Journal of Global Optimization

, Volume 41, Issue 2, pp 283–298 | Cite as

The optimization problem over a distributive lattice

  • Mahbobeh Hosseinyazdi


In this paper we give a necessary and sufficient condition for existence of minimal solution(s) of the linear system A * X ≥ b where A, b are fixed matrices and X is an unknown matrix over a lattice. Next, an algorithm which finds these minimal solutions over a distributive lattice is given. Finally, we find an optimal solution for the optimization problem min {Z = C * X | A * X ≥ b} where C is the given matrix of coefficients of objective function Z.


Distributive lattice Linear programming Fuzzy linear systems Fuzzy relational equation Optimization 

Mathematics Subject Classification (2000)

06Dxx 34A30 20M14 16Y60 


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Copyright information

© Springer Science+Business Media, LLC. 2007

Authors and Affiliations

  1. 1.Shiraz Payam-e-Noor UniversityShirazIran

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