Archimedean triangular operators form the basis of the tools for development, analysis
and designing of fuzzy systems. They are generated by simple, monotone, single-valued and
continuous functions. The basic sets of logical connectives of fuzzy systems are analyzed. It
is shown that they are divided into conditional and algebraic ones. The well-known methods
for generating of Archimedean triangular operators are described. Limitation of the functional
characteristics of such generated operators is shown. To expand them, a method for
generating has been created, which makes it possible to build new parameterized operators.
Examples of constructing both new operators and those that generalize the already known
ones are given. The tendency of the change of the characteristic hyper surface, which is
build by new operator, is revealed.