凸Fuzzy集（Ⅰ）

凸Fuzzy集（Ⅰ） CONVEX FUZZY SETS （I） 裴礼文 Pei Liwon first-author 早在1965年,L.A.Zadeh提出第一篇Fuzzy集论文中,就引入了凸Fuzzy集的概念,建立了它的基本性质。以后许多作者陆续对这个问题进行了研究,例如文献[2]至[9]。本文利用Fuzzy点来定义Fuzzy子空间和仿射Fuzzy集,形式上与经典的情况完全一致,并把经典的情况作为它的特例。同时这种定义证明与A.K.Katsaras,D.B.Liu引入的Fuzzy子空间,R.Lowen引入的仿射Fuzzy集等价。借助新定义.很快获得若干充要条件,讨论了Fuzzy集最小Fuzzy子空间、最小仿射Fuzzy集的结构,Cara-theodory型定理的推广,以及构造定理。正如我们在[13]中所作的那样,这里还引入了所谓"H-构造",并用它刻划包含两个Fuzzy仿射集的最小仿射Fuzzy集。 In this paper, using the notion and operation of the fuzzy points, we intro-duce new definitions of the fuzzy subspace and the affine fuzzy set, and prove that these definitions are equivalent respectively to the definition of the fuzzy. subspace, which was defined by A. K. Katsaras and D. B. Liu in [4], and the definition of the fuzzy affine fuzzy set, which was defined by R. Lowen in[5]. In terms of the new definitions we built up some of necessary and sufficient conditions, and discuss structures of the fuzzy subspace hull and fuzzy affine hull of a fuzzy set, and discuss also the type of Caratheodory theorem. Finally we introduce a structure which is called "H-structure" for a fuzzy set as we did in [13].In terms of it the fuzzy affine hull of two affine fuzzy sets is described. Being due to use fuzzy points, we make all result hold good in accord with non fuzzy case, and take crisp result as special cases. 1984-03-01 2021-04-01 3