Fuzzy Optimization on the Synthesis of Chitosan-Graft-Polyacrylic Acid with Montmorillonite as Filler Material: A Case Study

In this paper, the synthesis of a chitosan–montmorillonite nanocomposite material grafted with acrylic acid is presented based on its function in a case study analysis. Fuzzy optimization is used for a multi-criteria decision analysis to determine the best desirable swelling capacity (Y(Q)) of the material synthesis at its lowest possible variable cost. For Y(Q), the integrating the result’s cumulative uncertainty is an essential element to investigate the feasibility of the developed model equation. The Pareto set analysis is able to set the appropriate boundary limits for Y(Q) and the variable cost. Two case studies are presented in determining the lowest possible cost: Case 1 for maximum Y(Q), and Case 2 for minimum Y(Q). These boundary limits were used in the fuzzy optimization to determine its global optimum results that achieved the overall satisfaction ratings of 67.2% (Case 1) and 52.3% (Case 2). The synthesis of the polyacrylic acid/chitosan material for Case 1 resulted in 305 g/g Y(Q) and 10.8 USD/kg, while Case 2 resulted in 97 g/g Y(Q) and 12.3 USD/kg. Thus, the fuzzy optimization approach proves to be a practical method for examining the best possible compromise solution based on the desired function to adequately synthesize a material.