Abstract 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.

中文翻译：

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线性分数函数形式的模糊运算的加法生成器

摘要 本文致力于分析线性分数函数形式的加法生成器。定义了增加和减少生成器系数的限制。结果表明，递增和/或递减生成元的组合也是生成元。对于每种情况，都会找到相应的三角范数或共模数。确定了在线性分数函数的基础上得到的三角范数和共模数，它们也是对偶的，具有相同的结构。事实上，提出了一个新的双三角范数和共模数族。