A Robust Circular Complex Intuitionistic Fuzzy Framework for Optimizing Agricultural Robot Decision-Making Under Uncertain Environmental Conditions

Kaleem Ullah; Noor Rehman; Abbas Ali

doi:10.31181/sdmap41202770

Authors

Kaleem Ullah Department of Mathematics and Statistics, Bacha Khan University, Charsadda Khyber Pakhtunkhawa, Pakistan Author https://orcid.org/0009-0005-6793-9172
Noor Rehman Department of Mathematics and Statistics, Bacha Khan University, Charsadda Khyber Pakhtunkhawa, Pakistan Author https://orcid.org/0000-0003-3094-4865
Abbas Ali Department of Mathematics and Statistics, Riphah International University, Islamabad, Pakistan Author https://orcid.org/0000-0003-4328-8967

DOI:

https://doi.org/10.31181/sdmap41202770

Keywords:

Circular complex intuitionistic fuzzy set, Complex intuitionistic fuzzy set, Multi-criteria decision-making, Fuzzy sets, MCDM

Abstract

Agricultural robotic systems frequently operate in highly dynamic and uncertain environmental conditions, where incomplete sensor readings, weather variability, terrain irregularities, and crop-state ambiguity significantly affect decision-making performance. To address these challenges, this study introduces the concept of Circular Complex Intuitionistic Fuzzy Sets (CrC-IFS) as an advanced mathematical tool for modeling uncertainty in agricultural robot decision-making processes. The Circular Complex Intuitionistic Fuzzy Set extends classical complex intuitionistic and circular intuitionistic fuzzy structures by incorporating enhanced higher-order membership flexibility for representing imprecise and multidimensional environmental information. To strengthen uncertainty modeling capability, refined algebraic operational laws for CrC-IFS are developed, including direct sum, direct product, and scalar multiplication based on generalized t-norms and t-conorms. Furthermore, circular complex intuitionistic fuzzy weighted and ordered weighted aggregation operators are proposed to integrate multiple environmental and operational criteria, such as terrain conditions, obstacle density, energy consumption, crop maturity levels, and weather fluctuations. Building upon these theoretical developments, a robust multi-criteria decision-making framework is constructed to optimize agricultural robot strategies, enabling systematic prioritization of navigation paths, task allocation, harvesting schedules, and adaptive control actions. The results demonstrate that the proposed framework enhances decision robustness, improves operational efficiency, and supports intelligent autonomous behavior under highly uncertain agricultural field conditions.

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