The optimization problem over a distributive lattice |
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Authors: | Mahbobeh Hosseinyazdi |
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Institution: | (1) Shiraz Payam-e-Noor University, Shiraz, Iran |
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Abstract: | 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.
This research was completed while the author was a visitor of the Center for Informatics and Applied Optimization, University
of Ballarat, Ballarat, Australia. |
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Keywords: | Distributive lattice Linear programming Fuzzy linear systems Fuzzy relational equation Optimization |
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