Additive generators of fuzzy operations in the form of linear fractional functions

摘要

This paper is devoted to the analysis of additive generators in the form of linear fractional functions. The limitations on the coefficients of increasing and decreasing generators are defined. It is shown that the compositions of increasing and/or decreasing generators are also generators. For each case, the corresponding triangular norms or conorms are found. It is established that the triangular norms and conorms obtained on the basis of linear fractional functions, and which are also dual to them, have the same structure. In fact, a new family of dual triangular norms and conorms is proposed. (C) 2019 Elsevier B.V. All rights reserved.