria group decision-making based on the correlation coefficient under intuitionistic 2-tuple fuzzy linguistic environment. Expert systems with applications, 193, 116341.
[27]   Zhang, H. (2014). Linguistic intuitionistic fuzzy sets and application in MAGDM. Journal of applied mathematics, 2014, 1–11.
[28]   Bao, Z. (2022). Crop health monitoring through WSN and IoT. Big data and computing visions, 2(4), 163–169.
[29]   Smarandache, F. (1999). A unifying field in Logics: Neutrosophic Logic. In Philosophy (pp. 1–141). American Research Press.
[30]   Peng, J., Wang, J., Zhang, H., & Chen, X. (2014). An outranking approach for multi-criteria decision-making problems with simplified neutrosophic sets. Applied soft computing, 25, 336–346.
[31]   Zavadskas, E. K., Bausys, R., Kaklauskas, A., Ubarte, I., Kuzminske, A., & Gudiene, N. (2017). Sustainable market valuation of buildings by the single-valued neutrosophic MAMVA method. Applied soft computing, 57, 74–87.
[32]   Bolturk, E., & Kahraman, C. (2018). A novel interval-valued neutrosophic AHP with cosine similarity measure. Soft computing, 22, 4941–4958.
[33]   Smarandache, F., Broumi, S., Singh, P. K., Liu, C., Rao, V. V., Yang, H. L., …., & Elhassouny, A. (2019). Introduction to neutrosophy and neutrosophic environment. In Neutrosophic set in medical image analysis (pp. 3–29). Elsevier.
[34]   Yang, W., Cai, L., Edalatpanah, S. A., & Smarandache, F. (2020). Triangular single valued neutrosophic data envelopment analysis: application to hospital performance measurement. Symmetry, 12(4), 588.
[35]   Das, S. K., & Dash, J. K. (2020). Modified solution for neutrosophic linear programming problems with mixed constraints. Infinite Study.
[36]   Wang, Q., Huang, Y., Kong, S., Ma, X., Liu, Y., Das, S. K., & Edalatpanah, S. A. (2021). A novel method for solving multiobjective linear programming problems with triangular neutrosophic numbers. Journal of mathematics, 2021, 1–8.
[37]   Veeramani, C., Edalatpanah, S. A., & Sharanya, S. (2021). Solving the multiobjective fractional transportation problem through the neutrosophic goal programming approach. Discrete dynamics in nature and society, 2021, 1–17.
[38]   Zhang, K., Xie, Y., Noorkhah, S. A., Imeni, M., & Das, S. K. (2023). Neutrosophic management evaluation of insurance companies by a hybrid TODIM-BSC method: a case study in private insurance companies. Management decision, 61(2), 363–381.
[39]   Saberhoseini, S. F., Edalatpanah, S. A., & Sorourkhah, A. (2022). Choosing the best private-sector partner according to the risk factors in neutrosophic environment. Big data and computing visions, 2(2), 61–68.
[40]   Bhat, R., & Pavithra, K. N. (2023). Toward secure fault-tolerant wireless sensor communication: challenges and applications. Springer.
[41]   Hosseinzadeh, E., & Tayyebi, J. (2023). A compromise solution for the neutrosophic multi-objective linear programming problem and its application in transportation problem. Journal of applied research on industrial engineering, 10(1), 1–10.
[42]   Ihsan, M., Saeed, M., & Rahman, A. U. (2023). Optimizing hard disk selection via a fuzzy parameterized single-valued neutrosophic soft set approach. Journal of operational and strategic analytics, 1(2), 62–69.
[43]   Edalatpanah, S. A., Abdolmaleki, E., Khalifa, H. A. E. W., & Das, S. K. (2023). A novel computational method for neutrosophic uncertainty related quadratic fractional programming problems. Neutrosophic sets and systems, 58(1), 38.
[44]   Edalatpanah, S. A., & Smarandache, F. (2023). Introduction to the Special issue on advances in neutrosophic and plithogenic sets for engineering and sciences: theory, models, and applications. Computer modeling in engineering and sciences, 134, 817–819. DOI: 10.32604/cmes.2022.024060
[45]   Ye, J. (2014). Some aggregation operators of interval neutrosophic linguistic numbers for multiple attribute decision making. Journal of intelligent & fuzzy systems, 27(5), 2231–2241.
[46]   Ye, J. (2017). Multiple attribute group decision making based on interval neutrosophic uncertain linguistic variables. International journal of machine learning and cybernetics, 8, 837–848.
[47]   Broumi, S., Ye, J., & Smarandache, F. (2015). An extended TOPSIS method for multiple attribute decision making based on interval neutrosophic uncertain linguistic variables. Infinite study, 321.
[48]   Dey, P. P., Pramanik, S., & Giri, B. C. (2016). An extended grey relational analysis based multiple attribute decision making in interval neutrosophic uncertain linguistic setting. Neutrosophic sets and systems, 11, 21–30.
[49]   Tian, Z., Wang, J., Zhang, H., & Wang, J. (2018). Multi-criteria decision-making based on generalized prioritized aggregation operators under simplified neutrosophic uncertain linguistic environment. International journal of machine learning and cybernetics, 9, 523–539.
[50]   Liu, P., & Tang, G. (2016). Multi-criteria group decision-making based on interval neutrosophic uncertain linguistic variables and Choquet integral. Cognitive computation, 8, 1036–1056.
[51]   Khan, Q., Mahmood, T., & Ye, J. (2017). Multiple attribute decision-making method under hesitant single valued neutrosophic uncertain linguistic environment. Infinite Study.
[52]   Liu, P., & Teng, F. (2017). Some interval neutrosophic hesitant uncertain linguistic Bonferroni mean aggregation operators for multiple attribute decision-making. International journal for uncertainty quantification, 7(6), 525-572.
[53]   Liu, P., Khan, Q., Ye, J., & Mahmood, T. (2018). Group decision-making method under hesitant interval neutrosophic uncertain linguistic environment. International journal of fuzzy systems, 20, 2337–2353.
[54]   Liu, P., & Shi, L. (2017). Some neutrosophic uncertain linguistic number Heronian mean operators and their application to multi-attribute group decision making. Neural computing and applications, 28, 1079–1093.
[55]   Fan, C., Fan, E., & Hu, K. (2018). New form of single valued neutrosophic uncertain linguistic variables aggregation operators for decision-making. Cognitive systems research, 52, 1045–1055.
[56]   Yang, L., & Li, B. (2020). Multiple-valued neutrosophic uncertain linguistic sets with Dombi normalized weighted Bonferroni mean operator and their applications in multiple attribute decision making problem. IEEE access, 8, 5906–5927.
[57]   Song, H., & Geng, Y. (2021). Some single-valued neutrosophic uncertain linguistic maclaurin symmetric mean operators and their application to multiple-attribute decision making. Symmetry, 13(12), 2322.
[58]   Xu, Z. (2006). Induced uncertain linguistic OWA operators applied to group decision making. Information fusion, 7(2), 231–238.
[59]   Hara, T., Uchiyama, M., & Takahasi, S.-E. (1998). A refinement of various mean inequalities. Journal of inequalities and applications, 1998(4), 932025.
[60]   Wang, J., Wu, J., Wang, J., Zhang, H., & Chen, X. (2014). Interval-valued hesitant fuzzy linguistic sets and their applications in multi-criteria decision-making problems. Information sciences, 288, 55–72. DOI: