General Mathematical Principles for Determining the Engineering Concept of Apartment Buildings Based on Expert Analytical Methods and Decision Support Systems

A well-designed engineering blueprint for a residential apartment building can effectively mitigate potential hazards during the preparatory phase of construction. This approach enables the consideration of factors that, due to the constraints inherent in specialized expertise, frequently go unaddressed in practice. The theory of expert systems and mathematical apparatus based on fuzzy logic are put forward as the methodological basis and fundamental research methods. The objective of the present study is to formulate mathematical principles that facilitate the determination of the engineering concept of apartment buildings at the preparatory stage of construction, based on the theory of fuzzy sets and decision support methods. The research objective is to develop general mathematical principles for solving applied problems using specialized expert systems. The research yielded the development of the mathematical foundations of a multifunctional expert system for the conceptualization of apartment buildings during the preparatory phase of construction; a fuzzy knowledge base was created. The projection of a multidimensional response surface function has been restored, reflecting the dependence of linguistic variables. Mathematical principles for determining the engineering concept of multi-family residential buildings at the preparatory stage of construction have been developed.