Linear Diophantine Fuzzy Clustering Algorithm Based on Correlation Coefficient and Analysis on Logistic Efficiency of Food Products

The significance of clustering algorithms lies in their ability to distinguish problems and devise customized solutions. In the broader context of clustering, fuzzy clustering is one of the crucial aspects. In response to the real-world clustering problems, this research suggests a new fuzzy cluster scheme of data under the linear diophantine fuzzy set(LDFS) framework. More precisely, LDF clustering is initiated with the aid of the correlation coefficient( $\mathcal {CC}$ ) and weighted correlation coefficient( $\mathcal {WCC}$ ) for LDFS. Due to their ability to quantify the degree of similarity between two elements, $\mathcal {CC}$ are valuable in clustering problems. The LDF- clustering algorithm comprises a well-integrated algorithm for managing uncertainty and $\mathcal {CC}$ among LDFS. Also, our approach to LDF clustering is compared to existing fuzzy clustering studies to assess its effectiveness. Since LDFS broadens the score space, the experimental evaluation of our proposed scheme enables Decision makers(DM) to freely select their score values. The theme of this study is to impart the commencement of LDF-clustering analysis and attempt to apply $\mathcal {CC}$ to the clustering problem. An interpretative example provides the analysis of the logistic efficiency of food products by employing an LDF-clustering algorithm.