基于二元联系数可能度函数的区间数排序方法及应用  

Ranking Method of Interval Numbers Based on Possibility Function of Binary Connection Number and Its Application

作　　者：柯丽华[1,2] 唐华倩 王其虎 胡南燕[1,2] 肖泽宇 KE Lihua;TANG Huaqian;WANG Qihu;HU Nanyan;XIAO Zeyu(School of Resource and Environmental Engineering,Wuhan University of Science and Technology,Wuhan 430081;Industrial Safety Engineering Technology Center of HuBei Province,Wuhan 430081)

机构地区：[1]武汉科技大学资源与环境工程学院,武汉430081 [2]湖北省工业安全工程技术研究中心,武汉430081

出　　处：《系统科学与数学》2023年第2期417-430,共14页Journal of Systems Science and Mathematical Sciences

基　　金：湖北省重点研发计划项目(2020BCA082);湖北省安全生产专项资金科技项目(SJZX20211004);湖北省安全生产专项资金科技项目(HBYF-2021-C1078-1)资助课题。

摘　　要：针对因区间数排序方法差异或可能度函数失效带来的区间数排序结果与实际情况明显不符和保序性较差的问题,系统梳理两区间数在实数轴上相离、相交以及包含等三类6种位置关系,引入集对分析方法定义了区间数集对及其二元联系数,利用区间数长度、集对、同一集、差异集以及比较空间的3个特征量,构造了基于二元联系数的可能度函数,进而建立了基于二元联系数可能度函数的区间数排序方法,全面地反映和描述了区间数相对大小比较时的确定性信息与不确定性信息.通过二元联系数的可能度函数性质证明和实例分析,证明了二元联系数的可能度函数的有效性,也验证二元联系数可能度函数的区间数排序方法的保序性和广泛适用性.最后,将基于二元联系数可能度算法的区间数排序方法用于采矿方法优选中,证实了该方法的可行性和应用价值.In order to solve the problem of inconsistency of ranking results and inaccuracy of order-preservation caused by different interval number methods or the invalidity of possibility degree function,the relationships of two interval numbers have been summarized as separation,intersection and inclusion.After defining the interval number length,set pair,deterministic set,non-deterministic set and three parameters of comparison space,the possibility degree function has been constructed based on binary connection number by adopting the set pair analysis method.Furthermore,the ranking method of interval numbers has been built based on the possibility degree function in this paper.The possibility degree function can be proved to reflect and describe the certainty and uncertainty of compare interval numbers.The results show the function has practicability and the ranking method has favorable orderpreservation and wide applicability.Finally,the feasibility and application value of this method were verified through the selection of mining schemes.

关 键 词：区间数排序 可能度函数 二元联系数 集对分析 保序性 

分 类 号：O225[理学—运筹学与控制论]