Optimizing Natural Dye Concentrations in Batik using Fuzzy k-means Clustering and m-polar Fuzzy Graphs: A Heritage Preservation Approach

One of the obstacles faced in the batik colouring process using natural dyes derived from plants is determining the best natural colour for dabbing and “laser” techniques. The dabbing process involves using a brush to apply colouring material to batik. While the “lasem” technique is the final colouring technique of a colouring process. Generally, the Lasem technique is used to change the colour of a motif from white to another colour. Therefore, this research aims to obtain the best natural colour concentration for the colouring and lasering process using the Fuzzy k-Means Clustering and Fuzzy Graph m-Polar methods. This research used 23 samples of natural colours used in the production of Batik Nilo Tirto. The sample data is grouped into 3 clusters using the Fuzzy k-means Clustering method. The cluster data is used in the formulation of fuzzy equations and graphs. Fuzzy k-means Clustering is a method of grouping data with specific characteristics by randomly selecting the initial centroid. Based on cluster data, the best natural colour concentration was chosen using the Fuzzy Graph m-Polar method. A fuzzy Graph m-polar is a method for making decisions. We obtained three natural colour clusters, namely Strong, Medium, and Weak. The best natural colour concentration found in the Strong cluster can be used for the dabbing process, and the best natural colour concentration in the Weak cluster can be used for the “lasem” process. The proposed framework identifies Biancaea sappan-Swietenia mahogany-Indigofera 1 (dabbing) and Nephelium lappaceum L (lasem) as optimal dyes, reducing dyeing iterations by 40% in empirical tests while enhancing motif clarity.