American Journal of Mathematical and Computational Sciences  
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Tolerance Solution and Control Solution of Max-plus Interval Inequalities
American Journal of Mathematical and Computational Sciences
Vol.2 , No. 3, Publication Date: Aug. 31, 2017, Page: 19-23
523 Views Since August 30, 2017, 378 Downloads Since Aug. 30, 2017
 
 
Authors
 
[1]    

Lihua Wang, Institute of Operational Research and Cybernetic, Hangzhou Dianzi University, Hangzhou, China.

[2]    

Ruili Guo, College of Science, University of Shanghai for Science and Technology, Shanghai, China.

 
Abstract
 

In recent years, with the introduction of max-plus algebra architecture to the field of interval mathematics, some equivalent propositions of various solutions in max-plus algebra have been paid close attention to by many scholars in the world. In the paper, first of all, in the structure of max-plus algebras, we define tolerance solution and control solution of interval inequalities, and then we established equivalent conditions of tolerance solution and control solution of max-plus algebra. Finally, we give some corresponding examples to illustrate.


Keywords
 

Max-plus Algebra, Tolerance Solution, Control Solution, Interval Inequalities


Reference
 
[01]    

Fiedler M, Rohn J, Nedoma J. (2006) Linear optimization problems with inexact date. New York: Springer, pp.35-66.

[02]    

Shary S P. (2002) A new technique in systems analysis under interval uncertainty and ambiguity. Reliab. Comput.8 (5), pp.321–418.

[03]    

Hladik M. (2015) AE solutions and AE solvability to general interval linear systems. Linear Algebra and its Applications.465, pp.221-238.

[04]    

Li W, Wang H P, Wang Q. (2013) Localized solutions to interval linear equations. Journal of Computational and Applied Mathematics.238 (15), pp.29-38.

[05]    

Li W, Luo J, Wang Q, et al. (2014) Checking weak optimality of the solution to linear programming with interval right-hand side. Optim. Lett.8 (4), pp.1287-1299.

[06]    

Li W, Liu P Z, Li H H. (2016) Checking weak optimality of the solution to interval linear program in the general form. Optim. Lett.10(1), pp.77–88.

[07]    

Li W, Xia M, Li H. (2015) New method for computing the upper bound of optimal value in interval quadratic program. Journal of Computational and Applied Mathematics. 288, pp.70–80.

[08]    

Rohn J. (2004) A Manual of Results on Interval Linear Problems. http://uivtx.cs.cas.cz/~rohn.

[09]    

Myskova H. (2012) Interval max-plus systems of linear equations [J]. Linear Algebra and its Applications,. 437(8), pp.1992-2000.

[10]    

Cechlárová K, Cuninghame-Green R A. (2002) Interval systems of max-separable linear equations. Linear Algebra and its Applications.340 (1-3), pp. 215-224.

[11]    

Leela-apiradee W, Thipwiwatpotjana P. (2015) L-and R-localized solvabilities of max-separable interval linear equations and its applications. Journal of Computational and Applied Mathematics. 279, pp.306-317.

[12]    

Cuninghame-Green R. Minimax Algebra. (1979) Lecture Notes in Economics and Mathematical Systems. 166(4), pp.66-69.

[13]    

VorobEv N N. (2015) Extremal algebra of positive matrices// Elektron. Informationsverarbeit. Kybernetik. 2010, pp.39-71.

[14]    

Wang H L, Wang X P. (2015) A polynomial algorithm for solving system of inequalities in max-plus algebra. Information Sciences. 318(C), pp.1-13.

[15]    

Cechlárová K, Cuninghame-Green R A. (2002) Interval systems of max-separable linear equations. Linear Algebra and Its Applications. 403, pp.263-272.

[16]    

Nirmala T, Datta D, Kushwaha H S, et al. (2011) Inverse Interval Matrix: A New Approach. 5(13), pp.607-624.

[17]    

Zimmermann K. (2006) Interval linear systems and optimization problems over max-algebras// Linear Optimization Problems with Inexact Data. Springer US. pp.165-193.

[18]    

Mysková, Helena. (2006) Control solvability of interval systems of max-separable linear equations. Linear Algebra and Its Applications. 416 (2), pp.215-223.

[19]    

Mysková H. (2005) Interval solutions in max-plus algebra.

[20]    

Leake C. (1994) Synchronization and Linearity: An Algebra for Discrete Event Systems. Journal of the Operational Research Society.45 (1), pp.118-119.

[21]    

Heidergott B, Olsder G J, Woude J V D. (2014) Max Plus at Work: Modeling and Analysis of Synchronized Systems: A Course on Max-Plus Algebra and Its Applications. Princeton University Press.

[22]    

Schutter B D, Boom T V D.(2008) Max-plus algebra and max-plus linear discrete event systems: An introduction// International Workshop on Discrete Event Systems. IEEE. pp.36-42.

[23]    

Xu J, Boom T V D, Schutter B D.(2016) Optimistic optimization for model predictive control of max-plus linear systems. Automatica.74, pp.16-22.





 
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