Selecting the most suitable modulation technique in communication systems is challenging due to multiple alternatives and inherent uncertainty. Existing approaches often fail to simultaneously capture uncertainty and criteria interdependencies, and provide a reliable ranking, highlighting a clear research gap. This study proposes a novel criteria importance through intercriteria correlation (CRITIC) measurement of alternatives and ranking according to compromise solution (MARCOS) framework under triangular (p,q)-fuzzy numbers (T(p,q)-FNs), extending the (p,q)-rung orthopair fuzzy number, to address this problem. The methodology introduces new operational laws and a weighted average aggregation operator based on Dombi t-norms to effectively aggregate fuzzy information. The CRITIC method is used for objective criteria weighting, while MARCOS ranks alternatives to identify the optimal modulation technique. The framework is validated through a communication modulation selection case study and compared with existing methods. The results demonstrate that the proposed approach provides more accurate, realistic, and flexible decision-making, clearly highlighting its novelty and practical advantages.
Citation: Muhammad Ismail, Darjan Karabasevic, Pavle Brzakovic, Asghar Khan, Tahir Zaman. Development of the CRITIC-MARCOS method under triangular (p,q)-fuzzy numbers and its application in modulation technique selection[J]. AIMS Mathematics, 2026, 11(5): 14172-14210. doi: 10.3934/math.2026582
Selecting the most suitable modulation technique in communication systems is challenging due to multiple alternatives and inherent uncertainty. Existing approaches often fail to simultaneously capture uncertainty and criteria interdependencies, and provide a reliable ranking, highlighting a clear research gap. This study proposes a novel criteria importance through intercriteria correlation (CRITIC) measurement of alternatives and ranking according to compromise solution (MARCOS) framework under triangular (p,q)-fuzzy numbers (T(p,q)-FNs), extending the (p,q)-rung orthopair fuzzy number, to address this problem. The methodology introduces new operational laws and a weighted average aggregation operator based on Dombi t-norms to effectively aggregate fuzzy information. The CRITIC method is used for objective criteria weighting, while MARCOS ranks alternatives to identify the optimal modulation technique. The framework is validated through a communication modulation selection case study and compared with existing methods. The results demonstrate that the proposed approach provides more accurate, realistic, and flexible decision-making, clearly highlighting its novelty and practical advantages.
| [1] | D. Wang, M. Su, Y. Ren, J. Zuo, Y. Jin, C. Xu, Phase synchronization algorithm for high-speed space optical communication modulation baseband signal based on FPGA, In: 2024 International conference on optoelectronic information and optical engineering (OIOE 2024), 13182 (2024), 74–81. https://doi.org/10.1117/12.3030365 |
| [2] |
Y. Niu, Z. Wei, L. Wang, H. Wu, Z. Feng, Interference management for integrated sensing and communication systems: A survey, IEEE Internet Things J., 12 (2025), 8110–8134. https://doi.org/10.1109/JIOT.2024.3506162 doi: 10.1109/JIOT.2024.3506162
|
| [3] |
A. O. O. Esho, T. D. Iluyomade, T. M. Olatunde, O. P. Igbinenikaro, A comprehensive review of energy-efficient design in satellite communication systems, Int. J. Eng. Res. Updates, 6 (2024)., 013–025. https://doi.org/10.53430/ijeru.2024.6.2.0024 doi: 10.53430/ijeru.2024.6.2.0024
|
| [4] |
P. Patel, S. Pampaniya, A. Ghosh, R. Raj, D. Karuppaih, S. Kandasamy, Enhancing accessibility through machine learning: A review on visual and hearing impairment technologies, IEEE Access, 13 (2025), 33286–33307. https://doi.org/10.1109/ACCESS.2025.3539081 doi: 10.1109/ACCESS.2025.3539081
|
| [5] |
İ. Kaya, M. Çolak, F. Terzi, Use of MCDM techniques for energy policy and decision‐making problems: A review, Int. J. Energy Res., 42 (2018), 2344–2372. https://doi.org/10.1002/er.4016 doi: 10.1002/er.4016
|
| [6] |
C. Zhang, P. Xia, X. Zhang, Multi-attribute decision-making method of pumped storage capacity planning considering wind power uncertainty, J. Clean. Prod., 449 (2024), 141655. https://doi.org/10.1016/j.jclepro.2024.141655 doi: 10.1016/j.jclepro.2024.141655
|
| [7] |
R. M. A. Ikram, S. G. Meshram, M. A. Hasan, X. Cao, E. Alvandi, C. Meshram, et al., The application of multi-attribute decision making methods in integrated watershed management, Stoch. Environ. Res. Risk Assess., 38 (2024), 297–313. https://doi.org/10.1007/s00477-023-02557-3 doi: 10.1007/s00477-023-02557-3
|
| [8] |
L. A. Zadeh, Fuzzy sets, Inf. Control, 8 (1965), 338–353. https://doi.org/10.1016/S0019-9958(65)90241-X doi: 10.1016/S0019-9958(65)90241-X
|
| [9] | B. Oztaysi, S. C. Onar, S. Cebi, C. Kahraman, Fuzzy MCDM approaches in sustainability research: A literature review, In: Intelligent and fuzzy systems, Cham: Springer, 2025. https://doi.org/10.1007/978-3-031-97985-9_92 |
| [10] |
J. Khan, A. Ishizaka, M. Z. Babai, Enhancing multi-criteria inventory classification: Resolving boundary issues with VIKOR-fuzzy sorting, Int. J. Prod. Econ., 281 (2025), 109526. https://doi.org/10.1016/j.ijpe.2025.109526 doi: 10.1016/j.ijpe.2025.109526
|
| [11] | K. T. Atanassov, On intuitionistic fuzzy sets theory, Springer, 2012. https://doi.org/10.1007/978-3-642-29127-2 |
| [12] |
R. R. Yager, A. M. Abbasov, Pythagorean membership grades, complex numbers, and decision making, Int. J. Intell. Syst., 28 (2013), 436–452. https://doi.org/10.1002/int.21584 doi: 10.1002/int.21584
|
| [13] |
H. Z. Ibrahim, T. M. Al-Shami, O. G. Elbarbary, (3, 2)‐fuzzy sets and their applications to topology and optimal choices, Comput. Intell. Neurosci., 2021 (2021), 1272266. https://doi.org/10.1155/2021/1272266 doi: 10.1155/2021/1272266
|
| [14] |
T. Senapati, R. R. Yager, Fermatean fuzzy sets, J. Ambient Intell. Human. Comput., 11 (2020), 663–674. https://doi.org/10.1007/s12652-019-01377-0 doi: 10.1007/s12652-019-01377-0
|
| [15] |
K. H. Murad, H. Z. Ibrahim, (3,4)-fuzzy sets and their topological spaces, J. Math. Comput. Sci., 28 (2022), 158–170. http://dx.doi.org/10.22436/jmcs.028.02.04 doi: 10.22436/jmcs.028.02.04
|
| [16] |
R. R. Yager, Generalized orthopair fuzzy sets, IEEE Trans. Fuzzy Syst., 25 (2016), 1222–1230. https://doi.org/10.1109/TFUZZ.2016.2604005 doi: 10.1109/TFUZZ.2016.2604005
|
| [17] |
H. Z. Ibrahim, I. Alshammari, n, m-Rung orthopair fuzzy sets with applications to multicriteria decision making, IEEE Access, 10 (2022), 99562–99572. https://doi.org/10.1109/ACCESS.2022.3207184 doi: 10.1109/ACCESS.2022.3207184
|
| [18] |
S. Malik, S. C. Malik, N. Nandal, A. D. Yadav, Reliability assessment of a NSP system under constant triangular fuzzy failure rates, Int. J. Ind. Syst. Eng., 49 (2025), 405–420. https://doi.org/10.1504/IJISE.2025.146064 doi: 10.1504/IJISE.2025.146064
|
| [19] |
X. Sun, D. Wang, Conflict analysis of disputes in livelihood vulnerability assessment of flood using fuzzy TOPSIS method and GMCR with triangular fuzzy numbers, Sci. Rep., 15 (2025), 8609. https://doi.org/10.1038/s41598-025-93456-w doi: 10.1038/s41598-025-93456-w
|
| [20] |
L. Wang, S. Abdullah, A. A. Rahimzai, I. Ullah, A novel fuzzy neural network approach with triangular fuzzy information for the selection of logistics service providers, Artif. Intell. Rev., 58 (2025), 213. https://doi.org/10.1007/s10462-025-11209-7 doi: 10.1007/s10462-025-11209-7
|
| [21] |
J. Dong, S. Wan, S. M. Chen, Fuzzy best-worst method based on triangular fuzzy numbers for multi-criteria decision-making, Inf. Sci., 547 (2021), 1080–1104. https://doi.org/10.1016/j.ins.2020.09.014 doi: 10.1016/j.ins.2020.09.014
|
| [22] |
S. P. Wan, F. Wang, L. L. Lin, J. Y. Dong, Some new generalized aggregation operators for triangular intuitionistic fuzzy numbers and application to multi-attribute group decision making, Comput. Ind. Eng., 93 (2016), 286–301. https://doi.org/10.1016/j.cie.2015.12.027 doi: 10.1016/j.cie.2015.12.027
|
| [23] |
A. Fahmi, A. Hashmi, A. Khan, A. Mukheimer, T. Abdeljawad, R. Thinakaran, Triangular intuitionistic fuzzy frank aggregation for efficient renewable energy project selection, Eur. J. Pure Appl. Math., 18 (2025), 6227–6227. https://doi.org/10.29020/nybg.ejpam.v18i3.6227 doi: 10.29020/nybg.ejpam.v18i3.6227
|
| [24] |
P. Sharma, M. K. Mehlawat, S. Verma, P. Gupta, Multi-attribute group decision-making in site selection of solar photovoltaic cells under triangular Pythagorean fuzzy environment, Soft Comput., 2023. https://doi.org/10.1007/s00500-023-09009-8 doi: 10.1007/s00500-023-09009-8
|
| [25] |
M. Akram, S. M. U. Shah, M. M. A. Al-Shamiri, S. A. Edalatpanah, Extended DEA method for solving multi-objective transportation problem with Fermatean fuzzy sets, AIMS Mathematics, 8 (2023), 924–961. https://doi.org/10.3934/math.2023045 doi: 10.3934/math.2023045
|
| [26] |
A. Khan, S. Islam, M. Ismail, A. Alotaibi, Development of a triangular Fermatean fuzzy EDAS model for remote patient monitoring applications, Sci. Rep., 15 (2025), 22073. https://doi.org/10.1038/s41598-025-00914-6 doi: 10.1038/s41598-025-00914-6
|
| [27] |
B. Wan, R. Lu, M. Han, Weighted average LINMAP group decision-making method based on q-rung orthopair triangular fuzzy numbers, Granul. Comput., 7 (2022), 489–503. https://doi.org/10.1007/s41066-021-00280-4 doi: 10.1007/s41066-021-00280-4
|
| [28] |
J. Dombi, A general class of fuzzy operators, the demorgan class of fuzzy operators and fuzziness measures induced by fuzzy operators, Fuzzy Sets Syst, 8 (1982), 149–163. https://doi.org/10.1016/0165-0114(82)90005-7 doi: 10.1016/0165-0114(82)90005-7
|
| [29] |
P. Liu, J. Liu, S. M. Chen, Some intuitionistic fuzzy Dombi Bonferroni mean operators and their application to multi-attribute group decision making, J. Oper. Res. Soc., 2017. https://doi.org/10.1057/s41274-017-0190-y doi: 10.1057/s41274-017-0190-y
|
| [30] |
M. Akram, W. A. Dudek, J. M. Dar, Pythagorean Dombi fuzzy aggregation operators with application in multicriteria decision‐making, Int. J. Intell. Syst., 34 (2019), 3000–3019. https://doi.org/10.1002/int.22183 doi: 10.1002/int.22183
|
| [31] |
J. Ali, Z. Mehmood, p, q-Quasirung orthopair fuzzy multi-criteria group decision-making algorithm based on generalized Dombi aggregation operators, J. Appl. Math. Comput., 71 (2025), 69–102. https://doi.org/10.1007/s12190-024-02227-9 doi: 10.1007/s12190-024-02227-9
|
| [32] |
Z. Ali, Circular pq-quasirung orthopair fuzzy sets with Dombi power aggregation operators: Application to renewable natural gas, Int. J. Res. Ind. Eng., 14 (2025), 466–490. https://doi.org/10.22105/riej.2025.489830.1497 doi: 10.22105/riej.2025.489830.1497
|
| [33] |
T. Senapati, G. Chen, I. Ullah, M. S. A. Khan, F. Hussain, A novel approach towards multiattribute decision making using q-rung orthopair fuzzy Dombi–Archimedean aggregation operators, Heliyon, 10 (2024), 27969. https://doi.org/10.1016/j.heliyon.2024.e27969 doi: 10.1016/j.heliyon.2024.e27969
|
| [34] |
N. Yaqoob, M. Gulistan, M. M. Abbas, K. Hayat, M. M. Al-Shamiri, Dombi aggregation operator in terms of complex bipolar fuzzy sets with application in decision making problems, Complex Intell. Syst., 11 (2025), 483. https://doi.org/10.1007/s40747-025-02078-2 doi: 10.1007/s40747-025-02078-2
|
| [35] |
Z. Ali, M. Waqas, S. Moslem, T. Senapati, D. Esztergár-Kiss, Evaluation of public bus transport service quality based on circular Pythagorean fuzzy soft Einstein aggregation operators, Complex Intell. Syst., 11 (2025), 276. https://doi.org/10.1007/s40747-025-01864-2 doi: 10.1007/s40747-025-01864-2
|
| [36] |
S. Ullah, S. Khan, A. A. Rahimzai, S. Abdullah, M. Ismail, H. Ullah, Application of fractional fuzzy soft sets using hamacher aggregation operators in agriculture robots selection, Artif Intell Rev., 58 (2025), 395. https://doi.org/10.1007/s10462-025-11329-0 doi: 10.1007/s10462-025-11329-0
|
| [37] |
H. Dhumras, M. Kumar, R. K. Bajaj, Effectiveness of debris flow mitigation measures through T-spherical fuzzy soft Dombi aggregation operators with EDAS-based multi-criteria decision making in mountainous regions, J. Ind. Inf. Integr., 48 (2025), 100968. https://doi.org/10.1016/j.jii.2025.100968 doi: 10.1016/j.jii.2025.100968
|
| [38] | M. Pal, H. Dhumras, G. Garg, V. Shukla, On renewable energy source selection problem using T‐spherical fuzzy soft Dombi aggregation operators, In: Sustainable mobility: Policies, challenges and advancements, 2024,237–253. https://doi.org/10.1002/9781394166831.ch14 |
| [39] |
M. Akram, F. Ilyas, H. Garg, Multi-criteria group decision making based on ELECTRE I method in Pythagorean fuzzy information, Soft Comput., 24 (2020), 3425–3453. https://doi.org/10.1007/s00500-019-04105-0 doi: 10.1007/s00500-019-04105-0
|
| [40] |
A. Almjally, M. Khan, M. Ismail, A. Khan, Broadband technology selection based on three-way decision-making model under the tripolar fuzzy information, Int. J. Fuzzy Syst., 2025. https://doi.org/10.1007/s40815-025-02054-5 doi: 10.1007/s40815-025-02054-5
|
| [41] |
P. Liu, J. Shen, P. Zhang, B. Ning, Multi-attribute group decision-making method using single-valued neutrosophic credibility numbers with fairly variable extended power average operators and GRA-MARCOS, Expert Syst. Appl., 263 (2025), 125703. https://doi.org/10.1016/j.eswa.2024.125703 doi: 10.1016/j.eswa.2024.125703
|
| [42] |
Z. Ali, M. Waqas, K. Hila, Multi-attributive border approximation area comparison model based on Yager weighted aggregation operators for circular Pythagorean fuzzy information and their application in shortest path problems, J. Supercomput., 81 (2025), 1308. https://doi.org/10.1007/s11227-025-07327-2 doi: 10.1007/s11227-025-07327-2
|
| [43] |
D. Diakoulaki, G. Mavrotas, L. Papayannakis, Determining objective weights in multiple criteria problems: The critic method, Comput. Oper. Res., 22 (1995), 763–770. https://doi.org/10.1016/0305-0548(94)00059-H doi: 10.1016/0305-0548(94)00059-H
|
| [44] |
M. Žižović, B. Miljković, D. Marinković, Objective methods for determining criteria weight coefficients: A modification of the CRITIC method, Decis. Mak.: Appl. Manag. Eng., 3 (2020), 149–161. https://doi.org/10.31181/dmame2003149z doi: 10.31181/dmame2003149z
|
| [45] |
H. W. Wu, J. Zhen, J. Zhang, Urban rail transit operation safety evaluation based on an improved CRITIC method and cloud model, J. Rail Transp. Plan. Manag., 16 (2020), 100206. https://doi.org/10.1016/j.jrtpm.2020.100206 doi: 10.1016/j.jrtpm.2020.100206
|
| [46] |
B. Pan, S. Liu, Z. Xie, Y. Shao, X. Li, R. Ge, Evaluating operational features of three unconventional intersections under heavy traffic based on CRITIC method, Sustainability, 13 (2021), 4098. https://doi.org/10.3390/su13084098 doi: 10.3390/su13084098
|
| [47] | N. Yalcin, U. Ünlü, A multi-criteria performance analysis of initial public offering (IPO) firms using CRITIC and VIKOR methods, Technol. Econ. Dev. Econ., 24 (2018), 534–560. https://dx.doi.org/10.3846/20294913.2016.1213201 |
| [48] |
X. Peng, H. Huang, Fuzzy decision making method based on CoCoSo with critic for financial risk evaluation, Technol. Econ. Dev. Econ., 26 (2020), 695–724. https://doi.org/10.3846/tede.2020.11920 doi: 10.3846/tede.2020.11920
|
| [49] |
X. Peng, X. Zhang, Z. Luo, Pythagorean fuzzy MCDM method based on CoCoSo and CRITIC with score function for 5G industry evaluation, Artif. Intell. Rev., 53 (2020), 3813–3847. https://doi.org/10.1007/s10462-019-09780-x doi: 10.1007/s10462-019-09780-x
|
| [50] |
R. Rostamzadeh, M. K. Ghorabaee, K. Govindan, A. Esmaeili, H. B. K. Nobar, Evaluation of sustainable supply chain risk management using an integrated fuzzy TOPSIS-CRITIC approach, J. Clean. Prod., 175 (2018), 651–669. https://doi.org/10.1016/j.jclepro.2017.12.071 doi: 10.1016/j.jclepro.2017.12.071
|
| [51] |
V. Dutta, S. Haldar, P. Kaur, Y. Gajpal, Comparative analysis of TOPSIS and TODIM for the performance evaluation of foreign players in Indian premier league, Complexity, 2022 (2022), 9986137. https://doi.org/10.1155/2022/9986137 doi: 10.1155/2022/9986137
|
| [52] |
Ö. Işık, A. Çalık, M. Shabir, A consolidated MCDM framework for overall performance assessment of listed insurance companies based on ranking strategies, Comput. Econ., 65 (2025), 271–312. https://doi.org/10.1007/s10614-024-10578-5 doi: 10.1007/s10614-024-10578-5
|
| [53] | F. Xiong, Digital modulation techniques, 2006. |
| [54] |
J. Brodny, M. Tutak, Assessing the energy security of European Union countries from two perspectives–A new integrated approach based on MCDM methods, Appl. Energy, 347 (2023), 121443. https://doi.org/10.1016/j.apenergy.2023.121443 doi: 10.1016/j.apenergy.2023.121443
|
| [55] |
A. Saha, D. Pamucar, O. F. Gorcun, A. R. Mishra, Warehouse site selection for the automotive industry using a fermatean fuzzy-based decision-making approach, Expert Syst. Appl., 211 (2023), 118497. https://doi.org/10.1016/j.eswa.2022.118497 doi: 10.1016/j.eswa.2022.118497
|
| [56] |
Ž. Stević, D. Pamučar, A. Puška, P. Chatterjee, Sustainable supplier selection in healthcare industries using a new MCDM method: Measurement of alternatives and ranking according to COmpromise solution (MARCOS), Comput. Ind. Eng., 140 (2020), 106231. https://doi.org/10.1016/j.cie.2019.106231 doi: 10.1016/j.cie.2019.106231
|
| [57] |
K. Ghasemi, M. Behzadfar, K. Borhani, Spatial analysis of leisure land uses in Tehran: Assessing inequity using the MARCOS method within a GIS framework, Heliyon, 9 (2023), e19691. https://doi.org/10.1016/j.heliyon.2023.e19691 doi: 10.1016/j.heliyon.2023.e19691
|
| [58] |
S. Zeng, A. Ye, W. Su, M. Chen, C. Llopis-Albert, Site evaluation of subsea tunnels with sightseeing function based on dynamic complex MARCOS method, Technol. Forecast. Soc. Chang., 199 (2024), 123041. https://doi.org/10.1016/j.techfore.2023.123041 doi: 10.1016/j.techfore.2023.123041
|
| [59] |
S. Qu, X. Kong, A Bonferroni mean operator for p, q-Rung triangular Orthopair fuzzy environments and its application in COPRAS method, Symmetry, 17 (2025), 1422. https://doi.org/10.3390/sym17091422 doi: 10.3390/sym17091422
|
| [60] |
M. Hajiaghaei-Keshteli, Z. Cenk, B. Erdebilli, Y. S. Özdemir, F. Gholian-Jouybari, Pythagorean fuzzy TOPSIS method for green supplier selection in the food industry, Expert Syst. Appl., 224 (2023), 120036. https://doi.org/10.1016/j.eswa.2023.120036 doi: 10.1016/j.eswa.2023.120036
|
| [61] |
I. Ullah, S. Abdullah, M. Nawaz, Analyzing the traffic light control systems based on novel fuzzy neural network under triangular fuzzy numbers, Signal Image Video Process., 19 (2025), 1169. https://doi.org/10.1007/s11760-025-04697-1 doi: 10.1007/s11760-025-04697-1
|
| [62] | D. Rudolph, Modulation methods, In: Fundamentals of RF and microwave techniques and technologies, Cham: Springer, 2023, 1297–1508. https://doi.org/10.1007/978-3-030-94100-0_14 |
| [63] |
M. Khan, A. Khan, M. Ismail, R. A. Ziar, A development of the circular non-linear Diophantine fuzzy set and their application in cloud services provider selection, Int. J. Comput. Intell. Syst., 19 (2026), 13. https://doi.org/10.1007/s44196-025-01079-w doi: 10.1007/s44196-025-01079-w
|
| [64] |
S. S. Majd, A. Maleki, S. Basirat, A. Golkarfard, Fermatean fuzzy TOPSIS method and its application in ranking business intelligence-based strategies in smart city context, J. Oper. Intell., 3 (2025), 1–16. https://doi.org/10.31181/jopi31202532 doi: 10.31181/jopi31202532
|
| [65] |
S. Abdullah, M. Nawaz, N. Ali, S. Khan, A novel linguistic pq-rung orthopair fuzzy framework for decision-making using extended TOPSIS and enhanced GRA approaches, Int. J. Dynam. Control, 14 (2026), 1. https://doi.org/10.1007/s40435-025-01907-z doi: 10.1007/s40435-025-01907-z
|
| [66] |
S. Abdullah, H. Ali, A. A. Rahimzai, S. Khan, Novel concept of linguistic fractional fuzzy information for effective water filtration decision-making problem based on WASPAS method, Sci. Rep., 15 (2025), 33169. https://doi.org/10.1038/s41598-025-15817-9 doi: 10.1038/s41598-025-15817-9
|
| [67] |
M. Nawaz, S. Abdullah, I. Ullah, An integrated fuzzy neural network model for surgical approach selection using double hierarchy linguistic information, Comput. Biol. Med., 186 (2025), 109606. https://doi.org/10.1016/j.compbiomed.2024.109606 doi: 10.1016/j.compbiomed.2024.109606
|
| [68] |
S. Abdullah, I. Ullah, F. Ghani, Heterogeneous wireless network selection using feed forward double hierarchy linguistic neural network, Artif. Intell. Rev., 57 (2024), 191. https://doi.org/10.1007/s10462-024-10826-y doi: 10.1007/s10462-024-10826-y
|
Figures(11) / Tables(18)
Muhammad Ismail, Darjan Karabasevic, Pavle Brzakovic, Asghar Khan, Tahir Zaman. Development of the CRITIC-MARCOS method under triangular (p,q)-fuzzy numbers and its application in modulation technique selection[J]. AIMS Mathematics, 2026, 11(5): 14172-14210. doi: 10.3934/math.2026582
DownLoad: