Escala fuzzy não balanceada para tratamento de preferências alimentares em modelagem matemática

Abstract

Mathematical models for dieting are a useful tool for determining menus in a specific population. Much optimization research using mathematical modeling has already been done to solve the diet problem taking into account the nutritional needs and costs of food. However, an approach that values users' choices by adhering to their dietary preferences is still a challenge. One of the most common ways to obtain food preference data is through hedonic point scales. However, in this type of scale, the symmetrical distribution of categories and the inaccuracy of the responses may interfere with the results of the preference surveys. This paper proposes the use of the Unbalanced Fuzzy Scale as a new method for treatment of food preference data collected with 9-point hedonic scales. Data analysis based on the proposed scale aims to improve the limitations presented in research using hedonic point scales as a form of data collection, especially regarding the distribution of numerical category values and the inaccuracy of responses. To construct the proposed scale, preference was analyzed for Brazilian and Portuguese students. The food preference of 329 Brazilian students compared to 66 foods was analyzed through a survey previously conducted by Spack (2017) due to the behavior of the responses in each 9-point hedonic scale region. The food preference analysis carried out with 119 Portuguese students aimed to verify that there is a tendency of behavior in the food preference responses, in two distinct groups, but with the same characteristics, and thus to define a standard for an evaluation and treatment scale. of such data. To this end, a food preference survey was conducted at the University of Minho, Guimarães campus. The results obtained revealed that the behaviors of the experimental data in intermediate regions present intensity of perception and variability of responses different from other regions of the scale. Data treated with the proposed scale were more satisfactory regarding standard deviations, consensus index, compared to a traditional treatment. The proposed scale was applied to a mathematical model that considered food preference maximization, cost minimization and cholesterol minimization as objective functions, and considered the nutritional recommendations according to the Dietary Reference Intakes (DRIs) as model constraints. As a result the model presented a specific diet to be served in Portuguese university restaurants, with a price consistent with the academic reality and the food preferences of the interviewed students prevailing, also considering all the nutritional requirements presented. In other words, the scale proposed in this paper, besides dealing with uncertainty and considering psychometric differences between the regions of the scale in food preference data, behaves very well when used in a mathematical model for diet generation. Thus, it is concluded that the proposed Unbalanced Fuzzy Scale is a more efficient and robust method for treating food preference information compared to a traditional treatment.