中文摘要：

涉及三角模（T）和三角余模（S）的Frank方程，已有很多研究．其问题的提出涉及概率联合分布与边际分布的相互关系，在模糊多值逻辑、模糊偏好评价模型、粗糙集理论等领域有着广泛的应用,利用定义的T,S的对数凸线性函数，讨论了一类Frank方程TSλ=Min·Maxλ（0≤A≤∞）的解问题，推广了经典Frank方程研究．同时，针对所提出的对数copulas函数，讨论了对数copulas函数与三角模、三角余模之间的关系．

英文摘要：

Frank equation involved with triangular norm （T） and triangular conorm （S） and dealt with the probability joint distribution and marginal distributions, has been investigated by many scholars. It has been ap- plied in the fuzzy multiple - valued logic, fuzzy preference evaluation model, rough set theory and other fields. The solutions for a class of Frank equations TSλ= Min · Maxλ （0 ≤A≤ ∞ ） are discussed by means of the logarithmic convex linear function, and the classical Frank＇s equation are generalized. At the same time, the relationship be- tween logarithmic copulas function and triangular norm, triangular conorm are discussed.