|Table of Contents|

Some results of absolute value operations on interval numbers(PDF)

《纺织高校基础科学学报》[ISSN:1006-6977/CN:61-1281/TN]

Issue:
2019年03期
Page:
298-306
Research Field:
基础科学
Publishing date:

Info

Title:
Some results of absolute value operations on interval numbers
Author(s):
QIN Xiaoli12KHALIL Ahmed1ZHANG Chen3LI Shenggang1
1.College of Mathematics and Information Science,Shaanxi Normal University,Xi’an 710062,China; 2.Deyang High School,Chengdu Normal University,Deyang 618000,Sichuan,China; 3.School of Mathematics and Statistics,Longdong University, Qingyang 745000,Gansu, China
Keywords:
 interval number absolute value pseudometric metric arithmetic
PACS:
O 159
DOI:
10.13338/j.issn.1006-8341.2019.03.012
Abstract:
The paper defines a kind of new absolute value operation of interval numbers. According to the absolute value operation that has been defined on interval numbers, this paper further studies properties of absolute value operations on interval numbers,and properties on centers of interval numbers. What’s more, laws of arithmetic in real numbers are extended to interval numbers by the principle of the algorithm of real numbers, and the paper discusses laws of arithmetic in interval numbers.Due to the fundamental importance of interval numbers in representing and dealing with uncertainty,the distance between two interval numbers can be defined with the help of the defined absolute value operations of interval numbers.

References:

[1] STEFANINI L,BEDE B.Generalized Hukuhara differentiability of interval-valued functions and interval differential equations[J].Nonlinear Analysis:Theory,Methods and Applications,2009,71(3-4):1311-1328.
[2] WU H C.The Karush-Kuhn-Tucker optimality conditions in multiobjective programming problems with interval-valued objective functions[J].European Journal of Operational Research,2009,196(1):49-60.
[3] 包玉娥,吴梅花.一致凸模糊映射及其有关性质[J].纯粹数学与应用数学,2009,25(4):725-730. BAO Y E,WU M H.Uniformly convex fuzzy mappings and its properties[J].Pure and Applied Mathematics,2009,25(4):725-730.(in Chinese)
[4] TONG S C.Interval number and fuzzy number linear programmings[J].Fuzzy Sets and Systems,1994,66(3):301-306.
[5] 党耀国,刘思峰,刘斌,等.多指标区间数关联决策模型的研究[J].南京航空航天大学学报,2004,36(3):403-406. DANG Y G,LIU S F,LIU B,et al.Study on incidence decision making model of multi-attribute interval number[J].Journal of Nanjing University of Aeronautics and Astronautics,2004,36(3):403-406.(in Chinese)
[6] JIANG C,HAN X,GUAN F J,et al.An uncertain structural optimization method based on nonlinear interval number programming and interval analysis method[J].Engineering Structures,2007,29(11):3168-3177.
[7] 裴植,鲁建厦,郑力.广义区间值直觉模糊数及其在工位评估中的应用[J].系统工程理论与实践, 2012,32(10):2198-2206. PEI Z,LU J X,ZHENG L.Generalized interval-valued intuitionistic fuzzy numbers with applications in workstation assessment[J].Systems Engineering-Theory and Practice,2012,32(10):2198-2206.(in Chinese)
[8] 薛利敏,岳伟.基于模糊系数的投资组合选择模型[J].纺织高校基础科学学报,2007,20(2):133-136. XUE L M,YUE W.The optional model of portfolio investment with fuzzy-coefficient[J].Basic Sciences Journal of Textile Universities,2007,20(2):133-136.(in Chinese)
[9] 李振,尚云艳,郭鹏江,等.变化抽样区间和样本容量的EWMA标准差控制图[J].纺织高校基础科学学报,2012,25(4):476-479. LI Z,SHANG Y Y,GUO P J,et al.An EMWA standard deviation control chart with variable sampling sizes and sampling intervals[J].Basic Sciences Journal of Textile Universities,2012,25(4):476-479.(in Chinese)
[10] 张珍珍,刘华宁.关于短区间中 DH Lehmer 问题的一个推广[J].纺织高校基础科学学报,2015,28(1):27-31. ZHANG Z Z,LIU H N.On a generalization of the D.H.Lehmer problem in short intervals[J].Basic Sciences Journal of Textile Universities,2015,28(1):27-31.(in Chinese)
[11] 代兵,包玉娥.区间数的绝对值和区间值函数的极限[J].纯粹数学与应用数学,2016,32(6):583-590. DAI B,BAO Y E.The absolute value of interval numbers and the limit of the interval value function[J].Pure and Applied Mathmatics,2016,32(6):583-590.(in Chinese)
[12] 陈启浩,贲亮,李向明.模糊值度量空间的拓扑性质(I)[J].北京邮电大学学报,2000,23(2):16-20. CHEN Q H,BEN L,LI X M.Topological properties of fuzzy valued metric spaces(I)[J].Journal of Beijing University of Posts and Telecommunications,2000,23(2):16-20.(in Chinese)
[13] 陈启浩,贲亮,李向明.模糊值度量空间的拓扑性质(II)[J].北京邮电大学学报,2000,23(1):1-4. CHE Q H,BEN L,LI X M.The topological properties of fuzzy valued metric spaces(II)[J].Journal of Beijing University of Posts and Telecommunications,2000,23(1):1-4.(in Chinese)
[14] YOUNG R C.The algebra of many-valued quantities[J].Mathematische Annalen,1931,104(1):260-290.
[15] MOORE R E.Methods and applications of interval analysis[M].New Jersey:Prentice Hall,1966.
[16] 刘旺金,何家儒.模糊数学导论[M].成都:四川教育出版社,1992. LIU W J,HE J R.An introduce to fuzzy mathmatics[M].Chengdu:Sichuan Education Press,1992.(in Chinese)
[17] BEDE B,STEFANINI L.Generalized differentiability of fuzzy-valued functions[J].Fuzzy Sets and Systems,2013,230:119-141.

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Last Update: 2019-10-07