各种模糊凸映射的性质及关系-基础数学专业论文.docxVIP

哈尔滨工业大学理学硕士学位论文 哈尔滨工业大学理学硕士学位论文 - - I - 摘要 由于模糊集理论在模糊化逻辑上的应用及模糊数理论在极大可能性理论 中的应用，模糊数学吸引了许多工程师、计算机科学家和优化研究工作者的 兴趣。在经典理论中，凸性是优化理论的研究与应用中一个十分重要的内 容，它有助于寻找最优解。在模糊理论中，模糊凸的研究是非常广泛的。类 似于优化理论中的凸、invex 和 preinvex 概念, 在模糊领域中对上述的概念 也有类似的研究。 在本文，我们结合已有文献对各种模糊凸映射性质进行研究，将这些概 念推广到 n-cell 模糊数空间 L(Em ) 中。在模糊数空间 L(Em ) 中重新定义了模 糊凸、invex 和 preinvex 等映射，并对它们的性质也作了推广和研究，重点 是模糊 prequasiinvex 映射。最后附上一个图说明他们之间的关系。本文还 研究了模糊 B-凸、B-invex 和 B-preinvex 映射，对它们的性质也作了推广和 研究。 关键词 n-cell 模糊数；模糊 invex 映射；模糊 preinvex 映射；模糊 B-凸映 射；模糊 B-preinvex 映射 - - II - Abstract Because Fuzzy set theory applies in Fuzzy logic and Fuzzy number theory applies in maximal possibility theory. Fuzzy theory attracts a lot of engineers, computer scientists and operation researcher’s interesting. In classical theory, convexity is an most important part in the research and applied of optimum theory, if is helped in searching the optimum solution In Fuzzy theory, the is very general. And research on Fuzzy convexity as the concept of convexity, is research on the concept like those in Fuzzy. In this paper, we combine with the literature former to study the property of Fuzzy convex mappings, and generalize these concept to the n-cell Fuzzy number space L(Em ) .In the Fuzzy number space  L(Em ) .We definite the concept of Fuzzy convexity, the mappings of invex and preinvex, generalize and sturdy their property, our focus is Fuzzy pre-quasiinvex mapping. At last we give a diagram to show their relation. In this paper, we also study the Fuzzy B-vex mapping, B-invex mapping and B-preinvex mappings, and also generalize and study their property. Keywords n-cell Fuzzy numbers; Invex fuzzy mappings; Preinvex fuzzy mappings; B-vex fuzzy mappings; B-preinvex fuzzy mappings - -III- 目录 摘要 I Abstract II 第 1 章 绪论 1 1.1 课题的目的和意义 1 1.2 相应领域的研究现状 2 1.2.1 n-cell 模糊数的概念 2 1.2.2 模糊映射的可微性3 1.2.3 各种模糊凸映射及相关后继分析 3 1.3 本文主要内容与组织安排4 第 2 章 基本定义 6 2.1 模糊数空间 En 和 L(E m ) 空间 6 2.2 ν 空间上的运算和度量 8 2.3 Invex 集和模糊映射的全微分 9 2.4