A picture fuzzy SWARA–VIKOR framework for evaluating drone-swarm navigation and mission-coordination strategies under uncertainty
Abstract
Intelligent decision-making frameworks need to be able to handle operational uncertainty, ambiguous expert judgments, and interactions among mission attributes to navigate and coordinate missions in an autonomous drone swarm efficiently. Traditional optimization and decision models do not effectively represent ambiguous expert judgments and critical navigation and coordination factors that impact the behavior of the systems in a nonlinear way. To overcome all these limitations, this study proposes a Picture Fuzzy Stepwise Weight Assessment Ratio Analysis–VIšekriterijumsko KOmpromisno Rangiranje (PF-SWARA–VIKOR) framework for evaluating drone-swarm strategies under uncertain conditions. PF-SWARA weighting begins with an expert-based screening phase to determine the relevance of the criteria, allowing only the most relevant criteria to proceed to the weighting and ranking phase. Picture Fuzzy Sets (PFSs) provide a more complete representation of uncertainty and hesitation compared to ordinary or intuitionistic fuzzy sets by means of positive, neutral, negative, and refusal degrees that model expert ratings. While the criterion weights are obtained by PF-SWARA, the five strategies centralized, decentralized consensus-based, leader–follower, hybrid-adaptive, and behaviour-based reactive coordination strategies are ranked by PF-VIKOR. According to the hypothetical application, U4 is the first preference, since it has the minimum compromise value 𝒬4=0.0000 , and the preference order is U4≻ U2≻ U1≻ U5≻ U3 . The most influential criteria are L7 and L1 , with weights of 0.1360 and 0.1357 , respectively. Furthermore, U4 is first across all values of τ =0.1 to 0.9 , but the rankings in-between shift depending on the relative strength of the group's utility and the individual's regret. Since the case study uses simulated experts and hypothetical evaluations, the results are of methodological applicability and not empirically generalizable.
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BibTeX
@article{saadaoui2026picture,
title = {{A picture fuzzy SWARA–VIKOR framework for evaluating drone-swarm navigation and mission-coordination strategies under uncertainty}},
author = {Kheir Saadaoui and Asma Farhad and Kifayat Ullah},
journal = {Scientific Reports},
year = {2026},
month = oct,
doi = {10.1038/s41598-026-72313-4},
url = {https://www.nature.com/articles/s41598-026-72313-4},
note = {CC BY-NC-ND 4.0},
}
RIS
TY - JOUR
TI - A picture fuzzy SWARA–VIKOR framework for evaluating drone-swarm navigation and mission-coordination strategies under uncertainty
AU - Kheir Saadaoui
AU - Asma Farhad
AU - Kifayat Ullah
PY - 2026
DA - 2026/10/01
JO - Scientific Reports
DO - 10.1038/s41598-026-72313-4
UR - https://www.nature.com/articles/s41598-026-72313-4
AB - Intelligent decision-making frameworks need to be able to handle operational uncertainty, ambiguous expert judgments, and interactions among mission attributes to navigate and coordinate missions in an autonomous drone swarm efficiently. Traditional optimization and decision models do not effectively represent ambiguous expert judgments and critical navigation and coordination factors that impact the behavior of the systems in a nonlinear way. To overcome all these limitations, this study proposes a Picture Fuzzy Stepwise Weight Assessment Ratio Analysis–VIšekriterijumsko KOmpromisno Rangiranje (PF-SWARA–VIKOR) framework for evaluating drone-swarm strategies under uncertain conditions. PF-SWARA weighting begins with an expert-based screening phase to determine the relevance of the criteria, allowing only the most relevant criteria to proceed to the weighting and ranking phase. Picture Fuzzy Sets (PFSs) provide a more complete representation of uncertainty and hesitation compared to ordinary or intuitionistic fuzzy sets by means of positive, neutral, negative, and refusal degrees that model expert ratings. While the criterion weights are obtained by PF-SWARA, the five strategies centralized, decentralized consensus-based, leader–follower, hybrid-adaptive, and behaviour-based reactive coordination strategies are ranked by PF-VIKOR. According to the hypothetical application, U_4 is the first preference, since it has the minimum compromise value 𝒬_4=0.0000 , and the preference order is U_4≻ U_2≻ U_1≻ U_5≻ U_3 . The most influential criteria are L_7 and L_1 , with weights of 0.1360 and 0.1357 , respectively. Furthermore, U_4 is first across all values of τ =0.1 to 0.9 , but the rankings in-between shift depending on the relative strength of the group's utility and the individual's regret. Since the case study uses simulated experts and hypothetical evaluations, the results are of methodological applicability and not empirically generalizable.
SN - 2045-2322
ER -