The complexity of real-world scenarios often leads to uncertainty, prompting the introduction of neutrosophic theory as a tool for problem-solving. This paper aims to introduce a new distance measure on Fermatean neutrosophic sets and validate it through the axiomatic properties of distance measure. Additionally, it examines several characteristics of the distance measure and conducts a comparative analysis with existing distance measures on Fermatean neutrosophic sets. Finally, to demonstrate its practical relevance, we apply the proposed distance measure to address the problems associated with decision-making in crop farming within a Fermatean neutrosophic framework.
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Puzhakkara et al. (2024) studied this question.