A Neutrosophic Approach to the Diet Problem: Enhancing Accuracy and Flexibility in Dietary Planning

Abstract

The diet problem, as a critical challenge in the health science and the food industry, involves optimizing the combination of foods to meet nutritional requirements at minimal cost. This research presents a novel and flexible linear programming model for the diet problem, integrating neutrosophic triplets to manage the inherent uncertainties and indeterminacies in nutritional data. Neutrosophic logic extends fuzzy logic by introducing an indeterminacy component, allowing for a more nuanced representation of the variability in the food nutritional contents and costs. In our study, we examine eight types of food and four essential nutrients, representing each food’s cost and nutritional content as neutrosophic triplets. These triplets encapsulate the degrees of truth, indeterminacy, and falsity inherent in the data. By converting the neutrosophic triplets into crisp values using a specific score function, we enable the application of traditional linear programming techniques. Our model aims to minimize the cost while ensuring that the diet meets all specified nutritional constraints. The practical implications of the neutrosophic model are demonstrated through a comprehensive case study, highlighting its effectiveness in diet planning and its applications within the food industry. The results underscore the model’s ability to handle data uncertainties robustly, providing a reliable and adaptable solution to the diet problem. This approach not only enhances the precision of dietary planning but also supports improved decision-making processes within the food industry, ultimately contributing to better health outcomes and more efficient resource utilization.