云关系矩阵与云关系方程研究  

Study on the Cloud Relation Matrix and Cloud Relational Equation

作　　者：王洪利 费立国 冯玉强 WANG Hong-li;FEI Li-guo;FENG Yu-qiang(School of Economics and Trade,Fujian Jiangxia University,Fuzhou 350108,China;School of Economics and Management,Harbin University of Technology,Harbin 150001,China)

机构地区：[1]福建江夏学院经济贸易学院,福建福州350108 [2]哈尔滨工业大学经济管理学院,黑龙江哈尔滨150001

出　　处：《模糊系统与数学》2022年第2期36-48,共13页Fuzzy Systems and Mathematics

基　　金：国家自然科学基金资助项目(71429001;71429031);福建省自然科学基金面上项目(2019J01881)。

摘　　要：为了进一步研究云模型在集合理论与方法方面的拓展,本文参照模糊集合,基于云模型提出了云关系矩阵和云关系方程的相关理论和方法。首先在云集合元素的I运算和P运基础上,提出了云关系矩阵及其合成运算方法,接着提出了云关系方程及其求解方法,最后通过实例验证了提出的理论和方法。本文研究创新之处在于提出了云关系矩阵和云关系方程及其运算方法,对于进一步拓展云模型的集合理论与方法具有重要的基础作用,其为云模型进一步在其他领域的应用打下了基础。In order to further study the extension of cloud model in set theory and method in this paper cloud relation matrix and cloud relation equation based on cloud model referring to fuzzy set and proposes the theory and method is studied. Firstly the cloud relation matrix and its combination operation method are proposed on the basis of I operation and P operation of element of cloud set. Then the cloud relation equation and its solution method are proposed. Finally, the theory and method are verified by the case. The innovation of this paper is to propose cloud relational matrix and cloud relational equation and its operation method.The research in this paper has an important basic role for further expanding the set theory and method of cloud model. And it plays a foundation role for further application of cloud model in other fields.

关 键 词：云集合 云模型 云关系矩阵 云关系方程 模糊集合 

分 类 号：O159[理学—数学]