一类单调基因参数可调三角模

A Parameter-tunable Triangular Norm with Monotonic Genes

为了研究优化Zadeh算子,给出一类单调基因参数可调三角模的定义。先定义了一种由单调函数经初等运算生成的广义T三角模Fλ,再利用对偶性,定义广义S三角模Gλ,统一了部分作者提出的优化Zadeh算子;应用该定义生成一对新的三角模,验证该定义用于构造模糊算子的可行性,为三角模的构造提供了新方向;研究部分算子随参数λ调整的变化情况,以及和Zadeh算子的关系。Fλ和Gλ能够使模糊集的交并运算更加合理,提高了数据的利用率,避免信息丢失。在三角模Gλ的基础上给出了g-λ测度的定义及其定理,由此丰富了模糊测度的理论。

In order to study the optimization of Zadeh operator,a definition of parameter-tunable triangular norm with monotonic genes is given.First,we defined a kind of triangular norm F_(A) in the general sense generated by monotone functions using elementary operations,and then a definition of triangular conorm G_(λ)in the general sense is given by using duality.This type of definition unifies the optimal Zadeh operator proposed by some authors.Next,this definition is applied to generate a new pair of triangular norms.It is proved that the triangular norm and triangular conorm conditions are satisfied to verify the feasibility of the definition for constructing fuzzy operators,which gives new direction in the construction of triangular norms.Finally,we studied the variation of some operators parameter tuning and the relationship with the Zadeh operator.F_(A) and G_(λ) make the intersection and merging of fuzzy sets more reasonable,and the data usage more efficient to avoid information loss.On the basis of triangular conorm G_(λ),the definition and theorem of g-A measure are given,which enriches the theory of fuzzy measure.