Fuzzy Metrics Based on Generators of Archimedean Triangular Norms of the Class of Rational Functions

This article presents the results that relate to the development of an approach for constructing parametric fuzzy metrics based on additive generators of triangular norms. A family of continuous Archimedean triangular norms is chosen, represented by rational functions with the fractional linear function (LFAG) and the logarithm of the fractional linear function (lnLFAG) acting as generators. The restrictions on the parameters of generators are obtained, under which the corresponding triangular norm is strict. Fuzzy metrics that correspond to these generators are constructed, and their properties are investigated. The approbation of fuzzy metrics was carried out on the clustering problem, and the quality of the solution was evaluated according to various criteria for metric clustering algorithms.