基于二元联系数可能度函数的区间数排序方法及应用

doi:10.12341/jssms22318

系统科学与数学 ›› 2023, Vol. 43 ›› Issue (2): 417-430.DOI: 10.12341/jssms22318

基于二元联系数可能度函数的区间数排序方法及应用

柯丽华^1,2, 唐华倩^1,2, 王其虎^1,2, 胡南燕^1,2, 肖泽宇^1,2

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

收稿日期:2022-04-29 修回日期:2022-08-16 出版日期:2023-02-25 发布日期:2023-03-16
通讯作者: 王其虎,Email:wangqihu@wust.edu.cn
基金资助:
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

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柯丽华,唐华倩,王其虎,胡南燕,肖泽宇. 基于二元联系数可能度函数的区间数排序方法及应用[J]. 系统科学与数学, 2023, 43(2): 417-430.

KE Lihua, TANG Huaqian, WANG Qihu, HU Nanyan, XIAO Zeyu. Ranking Method of Interval Numbers Based on Possibility Function of Binary Connection Number and Its Application[J]. Journal of Systems Science and Mathematical Sciences, 2023, 43(2): 417-430.

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

KE Lihua^1,2, TANG Huaqian^1,2, WANG Qihu^1,2, HU Nanyan^1,2, XIAO Zeyu^1,2

1. School of Resource and Environmental Engineering, Wuhan University of Science and Technology, Wuhan 430081;
2. Industrial Safety Engineering Technology Center of HuBei Province, Wuhan 430081

Received:2022-04-29 Revised:2022-08-16 Online:2023-02-25 Published:2023-03-16

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.

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

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.

Key words: Interval numbers ranking, possibility degree function, binary connection number, set pair analysis, order-preservation

MR(2010)主题分类:

90B99

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[1] Moore R E. Interval Analysis. Englewood Cliffs, NJ:Prentice Hall, 1966.
[2] 曾文艺, 罗承忠, 肉孜阿吉.区间数的综合决策模型.系统工程理论与实践, 1997, 17(11):48-50. (Zeng W Y, Luo C Z, Rouziaji. Comprehensive decision model of interval-number. Systems Engineering——Theory & Practice, 1997, 17(11):48-50.)
[3] 刘进生, 王绪柱, 张宝玉.区间数排序.工程数学学报, 2001, 18(4):103-109. (Liu J S, Wang X Z, Zhang B Y. The ranking of interval numbers. Journal of Engineering Mathematics, 2001, 18(4):103-109.)
[4] 赵慧冬, 包玉娥, 关世霞.区间数的几何平均排序函数及其应用.内蒙古民族大学学(自然科学版), 2011, 26(6):624-628. (Zhao H D, Bao Y E, Guan S X. Geometry average sorting function about interval number and its application. Journal of Inner Mongolia University for the Nationalities (Natural Sciences), 2011, 26(6):624-628.)
[5] 王万军.区间数排序的一种联系数方法.计算机工程与设计, 2009, 30(8):2055-2057. (Wang W J. Connection numbers method for ranking interval number. Computer Engineering and Design, 2009, 30(8):2055-2057.)
[6] 叶跃祥, 糜仲春, 王宏宇, 等.一种基于集对分析的区间数多属性决策方法.系统工程与电子技术, 2006, 28(9):1344-1347. (Ye Y X, Mi Z C, Wang H Y, et al. Set-pair-analysis-based method for multiple attributes decision-making with intervals. Systems Engineering and Electronics, 2006, 28(9):1344-1347.)
[7] 叶义成, 姚囝, 王其虎.采用区间数排序的采矿方法优选模型及其应用.控制理论与应用, 2016, 33(8):1015-1022. (Ye Y C, Yao L, Wang Q H. Mining method optimal selection model and its application by using interval numbers ranking method. Control Theory & Applications, 2016, 33(8):1015-1022.)
[8] 王中兴, 邵翠丽, 唐芝兰.基于相对优势度的区间数排序及其在多属性决策中的应用.模糊系统与数学, 2013, 27(2):142-148. (Wang Z X, Shao C L, Tang Z L. Method for ranking interval numbers based on relative superiority and its application to multiple attribute decision making. Fuzzy Systems and Mathematics, 2013. 27(2):142-148.)
[9] 仇国芳, 李怀祖.区间数排序的包含度度量及构造方法.运筹与管理, 2003, 12(3):13-17. (Qiu G F, Li H Z. Measurement and construct with inclusion degree for priority of interval numbers. Operations Research and Management Science, 2003, 12(3):13-17.)
[10] 兰继斌, 胡明明, 叶新苗.基于相似度的区间数排序.计算机工程与设计, 2011, 32(4):1419-1421. (Lan J B, Hu M M, Ye X M. Ranking interval numbers based on similarity. Computer Engineering and Design, 2011, 32(4):1419-1421.)
[11] 李霞, 张绍林, 张淼,等.基于新距离测度的区间数排序.西华大学学报(自然科学版), 2008, 27(1):87-90. (Li X, Zhang S L, Zhang M, et al. Rank of interval numbers based on a new distance measure. Journal of Xihua University (Natural Science Edition), 2008, 27(1):87-90.)
[12] 白玉娟.基于期望和宽度的新距离测度的区间数排序.河西学院学报, 2015, 31(5):13-17. (Bai Y J. A new definition of distance measure of rank of interval numbers based on the expectation and width. Journal of Hexi University, 2015, 31(5):13-17.)
[13] 谭吉玉, 朱传喜, 张小芝,等.一种新的基于TOPSIS的区间数排序方法.统计与决策, 2015, 421(1):94-96. (Tan J Y, Zhu C X, Zhang X Z, et al. A new sort method of interval numbers based on TOPSIS. Statistics and Decision, 2015, 421(1):94-96.)
[14] 郭志林, 薛明志. Fuzzy区间数的一种排序方法及综合评判模型.数学的实践与认识, 2005, 35(7):244-247. (Guo Z L, Xiu M Z. The ranking method of fuzzy interval numbers. Mathematics in Practice and Theory, 2005, 35(7):244-247.)
[15] Sengupta A, Pal T K. On comparing interval numbers. European Journal of Operational Research, 2000, 127]:28-43.
[16] 龚日朝, 李诗音, 谭可星.带分布区间数的可能度计算模型及其排序.系统工程理论与实践, 2021, 41(9): 2428-2446. (Gong R Z, Li S Y, Tan K X. Possibility calculation model of symmetric distribution interval number and its ranking method. Systems Engineering——Theory & Practice, 2021, 41(9):2428-2446.)
[17] 徐泽水, 达庆利.区间数排序的可能度法及其应用.系统工程学报, 2003, 18(1):67-70. (Xu Z S, Da Q L. Possibility degree method for ranking interval numbers and its application. Journal of Systems Engineering, 2003, 18(1):67-70.)
[18] Nakahara Y, Sasaki M, Gen M. On the linear programming problems with interval coefficients. International Journal of Computer Industrial Engineering, 1992, 23(1-4):301-304.
[19] 高峰记.可能度及区间数综合排序.系统工程理论与实践, 2013, 33(8):2033-2040. (Gao F J. Possibility degree and comprehensive priority of interval numbers. Systems Engineering——Theory & Practice, 2013, 33(8):2033-2040.)
[20] 达庆利, 刘新旺.区间数线性规划及其满意解. 系统工程理论与实践, 1999, 19(4):3-7. (Da Q L, Liu X W. Interval number linear programming and its satisfactory solution. Systems Engineering——Theory & Practice, 1999, 19(4):3-7.)
[21] 李德清, 谷云东.一种基于可能度的区间数排序方法. 系统工程学报, 2008, 23(2):243-246. (Li D Q, Gu Y D. Method for ranking interval numbers based on possibility degree. Journal of Systems Engineering, 2008, 23(2):243-246.)
[22] 兰继斌, 曹丽娟, 林健.基于二维优先度的区间数排序方法. 重庆工学院学报(自然科学版), 2007, 21(10):63-67. (Lan J B, Cao L J, Lin J. Method for ranking interval numbers based on two-dimensional priority degree. Journal of Chongqing Institute of Technology, 2007, 21(10):63-67.)
[23] 李德清, 曾文艺, 尹乾.区间数排序方法综.北京师范大学学报(自然科学版), 2020, 56(4):483-492. (Li D Q, Zeng W Y, Yin Q. Ranking interval numbers: A review. Journal of Beijing Normal University (Natural Science), 2020, 56(4):483-492.)

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