Multi-attributed decision making for mining methods based on grey system and interval numbers

Abstract

In the case of unknown weights, theories of multi-attributed decision making based on interval numbers and grey related analysis were used to optimize mining methods. As the representative of independence for the indicator, the smaller the correlation of indicators is, the greater the weight is. Hence, the weights of interval numbers of indicators were determined by using correlation coefficient. Relative closeness based on positive and negative ideal methods was calculated by introducing distance between interval numbers, which made decision making more rational and comprehensive. A new method of ranking interval numbers based on normal distribution was proposed for the optimization of mining methods, whose basic properties were discussed. Finally, the feasibility and effectiveness of this method were verified by theories and practice.

Keywords

mining method / interval number / multi-attributed decision making / grey related analysis / correlation coefficient / normal distribution / ranking

References

[1] XuX-h, LiaoG-h, MaGuangMining manual: Vol. 2 [M], 1990BeijingMetallurgical Industry Press27-49

[2] YanS-l, YangW-c, XiaoX-ping. Attribute weight unknown hybrid multi-attribute decision making methods [J]. Statistics and Decision, 2008, 1: 16-18

[3] LiuP-d, GuanZ-liang. Research on multiple attribute decision-making under risk with continuous random variable and weight unknown [J]. Systems Engineering and Electronics, 2009, 31(9): 2133-2136

[4] RaoC-j, XiaoX-ping. Method of grey matrix relative degree for dynamic hybrid multi-attribute decision making under risk [J]. Systems Engineering and Electronics, 2006, 28(9): 1353-1357

[5] WangX-m, ZhaoB, ZhangQ-li. Mining method choice based on AHP and fuzzy mathematics [J]. Journal of Central South University: Science and Technology, 2008, 39(5): 875-880

[6] ParkD-g, KwunY-c, ParkJ-j, ParkI-young. Correlation coefficient of interval-valued intuitionist fuzzy sets and its application to multiple attribute group decision making problems [J]. Mathematical and Computer Modeling, 2009, 50(9/10): 1279-1293

[7] OlsonD L, ZhangJ-j, WuD-sheng. The method of grey related analysis to multiple attribute decision making problems with interval numbers [J]. Mathematical and Computer Modeling, 2005, 42(9/10): 991-998

[8] XuZ-s, DaQ-li. Research on method for ranking interval numbers [J]. Systems Engineering, 2001, 19(6): 94-96

[9] XuZ-s, DaQ-li. Possibility degree method for ranking interval numbers and its application [J]. Journal of Systems Engineering, 2003, 18(1): 67-70

[10] WanS-ping. Interval multi-attribute decision-making method based on index of attitude [J]. Systems Engineering, 2008, 26(8): 108-112

[11] HanY-j, ChenJ-h, ZhouZ-yong. Fuzzy assessment method of interval number for gas explosion in coal mines based on index of attitude [J]. China Safety Science Journal, 2010, 20(2): 83-88

[12] PengZ-qi. Application of uncertain multi-attribute decision-making in optimizations of mining methods [J]. Mining and Metallurgical Engineering, 2003, 23(6): 14-16

[13] XiaY-q, WuQ-zong. A technique of order preference by similarity to ideal solution for hybrid multiple attribute decision making problems [J]. Journal of Systems Engineering, 2004, 19(6): 630-634

[14] WeiG-wu. Grey relational analysis method for multiple attribute decision making with incomplete attribute weights [J]. Mathematics in Practice and Theory, 2007, 37(19): 94-98

[15] WeiG-wu. New method of grey relational analysis to multiple attribute decision making with interval number [J]. Systems Engineering and Electronics, 2006, 28(9): 1358-1359

[16] ZhangJ-jun. Method of grey related analysis to multiple attribute decision making problems with interval numbers [J]. Systems Engineering and Electronics, 2005, 27(6): 1030-1033

[17] HanX-liMathematics tutorial [M], 2004BeijingScience Press112-135