Development of Mathematical Apparatus of the Expert System for Modelling Ice Cream Recipes with Specified Quality Parameters

Abstract

Introduction. Application of new methods, in particular, expert systems with mathematical apparatus, enables improving the recipe composition of multi-component food products in a wide range of content of components with their full or partial replacement by alternative ones, including natural functional and technological ingredients. Problem Statement. The creation and use of hybrid expert system of ice cream recipe modelling is impossible without using special mathematical apparatus. Purpose. To develop mathematical models and methods that enable to calculate the multicomponent ice cream recipes with the standard chemical composition taking into account the raw materials and functional and technological ingredients available at the manufacturer and to get the finished products of guaranteed quality. Materials and Methods. The methods of analysis and synthesis, generalization and scientific abstraction, as well as the method of mathematical modelling are used. The information base of the research is the results of laboratory studies of the quality of recipe components and ice creams of different chemical composition. Mathematical modelling with the use of tuples, systems of equations and restrictions, is made in MathCad and MathLab software packages. Results. As a result of the development of the expert system mathematical apparatus, a set-theoretical mathematical model of the finished product quality control at the stage of operative planning of new types of ice cream with increased nutritional value has been obtained; multi-component ice cream recipes have been optimized in terms of composition; and a model for determining the optimal set of control actions in the presence of technological defects in the calculation of recipes has been built. Conclusions. The created mathematical apparatus for modeling ice cream recipes has a large-scale application due to interchangeability of separate functional and technological components, which has been tested and confirmed during the trials in research laboratories.