Calculation of centroid of high dimensional fuzzy number and application

IF 1.9 4区 数学 Q1 MATHEMATICS
G. Wang, Y. Xu
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引用次数: 0

Abstract

In this paper, the conception of centroid of $n$-dimensional fuzzy number is introduced viaregarding its membership function as the density function on its support set, and some properties of it are obtained. Compared with the mean of the multi dimensional fuzzy number, the centroid takes into account the overall relationship between the edge membership functions of the membership function of the multi dimensional fuzzy number. Therefore, it can approximate (characterize) the fuzzy number more objectively and reasonably than using the mean of the multi dimensional fuzzy number. The most important work of this paper is that for two special kinds of multi dimensional fuzzy numbers (fuzzy $n$-cell numbers and fuzzy $n$-ellipsoid numbers), we respectively give calculation formulas, which can be used conveniently in application since the formulas are based on a definite integral of the level set functions of the multi dimensional fuzzy number on the unit interval $[0,1]$, rather than the multiple integral of the membership function of the multi dimensional fuzzy number itself on its support set. Then, by using the calculation formulas, we obtain another special property of the centroid for fuzzy $n$-cell number and fuzzy $n$-ellipsoid number. Finally, as an example of application, by using the centroid of multi dimensional fuzzy number, we define a fuzzy order on $n$-dimensional fuzzy number space, which can be used to rank uncertain or imprecise multichannel digital information.
高维模糊数质心的计算及应用
本文引入了n维模糊数的质心概念,将其隶属函数视为其支持集上的密度函数,得到了它的一些性质。与多维模糊数的均值相比,质心考虑了多维模糊数的隶属函数的边缘隶属函数之间的整体关系。因此,它比使用多维模糊数的平均值更客观、更合理地逼近(表征)模糊数。本文最重要的工作是,对于两种特殊的多维模糊数(模糊n元-单元数和模糊n元-椭球数),分别给出了计算公式,这些公式是基于多维模糊数的水平集函数在单位区间$[0,1]$上的定积分,便于应用。而不是对多维模糊数本身的隶属函数在其支持集上的多重积分。然后,利用计算公式,得到了模糊单元数和模糊椭球数的质心的另一个特殊性质。最后,作为应用实例,利用多维模糊数的质心,在$n$维模糊数空间上定义了一个模糊阶,用于对不确定或不精确的多通道数字信息进行排序。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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来源期刊
CiteScore
3.50
自引率
16.70%
发文量
0
期刊介绍: The two-monthly Iranian Journal of Fuzzy Systems (IJFS) aims to provide an international forum for refereed original research works in the theory and applications of fuzzy sets and systems in the areas of foundations, pure mathematics, artificial intelligence, control, robotics, data analysis, data mining, decision making, finance and management, information systems, operations research, pattern recognition and image processing, soft computing and uncertainty modeling. Manuscripts submitted to the IJFS must be original unpublished work and should not be in consideration for publication elsewhere.
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