凸空间的数值特征主要包括arity、独立性与相关性，以及凸不变量，是凸空间理论的重要组成部分. 本项目主要研究M-模糊化凸空间的数值特征. 首先，建立M-模糊化凸空间arity n的度以及多面体度的概念，并研究其相关性质，完善M-模糊化凸空间理论的基本框架. 其次，研究M-模糊化凸空间的独立性，相关性以及凸不变量. 建立Helly独立性、Radon独立性、Caratheodory独立性以及Exchange独立性等概念. 利用M-模糊自然数，给出M-模糊化凸空间框架下的Helly数、Radon数、Caratheodory数以及Exchange数的定义，研究其相关性质. 并进一步考虑这些不变量在乘积空间以及子空间下的性质. 最后，研究两类特殊的M-模糊化凸空间，即：M-模糊化拟阵与M-模糊化凸几何. 考察M-模糊化拟阵的基以及秩函数，研究M-模糊化凸几何与相应的模糊代数之间的范畴关系.

Numerical characteristics of convex spaces include convex invariants. And the theory of convex invariants is an important part of convex space theory. The purpose of this project is to study convex invariants of M-fuzzifying convex spaces...Firstly, the degree of polytope of a setting and the degree of arity n of an M-fizzifying convex space are defined. Some properties are discussed...Secondly, the dependence, independence and convex invariants of M-fuzzifying convex spaces are discussed. By M-fuzzy natural number, the notions of Helly number, Radon number, Caratheodory number and Exchange number are introduced. Besides, some properties are investigated and the convex invariants of product spaces and subspaces are surveyed...Finally, M-fuzzifying matroid and M-fuzzifying convex geometry are introduced. The rank functions and the basises of M-fuzzifying matroids are studied. Some relations between M-fuzzifying convex geometries and algebra structures are researched.