SciELO - Scientific Electronic Library Online

vol.22 número1The performance of South African shared servicesDeveloping a modular portfolio selection model for short-term and long-term market trends and mass psychology índice de autoresíndice de assuntospesquisa de artigos
Home Pagelista alfabética de periódicos  

Serviços Personalizados



Links relacionados

  • Em processo de indexaçãoCitado por Google
  • Em processo de indexaçãoSimilares em Google


South African Journal of Industrial Engineering

versão On-line ISSN 2224-7890
versão 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



V. ZharfiI; A. MirzazadehII

IDepartment of Industrial Engineering, University of Tarbiat Moallem (Kharazmi), Tehran, Iran.
IIDepartment of Industrial Engineering, University of Tarbiat Moallem (Kharazmi), Tehran, Iran.




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.


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.



“Full text available only in PDF format”




[1] Adamopoulos, G.I. & Pappis, C.P. 1993. Some result on the resolution of fuzzy relation equation, Fuzzy Sets and Systems, 60, pp 83-88.         [ Links ]

[2] Aliasing, K.P. 1986. Fuzzy set theory in medical diagnosis, IEEE Transactions on Systems, Man and Cybernetics, 16, pp 260-265.         [ Links ]

[3] Bellman, R.E. & Zadeh, L.A. 1970. Decision-making in fuzzy environment, Management Science, 17, pp 41-164.         [ Links ]

[4] Di Nola, A. 1985. Relational equations in totally ordered lattices and their complete resolution, Journal de Mathematiques Pures et Appliquees, 107, pp 148-155.         [ Links ]

[5] Zimmermann, H.J. 1999. Fuzzy set theory and its application, Kluwer Academic Publishers, Boston / Dordrecht / London.         [ Links ]

[6] Pedrycz, W. 1981. An approach to the analysis of fuzzy systems, International Journal on Control, 34, pp 403-421.         [ Links ]

[7] Dubois, D. & Prade, H. 1980. Fuzzy sets and systems: Theory and applications, New York, Academic Press.         [ Links ]

[8] Wenstop, F. 1976. Deductive verbal models of organizations, International Journal of Man-Machine Studies, 8, pp 93-311.         [ Links ]

[9] Klir, G.J. & Folger, T.A. 1988. Fuzzy sets, uncertainty, and information, Prentice-Hall, Englewood Cliffs.         [ Links ]

[10] Sanchez, E. 1976. Resolution of composite fuzzy relation equations, Information and Control, 30, pp 38-48.         [ Links ]

[11] Di Nola, A., Sessa, S., Pedrycz, W. & Sanchez, E. 1989. Fuzzy relation equations and their applications to knowledge engineering, Dordrecht, Kluwer Academic Press.         [ Links ]

[12] Higashi, M. & Klir, G.J. 1984. Resolution of finite fuzzy relation equations, Fuzzy Sets and Systems, 13, pp 65-82.         [ Links ]

[13] Wu, Y.-K. & Guu, S.-M. 2005. Minimizing a linear function under a fuzzy max-min relational equation constraint, Fuzzy Sets and Systems, 150, pp 147-162.         [ Links ]

[14] Wu, Y.-K. 2007. Optimization of fuzzy relational equations With max-av composition, Journal of Information Sciences, 177, pp 4216-4229.         [ Links ]

[15] Khorram, E., Ghodousian, A. & Molai, A. 2006. Solving linear optimization problems with max-star composition equation constraints, Applied Mathematics and Computation, 179, pp 654- 661.         [ Links ]



* 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.

Creative Commons License Todo o conteúdo deste periódico, exceto onde está identificado, está licenciado sob uma Licença Creative Commons