A Novel Distance Based Decision Making Approach Using Fermatean Picture Fuzzy Sets For Smart Agriculture Land Suitability

Abstract

Distance measures are fundamental tools for similarity analysis and classification in fuzzy decision-making systems. However, the existing literature does not provide Euclidean and Normalized Euclidean Distance Measures specifically developed for Fermatean Picture Fuzzy Sets (FPFS), limiting their application in distance-based intelligent decision-making. To address this limitation, this paper proposes new Euclidean and Normalized Euclidean Distance Measures for FPFS and establishes their essential mathematical properties. The effectiveness of the proposed measures is demonstrated through a K-Nearest Neighbour (KNN)-based agricultural land suitability assessment under the Fermatean picture fuzzy environment. The obtained results show that both measures accurately evaluate the similarity among alternatives and produce consistent classification outcomes. Moreover, the normalized measure expresses distance values within a common interval, enabling meaningful comparison while preserving the relative ranking of alternatives. The proposed framework provides a mathematically sound and computationally efficient approach for similarity analysis and intelligent decision-making under Fermatean Picture Fuzzy information.