南京大学学报(自然科学版) ›› 2022, Vol. 58 ›› Issue (1): 49–59.doi: 10.13232/j.cnki.jnju.2022.01.006

• • 上一篇    下一篇

软集优势矩阵的高低对角线性质及其诱导的还原算法

田峻奇, 韩邦合()   

  1. 西安电子科技大学数学与统计学院, 西安, 710126
  • 收稿日期:2021-06-23 出版日期:2022-01-30 发布日期:2022-02-22
  • 通讯作者: 韩邦合 E-mail:bhhan@mail.xidian.edu.cn
  • 作者简介:E⁃mail：bhhan@mail.xidian.edu.cn
  • 基金资助:
    国家自然科学基金(61862055);中央高校基本科研业务费(JB180712)

The high and low diagonals' properties for the soft set's matrix of dominant support parameters and their induced retrieving algorithm

Junqi Tian, Banghe Han()   

  1. School of Mathematics and Statistics, Xidian University, Xi'an, 710126, China
  • Received:2021-06-23 Online:2022-01-30 Published:2022-02-22
  • Contact: Banghe Han E-mail:bhhan@mail.xidian.edu.cn

RichHTML

7

PDF (PC)

564

摘要：

软集是利用参数化方法处理不确定性问题的重要工具，在决策领域其基本思想是在不同的参数下采取不同的决策，属于软决策模式.而软集的优势矩阵作为软集合的一种表示方法，蕴藏着丰富的信息，如何在软集的优势矩阵部分已知的情况下依旧能够完整还原软集是讨论的重点.专注于软集优势矩阵高低对角线的讨论，通过研究发现优势矩阵的高低对角线上的性质对于还原软集十分有帮助.首先给出优势矩阵高低对角线的基本定义及其结构特点；其次，针对软集合的不交性、单调性、分块等信息特征，给出高低对角线上对应的特征和性质；最后，依据优势矩阵高低对角线上的元素分两个阶段设计还原算法，并针对算法还原时间以及算法第一阶段还原率等指标进行仿真实验.实验结果显示，对于第一阶段还原率，在0，1元素个数比为0.5时，第一阶段还原率最高，而在软集中，0，1元素个数之比不变时，增加参数与对象的个数对于第一阶段还原率影响不大，即还原率依旧取决于0，1元素个数比.算法运行时间方面，在控制其他变量下，增加参数个数或对象个数都会直接的导致还原时间增加.

关键词: 软集, 优势矩阵, 高低对角线, 还原算法

Abstract:

Soft set is an important tool to deal with uncertainty problem by parameterization method. In the field of decision making，its basic idea is to take different decisions under different parameters，which belongs to soft decision mode. As a representation method of soft set，the matrix of dominant support parameters of soft sets contains abundant information. How to restore the soft set completely when the matrix of dominant support parameters of the soft set is partly known is the focus of this paper. This paper investigates the high and low diagonals of the matrix of dominant support parameters,and their properties are found very helpful to the retrieve of soft sets. Firstly，we give the basic definition and structural characteristics of the high and lower diagonals of the matrix of dominant support parameters. Secondly，according to the information characteristics of soft set，such as non?intersecting，monotony and partition，the corresponding characteristics and properties of high and low diagonals are given. Finally,according to the elements on the high and low diagonal of the matrix of dominant support parameters,the reduction algorithm is designed in two stages,and simulation experiments are carried out for the algorithm reduction time and the algorithm reduction rate of the first stage. Experimental results show that the reduction rate of the first stage is the highest when the ratio of 0 to 1 elements is 0.5. In soft set,when the ratio of 0 and 1 elements remains unchanged,increasing the number of parameters and objects has little influence on the reduction rate of the first stage,that is,the reduction rate still depends on the ratio of 0 and 1 elements. In terms of algorithm running time,when controlling other variables,increasing the number of parameters or objects will directly increase the reduction time.

Key words: soft sets, the matrix of dominant support parameters, high and low diagonals, retrieving algorithm

中图分类号: 

  • O24

表1

例1中软集S=F,E的0?1信息系统表示"

beautifulexpensivewoodenmodern
u11010
u20101
u31101
u40001

图5

各阶段还原时间与还原率关于0?1比例的对比图"

图6

各阶段还原时间与还原率关于参数个数变化的对比图"

图7

各阶段还原时间关于参数个数变化的对比图"

1 Pawlak Z. Rough set. International Journal of Computer and Information Sciences，1982，11(5)：341-356.
2 Zadeh L A. Fuzzy sets. Information and Control，1965，8(3)：338-353.
3 Maistrov L. 1974，probability theory：A historical sketch. New York：Academic Press，1974.
4 Yao Y Y. Set?theoretic models of three?way decision. Granular Computing，2021，6(1)：133-148.
5 Yang J L，Yao Y Y. Semantics of soft sets and three?way decision with soft sets. Knowledge?Based Systems，2020(194)：105538.
6 Molodtsov D. Soft set theory：First results. Computers and Mathematics with Applications，1999，37(4-5)：19-31.
7 Feng F，Cho J，Pedrycz W，et al. Soft set based association rule mining. Knowledge?Based Systems，2016(111)：268-282.
8 Sun B Z，Ma W M，Li X N. Linguistic value soft set?based approach to multiple criteria group decision?making. Applied Soft Computing，2017(58)：285-296.
9 Han B H，Geng S L. Pruning method for optimal solutions of intm?intn decision making scheme. European Journal of Operational Research，2013，231(3)：779-783.
10 Akram M，Adeel A，Alcantud J C R. Group decision?making methods based on hesitant N?soft sets. Expert Systems with Applications，2019(115)：95-105.
11 Hu J H，Pan L，Yang Y，et al. A group medical diagnosis model based on intuitionistic fuzzy soft sets. Applied Soft Computing，2019(77)：453-466.
12 方君炜，张其文. 基于软集理论的多属性决策方法研究及应用. 硕士学位论文. 兰州：兰州理工大学，2019.
Fang J W，Zhang W Q. Research of multi?attribute decision?making method and application based on soft set theory. Master Dissertation. Lanzhou：Lanzhou University of Technology，2019.
13 王庆亮. 软集在决策问题中的应用研究. 硕士学位论文. 无锡：江南大学，2018.
Wang Qingliang. Application of soft sets in decision?making problems. Master Dissertation. Wuxi：Jiangnan University，2018.
14 Feng F，Li C X，Davvaz B，et al. Soft sets combined with fuzzy sets and rough sets：A tentative approach. Soft Computing，2010，14(9)：899-911.
15 Feng F，Liu X Y，Leoreanu?Fotea V，et al. Soft sets and soft rough sets. Information Sciences，2011，181(6)：1125-1137.
16 Ali M I. A note on soft sets，rough soft sets and fuzzy soft sets. Applied Soft Computing，2011，11(4)：3329-3332.
17 Maji P K，Roy A R，Biswas R. Fuzzy soft sets. Journal of Fuzzy Mathematics，2001，9(3)：589-602.
18 Majumdar P，Samanta S K. Generalised fuzzy soft sets. Computers & Mathematics with Applications，2010，59(4)：1425-1432.
19 Roy A R，Maji P K. A fuzzy soft set theoretic approach to decision making problems. Journal of Computational and Applied Mathematics，2007，203(2)：412-418.
20 Feng F，Jun Y B，Liu X Y，et al. An adjustable approach to fuzzy soft set based decision making. Journal of Computational and Applied Mathematics，2010，234(1)：10-20.
21 Yang X B，Lin T Y，Yang J Y，et al. Combination of interval?valued fuzzy set and soft set. Computers and Mathematics with Applications，2009，58(3)：521-527.
22 Jiang Y C，Tang Y，Chen Q，et al. Interval?valued intuitionistic fuzzy soft sets and their properties. Computers & Mathematics with Applications，2010，60(3)：906-918.
23 Xu W，Ma J，Wang S Y，et al. Vague soft sets and their properties. Computers & Mathematics with Applications，2010，59(2)：787-794.
24 Akta? H，?a?man N. Soft sets and soft groups. Information Sciences，2007，177(13)：2726-2735.
25 Karaaslan F，?a?man N，Engino?lu S. Soft lattices. Journal of New Results in Science，2012(1)：5-17.
26 Jun Y B，Lee K J，Khan A. Soft ordered semigroups. Mathematical Logic Quarterly，2010，56(1)：42-50.
27 Feng F，Jun Y B，Zhao X Z. Soft semirings. Computers & Mathematics with Applications，2008，56(10)：2621-2628.
28 Acar U，Koyuncu F，Tanay B. Soft sets and soft rings. Computers & Mathematics with Applications，2010，59(11)：3458-3463.
29 Sun Q M，Zhang Z L，Liu J. Soft sets and soft modules∥Wang G，Li T，Grzymala?Busse J W，et al. Rough sets and knowledge technology. Springer Berlin Heidelberg，2008(5009)：403-409.
30 Qin K Y，Hong Z Y. On soft equality. Journal of Computational and Applied Mathematics，2010，234(5)：1347-1355.
31 Zhan J M，Jun Y B. Soft BL?algebras based on fuzzy sets. Computers & Mathematics with Applications，2010，59(6)：2037-2046.
32 Jiang Y C，Tang Y，Chen Q M，et al. Extending soft sets with description logics. Computers & Mathematics with Applications，2010，59(6)：2087-2096.
33 Tanay B，Kandemir M B. Topological structure of fuzzy soft sets. Computers & Mathematics with Applications，2011，61(10)：2952-2957.
34 Shabir M，Naz M. On soft topological spaces. Computers & Mathematics with Applications，2011，61(7)：1786-1799.
35 ?etkin V，Aygüno?lu A，Ayün H. A topological view on application of L?fuzzy soft sets：Compactness. Journal of Intelligent and Fuzzy Systems，2017，32(1)：781-790.
36 Al?Shami T M，El?Shafei M E，Abo?Elhamayel M. On soft topological ordered spaces. Journal of King Saud University?Science，2019，31(4)：556-566.
37 Zhan J M，Alcantud J C R. A survey of parameter reduction of soft sets and corresponding algorithms. Artificial Intelligence Review，2019，52(3)：1839-1872.
38 Chen D G，Tsang E C C，Yeung D S，et al. The parameterization reduction of soft sets and its applications. Computers & Mathematics with Applications，2005，49(5-6)：757-763.
39 Kong Z，Gao L Q，Wang L，et al. The normal parameter reduction of soft sets and its algorithm. Computers & Mathematics with Applications，2008，56(12)：3029-3037.
40 Han B H，Li X N. Propositional compilation for all normal parameter reductions of a soft set∥The 9th International Conference on Rough Sets and Knowledge Technology. Springer Berlin Heidelberg，2014：10.
41 Gong K，Wang Y，Xu M Z，et al. BSSReduce an OU incremental feature selection approach for large?scale and high?dimensional data. IEEE Transactions on Fuzzy Systems，2018，26(6)：3356-3367.
42 Ma X Q，Sulaiman N，Qin H W，et al. A new efficient normal parameter reduction algorithm of soft sets. Computers & Mathematics with Applications，2011，62(2)：588-598.
43 李炯. 基于软辨识矩阵的软集参数约简方法研究. 硕士学位论文. 临汾：山西师范大学，2016.
Li J. Research on parameter reduction in soft sets based on soft discernibility matrix. Master Dissertation. Linfen：Shanxi Normal University，2016.
44 Han B H，Li Y M，Geng S l.0?1 Linear programming methods for optimal normal and pseudo parameter reductions of soft sets. Applied Soft Computing，2017(54)：467-484.
45 Han B H. Comments on “Normal parameter reduction in soft set based on particle swarm optimization algorithm”. Applied Mathematical Modelling，2016，40(23-24)：10828-10834.
46 Feng Q R，Zhou Y. Soft discernibility matrix and its applications in decision making. Applied Soft Computing，2014(24)：749-756.
47 Pei D W，Miao D Q. From soft sets to information systems∥2005 IEEE International Conference on Granular Computing. Beijing，China：IEEE，2005：617-621.
48 Han B H，Nie X Y，Wu R Z，et al. Characterizations for matric of dominant support parameters in soft sets. IEEE Access，2020(8)：227610-227628.
No related articles found!
Viewed
Full text


Abstract

Cited
  Shared   
  Discussed   
No Suggested Reading articles found!

版权所有 © 2021 《南京大学学报(自然科学)》

地址：江苏省南京市鼓楼区汉口路22号，南京大学学报编辑部，210093

电话：025-83592704 , 传真：025-83592704        技术支持：北京玛格泰克科技发展有限公司