Document Type : Research Paper


Department of Mathematics, Alagappa University,Karaikudi, Tamilnadu India.


The q-Rung Orthopair Fuzzy set (qROF-set) environment is a contemporary tool for handling uncertainty and vagueness in decision-making scenarios. In this paper, we delve into the algebraic examination of q-rung orthopair Multi-Fuzzy Sets (MFSs) and explore their operational laws. The novel q-Rung Orthopair Multi-Fuzzy subgroup (qROMF-subgroup) is the extension of Intuitionistic Multi-Fuzzy Subgroup (IMF-subgroup) to encompass the domain of groups. The properties of the proposed fuzzy subgroup are examined in detail, and the paper concludes by defining two additional concepts: qROMF-coset and qROMF-normal subgroup. Finally, we present a comparison of the newly introduced model with existing approaches to validate its superior performance.


Main Subjects

[1]      Zadeh, L. A. (1965). Fuzzy sets. Information and control, 8(3), 338–353. DOI:10.1016/S0019-9958(65)90241-X
[2]      Atanassov, K. T. (1986). Intuitionistic fuzzy sets. Fuzzy sets and systems. DOI:10.5555/1708507.1708520
[3]      Yager, R. R. (2013). Pythagorean fuzzy subsets [presentation]. Proceedings of the 2013 joint ifsa world congress and nafips annual meeting, IFSA/NAFIPS 2013 (pp. 57–61). DOI: 10.1109/IFSA-NAFIPS.2013.6608375
[4]      Yager, R. R. (2017). Generalized orthopair fuzzy sets. IEEE transactions on fuzzy systems, 25(5), 1222–1230. DOI:10.1109/TFUZZ.2016.2604005
[5]      Blizard, W. D. (1989). Multiset theory. Notre dame journal of formal logic, 30(1), 36–66.
[6]      Yager, R. R. (1986). On the theory of bags. International journal of general system, 13(1), 23–37.
[7]      Shinoj, T. K., & John, S. J. (2012). Intuitionistic fuzzy multisets and its application in medical diagnosis. World academy of science, engineering and technology, 6(1), 1418–1421.
[8]      Shinoj, T. K., Baby, A., & Sunil, J. J. (2015). On some algebraic structures of fuzzy multisets. Annals of fuzzy mathematics and informatics, 9(1), 77–90.
[9]      Sebastian, S., & Ramakrishnan, T. V. (2011). Multi-fuzzy sets: an extension of fuzzy sets. Fuzzy information and engineering, 3(1), 35–43. DOI:10.1007/s12543-011-0064-y
[10]    Sabu, S., & Ramakrishnan, T. V. (2010). Multi-fuzzy sets [presentation]. International mathematical forum (Vol. 50, pp. 2471–2476).
[11]    Goguen, J. A. (1967). L-fuzzy sets. Journal of mathematical analysis and applications, 18(1), 145–174.
[12]    Yang, Y., Tan, X., & Meng, C. (2013). The multi-fuzzy soft set and its application in decision making. Applied mathematical modelling, 37(7), 4915–4923. DOI:10.1016/j.apm.2012.10.015
[13]    Dey, A., Senapati, T., Pal, M., & Chen, G. (2020). A novel approach to hesitant multi-fuzzy soft set based decision-making. AIMS mathematics, 5(3), 1985–2008. DOI:10.3934/math.2020132
[14]    Das, S., & Kar, S. (2013). Intuitionistic multi fuzzy soft set and its application in decision making [presentation]. Pattern recognition and machine intelligence: 5th international conference, premi 2013 (pp. 587–592).
[15]    Rosenfeld, A. (1971). Fuzzy groups. Journal of mathematical analysis and applications, 35(3), 512–517.
[16]    Sebastian, S., & Ramakrishnan, T. V. (2011). Multi-fuzzy subgroups. Int. j. contemp. math. sciences, 6(8), 365–372.
[17]    Muthuraj, R., & Balamurugan, S. (2013). Multi - fuzzy group and its level subgroups. Gen, 17(1), 74–81.
[18]    Muthuraj, R., & Balamurugan, S. (2014). A study on intuitionistic multi-anti fuzzy subgroups. Applied mathematics and sciences: an international journal (MATHSJ), 1(2), 35–52.
[19]    Rasuli, R. (2020). t-norms over Fuzzy Multigroups. Earthline journal of mathematical sciences, 3(2), 207–228. DOI:10.34198/ejms.3220.207228
[20]    Naseem, A., Akram, M., Ullah, K., & Ali, Z. (2023). Aczel-Alsina aggregation operators based on complex single-valued neutrosophic information and their application in decision-making problems. Decision making advances, 1(1), 86–114. DOI:10.31181/dma11202312
[21]    Alsarahead, M. O., & Al-Husban, A. (2022). Complex multi--fuzzy subgroups. Journal of discrete mathematical sciences and cryptography, 25(8), 2707–2716.
[22]    Akin, C. (2021). Multi-fuzzy soft groups. Soft computing, 25(1), 137–145. DOI:10.1007/s00500-020-05471-w
[23]    Mahmood, T., & ur Rehman, U. (2023). Bipolar complex fuzzy subalgebras and ideals of BCK/BCI-algebras. Journal of decision analytics and intelligent computing, 3(1), 47–61.
[24]    Dresher, M., & Ore, O. (1938). Theory of multigroups. American journal of mathematics, 60(3), 705–733.
[25]    Razzaque, A., & Razaq, A. (2022). On q-Rung orthopair fuzzy subgroups. Journal of function spaces, 2022. DOI:10.1155/2022/8196638
[26]    Ejegwa, P. A., Awolola, J. A., Agbetayo, J. M., & Adamu, I. M. (2021). On the characterisation of anti-fuzzy multigroups. Annals of fuzzy mathematics and informatics, 21(3), 307–318.
[27]    Ali, A., Ullah, K., & Hussain, A. (2023). An approach to multi-attribute decision-making based on intuitionistic fuzzy soft information and Aczel-Alsina operational laws. Journal of decision analytics and intelligent computing, 3(1), 80–89. DOI:10.31181/jdaic10006062023a
[28]    Deli, İ., & Keleş, M. A. (2021). Distance measures on trapezoidal fuzzy multi-numbers and application to multi-criteria decision-making problems. Soft computing, 25(8), 5979–5992.
[29]    Natarajan, R., & Vimala, J. (2007). Distributive l-ideal in commutative Lattice ordered group. Acta ciencia indica mathematics, 33(2), 517.
[30]    Sahoo, S. K., & Goswami, S. S. (2023). A comprehensive review of multiple criteria decision-making (MCDM) methods: advancements, applications, and future directions. Decision making advances, 1(1), 25–48. DOI:10.31181/dma1120237
[31]    Uluçay, V., Deli, I., & Şahin, M. (2018). Trapezoidal fuzzy multi-number and its application to multi-criteria decision-making problems. Neural computing and applications, 30, 1469–1478.
[32]    Uluçay, V., Deli, I., & Şahin, M. (2019). Intuitionistic trapezoidal fuzzy multi-numbers and its application to multi-criteria decision-making problems. Complex and intelligent systems, 5(1), 65–78.
[33]    Vimala, J., Mahalakshmi, P., Rahman, A. U., & Saeed, M. (2023). A customized TOPSIS method to rank the best airlines to fly during COVID-19 pandemic with q-rung orthopair multi-fuzzy soft information. Soft computing, 27(20), 14571–14584. DOI:10.1007/s00500-023-08976-2