一类凸模糊映射的注记

本文讨论了一些凸模糊映射与拟凸模糊映射的性质及其在凸模糊优化的应用 .     

凸模糊映射的共轭映射

本文在Goetschel和Voxman所建立的拓扑向量空间中引入了反模糊数的概念,并建立了反模糊数空间,讨论了有关的基本性质.在此基础上,引入了凸模糊映射的共轭映射的定义,并证明了凸模糊映射的共轭集合和共轭映射都是凸的.     

凸直觉模糊映射

在模糊数、凸模糊映射和凸直觉模糊集定义基础上,给出了直觉模糊数及其序的定义,给出了凸直觉模糊映射的定义并讨论其有关性质,在此基础上,研究了凸直觉模糊规划问题。     

广义凸模糊映射

给出广义凸模糊映射、广义弱凸模糊映射等概念和若干特例。其次,构造集合Axf,y、Af,证明当f为下半连续广义弱凸模糊映射时Afx,y为闭弱凸集,进而得到广义凸模糊映射的充分条件。最后,给出广义凸模糊映射的性质,并指出半严格广义凸模糊映射成为严格广义凸模糊映射的条件。     

广义B-凸模糊映射及其应用

提出B-E-凸模糊映射的概念,并讨论了其一些性质,得到了这一类广义B-凸模糊映射的若干刻划定理,还讨论了这一类广义B-凸模糊映射在模糊优化中的应用,并得到了和最优解有关的一些结果。     

对数凸模糊映射

利用模糊数的表示定理,本文证明了对数凸模糊映射一些基本性质,并纠正了S.N anda和K.K ar对数凸模糊映射定义的不合理性和其证明中的错误。     

L-模糊理想的新刻画及其诱导的凸结构

在本文中,我们根据模糊理想的概念,给出了L-模糊理想度的定义,并给出了相应的例子,然后利用四种截集对L-模糊理想度进行了等价刻画。最后,我们通过L-模糊理想度诱导出了L-模糊凸结构,并指出环同态是L-模糊凸保持的和L-模糊凸到凸的映射。     

模糊保凸映射

本文是文[6]的继续,研究模糊保凸映射,用子基线段给出其特征定义1 设ψ是fts(x,J)的闭子基,非空模糊集c称为ψ-闭(或ψ-凸)如果有族■■ψ使得c=∩■。记H(X,ψ)是所有ψ-闭模糊集的全体。F-映射f:(X,J)→(Y,U)称为关于它们的闭子基ψ和ψ的F-保凸映射(简记F—cp映射)如果■T∈     

(λ,μ]-模糊映射与HX-模糊映射

通过引入((β),(α),)-模糊映射的定义,给出了(α,β)-模糊映射的另外四种形式,并将(∈,∈)-模糊映射、(∈,∈∨(q))-模糊映射和(∈,∈,∨,q)-模糊映射推广成具有边界值的(λ,μ]-模糊映射. 讨论了(λ,μ]-模糊映射与HX-模糊映射的关系. 使人们更加清楚地认识到了HX-模糊映射的意义.     

凸合成模糊对策的模糊稳定集

本建立了凸合成模糊对策的模型，并得到了凸合成模糊对策的模糊稳定集，可由子对策的模糊稳定集表达出来。从而解决了凸合成模糊对策的解的结构问题。     

Generalization of preinvex and B-vex fuzzy mappings

A class of fuzzy mappings, called B-preinvex, and strictly B-preinvex fuzzy mappings, is introduced by relaxing the definition of preinvexity of a fuzzy mapping. Similarly, based on a notion of differentiability of fuzzy mappings different from the usual one, the class of pseudo-B-vex, B-invex, and pseudo-B-invex fuzzy mappings is defined as a generalization of pseudo-convex, invex, and pseudo-invex fuzzy mappings. We prove that a strictly B-vex, or B-preinvex fuzzy mapping has at most one global minimum point, and that the class of B-vex fuzzy mappings forms a subset of the class of quasi-convex fuzzy mappings. B-vex (resp. B-preinvex) fuzzy mappings satisfy most of the basic properties of convex (resp. preinvex) fuzzy mappings. In addition characterizations and sufficient optimality conditions are obtained for B-vex and B-preinvex fuzzy mappings.     

半模糊凸模糊映射

In this paper, a new class of fuzzy mappings called semistrictly convex fuzzy mappings is introduced and we present some properties of this kind of fuzzy mappings. In particular, we prove that a local minimum of a semistrictly convex fuzzy mapping is also a global minimum. We also discuss the relations among convexity, strict convexity and semistrict convexity of fuzzy mapping, and give several sufficient conditions for convexity and semistrict convexity.     

On Fuzzy Simplex and Fuzzy Convex Hull

In this paper,we discuss fuzzy simplex and fuzzy convex hull,and give several representation theorems for fuzzy simplex and fuzzy convex hull.In addition,by giving a new characterization theorem of fuzzy convex hull,we improve some known results about fuzzy convex hull.     

Fuzzy真凸集的公理化定义

本文以基本Ｆｕｚｚｙ点、Ｆｕｚｚｙ点为基础，给出Ｆｕｚｚｙ真凸集的公理化定义，并对其性质进行了讨论     

B-vex Fuzzy Mappings and Its Application to Fuzzy Optimization Problems

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渐近伪压缩映象的收敛性定理

在任意的实Banach空间中,证明了一致Lipschitzian和渐近伪压缩映象的具误差的Ishikawa和Mann迭代序列的一些收敛性定理.