Decomposition of a Decision-Making Problem Into Levels of Preference of the Majority Graph

Decision-making problems with a large number of alternatives are considered. It is proposed to preliminarily narrow the initial set of alternatives, excluding the obviously worse options. For this purpose, the decomposition of the original problem into preference levels of the majority graph is carried out. Graph levels containing the least preferred alternatives are removed. An algorithm for constructing an aggregated full quasi-order for ordering the set of best alternatives is developed. Majority graph preference levels are used to rank alternatives using Hamiltonian paths in a digraph. An algorithm for finding Hamiltonian paths in a digraph is proposed by raising the adjacency matrix to a power. An applied problem of ordering drone models using an algorithm for constructing a complete quasi-order is presented.