Smart Irrigation Frameworks Using Complex Neutrosophic Fuzzy Hesitant Distance Measures

Abstract

In decision-making and intelligent systems, accurately measuring distances in uncertain and high-dimensional environments remains a challenge. Traditional distance measures oftenly missed the hesitancy, indeterminacy, and blurriness intrinsic in real-world statistics. To address this limitation, we propose novel complex neutrosophic fuzzy hesitance distance measures, specifically the complex neutrosophic fuzzy Euclidean distance measure with hesitance degree. These measures extend existing fuzzy distance concepts by incorporating truth, indeterminacy, and falsity components, allowing for more comprehensive and precise analysis of uncertainty. This paper contains various definition of basic neutrosophic fuzzy set with their theorems and examples, Euclidean distance measure’s definitions and its operations. Furthermore, through computational modeling, we integrate complex neutrosophic fuzzy Euclidean hesitance distance measure (CNFEHDM) into a MCDM framework, apply to smart irrigation system for small-scale farmers. The proposed approach demonstrates enhanced precision and adaptability in managing vague and inconsistent data. Application results show that water availability is the most influential factor, enabling the smart irrigation system to optimize water usage, prevent over-irrigation, and support sustainable farming practices. A comparative analysis highlights the advantages of normalized Euclidean distance measure over existing methods, showcasing its
superior ability to navigate complex, vague, and inconsistent data sets.