An interval-valued q-rung orthopair fuzzy FUCOM-RAFSI framework for simulation-based benchmarking of robotic-manipulator control strategies

Abstract

Comparing robotic-manipulator control strategies is difficult because performance is multi-criteria and replicated runs yield distributions rather than single values. This study benchmarks six strategies: proportional-integral-derivative control, PI-D control, sliding-mode control, fuzzy gain-scheduled PID control, model predictive control implemented as a fixed-gain finite-horizon linear-quadratic law (MPC-LQ) and active disturbance rejection control. Thirty common-random-number replications of a two-degree-of-freedom manipulator simulation are conducted with randomised payload, friction, disturbance torque and sensor noise. Six cost metrics are converted to goodness values using pooled fifth- and ninety-fifth-percentile anchors and summarised as interval-valued q-rung orthopair fuzzy numbers. A fixed radial-projection rule enforces q-rung admissibility where required. The score is adopted from the published interval-valued q-rung literature, while the four-endpoint distance is an explicit adaptation of Du’s published Minkowski-type q-rung distance principle. Literature-informed, author-specified scenario weights are generated with the full consistency method (FUCOM) and the strategies are ranked with RAFSI (ranking of alternatives through functional mapping of criterion sub-intervals into a single interval) using fixed external anchors. Under the stated model, tunings and baseline weights, active disturbance rejection control ranks first (0.735), followed by sliding-mode control (0.635) and PI-D control (0.593). The leading strategy remains unchanged under equal weights, four emphasis profiles, 10,000 seeded FUCOM-ratio perturbations, q values from 2 to 5 and an alternative projection rule; however, some middle ranks change across emphasis profiles. A distance-based ideal-solution comparison reproduces the baseline order. The study provides a transparent worked benchmarking example and does not establish hardware performance.

Keywords

• interval-valued q-rung orthopair fuzzy sets
• FUCOM
• RAFSI
• control strategy
• benchmarking
• two-degree-of-freedom manipulator simulation

Supporting Institution

This research received no external funding.

Ethical Statement

The research presented in this manuscript does not involve human participants, animal subjects or clinical trials. The study used no personal, biometric or health-related data.

Thanks

The author sincerely thanks the anonymous reviewers for their careful reading and constructive comments, which have substantially improved the quality and clarity of this manuscript.

Robotik manipülatör kontrol stratejilerinin benzetim tabanlı kıyaslanması için aralık değerli q-rung ortopair bulanık FUCOM-RAFSI çerçevesi

Abstract

Bir robotik manipülatör için kontrol stratejilerini karşılaştırmak güçtür; çünkü performans çok kriterlidir ve tekrarlanan benzetim koşuları tek bir değer yerine sonuç dağılımları üretir. Bu çalışma altı stratejiyi kıyaslamaktadır: oransal-integral-türev (PID) kontrol, PI-D kontrol, kayan kipli kontrol, bulanık kazanç ayarlamalı PID kontrol, sabit kazançlı sonlu ufuklu doğrusal-karesel biçimde gerçeklenen model öngörülü kontrol (MPC-LQ) ve aktif bozucu bastırma kontrolü. İki serbestlik dereceli bir manipülatör benzetiminin otuz ortak-rassal-sayı (common-random-number) tekrarı; rassallaştırılmış yük, sürtünme, bozucu tork ve sensör gürültüsü ile gerçekleştirilmiştir. Altı maliyet ölçütü, havuzlanmış 5. ve 95. yüzdelik çapalar kullanılarak uygunluk değerlerine dönüştürülmüş ve aralık değerli q-rung ortopair bulanık sayılar olarak özetlenmiştir. Sabit bir radyal izdüşüm kuralı, gerektiğinde q-rung uygunluğunu sağlamaktadır. Skor, yayımlanmış aralık değerli q-rung literatüründen alınmış; dört uç noktalı uzaklık ise Du’nun yayımlanmış Minkowski tipi q-rung uzaklık ilkesinin açık bir uyarlaması olarak kullanılmıştır. Literatürden beslenen ve yazar tarafından belirlenen senaryo ağırlıkları Tam Tutarlılık Yöntemi (FUCOM; Full Consistency Method) ile üretilmiş ve stratejiler, ölçüt alt aralıklarının tek bir aralığa işlevsel eşlenmesine dayanan RAFSI (Ranking of Alternatives through Functional mapping of criterion Sub-intervals into a Single Interval) yöntemiyle sabit dış çapalar kullanılarak sıralanmıştır. Belirtilen model, ayarlar ve temel ağırlıklar altında aktif bozucu bastırma denetleyicisi ilk sırada (0.735) yer almış, onu kayan kipli kontrol (0.635) ve PI-D kontrol (0.593) izlemiştir. Lider strateji; eşit ağırlıklar, dört vurgu profili, sabit tohumla üretilen 10.000 FUCOM oranı pertürbasyonu, q = 2-5 değerleri ve alternatif bir izdüşüm kuralı altında birinci sırada kalmıştır; ancak bazı orta sıralar vurgu profillerine göre değişiklik göstermiştir. Uzaklığa dayalı bir ideal çözüm karşılaştırması temel sıralamayı doğrulamaktadır. Çalışma, şeffaf ve uygulamalı bir kıyaslama örneği sunmaktadır; sonuçlar donanım performansının doğrulanması olarak yorumlanmamalıdır.

Keywords

• aralık değerli q-rung ortopair bulanık kümeler
• FUCOM
• RAFSI
• kontrol stratejisi
• kıyaslama
• iki serbestlik dereceli manipülatör benzetimi

References

1. Zhai, J., & Xu, G. (2021). A novel non-singular terminal sliding mode trajectory tracking control for robotic manipulators. IEEE Transactions on Circuits and Systems II: Express Briefs, 68(1), 391–395. https://doi.org/10.1109/TCSII.2020.2999937
2. Yin, X., Pan, L., & Cai, S. (2021). Robust adaptive fuzzy sliding mode trajectory tracking control for serial robotic manipulators. Robotics and Computer-Integrated Manufacturing, 72, 101884. https://doi.org/10.1016/j.rcim.2019.101884
3. Zhong, G., Wang, C., & Dou, W. (2021). Fuzzy adaptive PID fast terminal sliding mode controller for a redundant manipulator. Mechanical Systems and Signal Processing, 159, 107577. https://doi.org/10.1016/j.ymssp.2020.107577
4. Ashagrie, A., Salau, A. O., & Weldcherkos, T. (2021). Modeling and control of a 3-DOF articulated robotic manipulator using self-tuning fuzzy sliding mode controller. Cogent Engineering, 8(1), 1950105. https://doi.org/10.1080/23311916.2021.1950105
5. Raoufi, M., Habibi, H., Yazdani, A., & Wang, H. (2022). Robust prescribed trajectory tracking control of a robot manipulator using adaptive finite-time sliding mode and extreme learning machine method. Robotics, 11(5), 111. https://doi.org/10.3390/robotics11050111
6. Rishabh, R., & Das, K. N. (2025). A critical review on metaheuristic algorithms based multi-criteria decision-making approaches and applications. Archives of Computational Methods in Engineering, 32(2), 963–993. https://doi.org/10.1007/s11831-024-10165-9
7. Halim, A. H., Ismail, I., & Das, S. (2021). Performance assessment of the metaheuristic optimization algorithms: An exhaustive review. Artificial Intelligence Review, 54(3), 2323–2409. https://doi.org/10.1007/s10462-020-09906-6
8. Weerasuriya, A. U., Zhang, X., Wang, J., Lu, B., Tse, K. T., & Liu, C. H. (2021). Performance evaluation of population-based metaheuristic algorithms and decision-making for multi-objective optimization of building design. Building and Environment, 198, 107855. https://doi.org/10.1016/j.buildenv.2021.107855

9. Sadhu, T., Chowdhury, S., Mondal, S., Roy, J., Chakrabarty, J., & Lahiri, S. K. (2023). A comparative study of metaheuristics algorithms based on their performance of complex benchmark problems. Decision Making: Applications in Management and Engineering, 6(1), 341–364. https://doi.org/10.31181/dmame0306102022r
10. Goula, E.-M. K., & Sotiropoulos, D. G. (2024). HRA: A multi-criteria framework for ranking metaheuristic optimization algorithms. In 2024 Sixth International Conference on Intelligent Computing in Data Sciences (ICDS) (pp. 1–8). IEEE. https://doi.org/10.1109/ICDS62089.2024.10756478
11. Gharib, H., & Kovács, G. (2025). Multi-criteria decision-making algorithm selection and adaptation for performance improvement of two stroke marine diesel engines. Journal of Marine Science and Engineering, 13(10), 1916. https://doi.org/10.3390/jmse13101916
12. Nassereddine, K., & Turzynski, M. (2025). Comparison of metaheuristic algorithms set-point tracking-based weight optimization for model predictive control. Scientific Reports, 15, 41414. https://doi.org/10.1038/s41598-025-25319-3
13. [Baydaş, M., Eren, T., Stević, Ž., Starčević, V., & Parlakkaya, R. (2023). Proposal for an objective binary benchmarking framework that validates each other for comparing MCDM methods through data analytics. PeerJ Computer Science, 9, e1350. https://doi.org/10.7717/peerj-cs.1350
14. Yager, R. R. (2017). Generalized orthopair fuzzy sets. IEEE Transactions on Fuzzy Systems, 25(5), 1222–1230. https://doi.org/10.1109/TFUZZ.2016.2604005
15. Joshi, B. P., Singh, A., Bhatt, P. K., & Vaisla, K. S. (2018). Interval valued q-rung orthopair fuzzy sets and their properties. Journal of Intelligent & Fuzzy Systems, 35(5), 5225–5230. https://doi.org/10.3233/JIFS-169806
16. Du, W. S. (2018). Minkowski-type distance measures for generalized orthopair fuzzy sets. International Journal of Intelligent Systems, 33(4), 802–817. https://doi.org/10.1002/int.21968
17. Pamučar, D., Stević, Ž., & Sremac, S. (2018). A new model for determining weight coefficients of criteria in MCDM models: Full consistency method (FUCOM). Symmetry, 10(9), 393. https://doi.org/10.3390/sym10090393
18. Žižović, M., Pamučar, D., Albijanić, M., Chatterjee, P., & Pribićević, I. (2020). Eliminating rank reversal problem using a new multi-attribute model—The RAFSI method. Mathematics, 8(6), 1015. https://doi.org/10.3390/math8061015
19. Pamucar, D., & Ecer, F. (2020). Prioritizing the weights of the evaluation criteria under fuzziness: The fuzzy full consistency method – FUCOM-F. Facta Universitatis, Series: Mechanical Engineering, 18(3), 419–437. https://doi.org/10.22190/FUME200602034P
20. Deveci, M., Pamucar, D., & Oguz, E. (2022). Floating photovoltaic site selection using fuzzy rough numbers based LAAW and RAFSI model. Applied Energy, 324, 119597. https://doi.org/10.1016/j.apenergy.2022.119597