## versão On-line ISSN 2224-7890versão impressa ISSN 1012-277X

### S. Afr. J. Ind. Eng. vol.22 no.1 Pretoria  2011

A new algorithm for optimization of the fuzzy relation equation with max-algebraic sum composition

IDepartment of Industrial Engineering, University of Tarbiat Moallem (Kharazmi), Tehran, Iran. v.zharfi@tmu.ac.ir
IIDepartment of Industrial Engineering, University of Tarbiat Moallem (Kharazmi), Tehran, Iran. a.mirzazadeh@aut.ac.ir

ABSTRACT

This paper considers an optimization problem with a linear objective function under the constraints expressed by a system of fuzzy relation equations using max-as (Algebraic Sum) composition. First, some properties of minimal solutions of the system with fuzzy relation equations and max-as composition are shown. Then, a new algorithm for solving the optimization problem is derived. The numerical examples have been provided to illustrate the theoretical results.

OPSOMMING

Hierdie artikel bestudeer 'n optimiseringsprobleem met 'n lineêre doelwitfunksie en wasige randvoorwaardes met 'n algebraïese somsamestelling. Aanvanklik word sommige eienskappe van die minimale oplossings van die wasige vergelykings en die algebraïese samestelling getoon. Daarna word 'n nuwe algoritme vir die oplossing van die optimiseringsprobleem afgelei. Numeriese voorbeelde word voorsien om die teoretiese resultate te ondersteun.

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* Corresponding author.
1 The author was enrolled for an MEng (Industrial) degree in the Department of Industrial Engineering, University of Tarbiat Moallem.
2 The author was enrolled for a DPhil (Engineering Management) degree in the Department of Industrial Engineering, University Tarbiat Moallem.

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