In collaboration with Payame Noor University and the Iranian Society of Instrumentation and Control Engineers

Document Type : Research Article

Author

Teacher

Abstract

Jahanshahloo has suggested a method for the solving linear programming problems with zero-one variables‎. ‎In this paper we formulate fully fuzzy linear programming problems with zero-one variables and a method for solving these problems is presented using the ranking function and also the branch and bound method along with an example is presented.

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Main Subjects

[1] Bellman ‎R‎. ‎E.‎, ‎Zadeh‎ ‎L‎. ‎A. (1970) " ‎Decision making in a fuzzy environment ''‎, ‎Management Sciences‎, ‎17‎, ‎141-164‎.
[2] Campos ‎L.‎, ‎Verdegay ‎J‎. ‎L. (1989) " ‎Linear programming problems and ranking of fuzzy numbers ''‎, ‎Fuzzy Set and Systems‎, ‎Elsevier Science Publishers‎, ‎32‎, ‎1-11‎.
[3] Ebrahimnejad ‎A.‎, ‎Nasseri ‎Sh.‎, ‎Lotfi‎ ‎F‎. ‎H.‎, ‎Soltanifar‎ ‎M. (2010) " ‎A primal‎- ‎dual method for linear programming problems with fuzzy variables ''‎, ‎European Journal of Industrial Engineering‎, ‎4‎, ‎189-209‎.
[4] Ganesan‎ ‎K.‎, ‎Veeramani ‎P. (2006) " ‎Fuzzy linear programs with trapezoidal fuzzy numbers ''‎, ‎Annals Of Operation Research-incl‎, ‎143‎, ‎305-315‎.
[5] Jahanshahloo ‎Gh. (2003) " ‎Operations research 2 ''‎, ‎Pnu‎, ‎74‎, ‎Tehran‎.
[6] Liou ‎T‎. ‎S.‎, ‎Wang ‎M‎. ‎J. (1992) " ‎Ranking fuzzy numbers with integral value ''‎, ‎Fuzzy Sets and Systems‎, ‎Elsevier Science Publishers‎, ‎50‎, ‎247-255‎.
[7] Maleki ‎H‎. ‎R‎.  ‎(2002) " ‎Ranking function and their application to fuzzy linear programming ''‎, ‎Far East Journal of Mathematics Sciences‎, ‎4‎, ‎283-301‎.
[8] Maleki‎ ‎H‎. ‎R.‎, ‎Tata ‎M.‎, ‎Mashinchi ‎M. (2000) " ‎Linear programming with fuzzy variables ''‎, ‎Fuzzy Set and System‎, ‎Elsevier Science Publishers‎, ‎109‎, ‎21-33‎.
[9] Tanaka ‎H.‎, ‎Okada ‎T.‎, ‎Asai‎ ‎K. (1973) " ‎On fuzzy mathematical programming '', Journal of Cybernetics Systems‎, ‎3‎, ‎37-46‎.
[10] Zimmerman ‎H‎. ‎J. (1978) " ‎Fuzzy programming and linear programming with several objective function ''‎, ‎Fuzzy Set and Systems‎, ‎Elsevier Science Publishers‎, ‎1‎, ‎45-55‎.