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Research Articles

Goal programming approach to fully fuzzy fractional transportation problem

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Pages 864-874 | Received 20 Jul 2018, Accepted 24 Jul 2019, Published online: 12 Aug 2019

References

  • Hitchcock FL. The distribution of a product from several sources to numerous localities. J Math Phys. 1941;20:224–230. doi: 10.1002/sapm1941201224
  • Buckley JJ, Feuring T. Evolutionary algorithm solution to fuzzy problems: fuzzy linear programming. Fuzzy Sets Syst. 2000;109:35–53. doi: 10.1016/S0165-0114(98)00022-0
  • Lee SM, Moore LJ. Optimizing transportation problems with multiple objectives. AIIE Trans. 1973;5:333–338. doi: 10.1080/05695557308974920
  • Anukokila P, Radhakrishnan B. Goal programming approach for solving multi-objective fractional transportation problem with fuzzy parameters. RAIRO Oper Res.2019;1:157–178. doi: 10.1051/ro/2019005
  • Li G. Fuzzy goal programming – a parametric approach. Inf Sci. 2012;195:287–95. doi: 10.1016/j.ins.2012.01.043
  • Mohamed RH. The relationship between goal programming and fuzzy programming. Fuzzy Sets Syst. 1997;89:215–222. doi: 10.1016/S0165-0114(96)00100-5
  • Pal BB, Moitra BN, Moulik U. A goal programming procedure for fuzzy multiobjective linear fractional programming problem. Fuzzy Sets Syst. 2003;139:395–405. doi: 10.1016/S0165-0114(02)00374-3
  • Waiel F, Abd El-Wahed, Lee Sand M. Interactive fuzzy goal programming for multi-objective transportation problem. Omega. 2006;34:158–166. doi: 10.1016/j.omega.2004.08.006
  • Pop B, Stancu-Minasian IM. On solving fully fuzzified linear fractional programs. Adv Model Optim. 2009;11:503–523.
  • Lingo user's guide. Chicago: LINDO systems Inc.; 1999.
  • Chang CT. A goal programming approach for fuzzy multi-objective fractional programming problems. Int J Syst Sci. 2009;40:867–874. doi: 10.1080/00207720902974538
  • Stanojevic B, Stancu-Minasian IM. Evaluating fuzzy inequalities and solving fully fuzzified linear fractional programs. Yugoslav J Oper Res. 2012;22:41–50. doi: 10.2298/YJOR110522001S
  • Craven BD. Fractional programming. Berlin, Germany: Helderman; 1988.
  • Stancu-Minasian IM, Pop B. On a fuzzy set approach to solving multiple objective linear fractional programming problem. Fuzzy Sets Syst. 2003;134:397–405. doi: 10.1016/S0165-0114(02)00142-2
  • Stancu-Minasian IM. Fractional programming. Dordrecht, Boston, London: Kluwer Academic Publishers; 1997.
  • Pramanik S, Kumar Roy T. Fuzzy goal programming approach to multilevel programming problems. Eur J Oper Res. 2007;176:1151–1166. doi: 10.1016/j.ejor.2005.08.024
  • Pop B, Stancu-Minasian IM. A method of solving fully fuzzified linear fractional programming problems. J Appl Math Comput. 2008;27:227–242. doi: 10.1007/s12190-008-0052-5
  • Zadeh LA. Fuzzy sets. Inf Control. 1965;8:338–353. doi: 10.1016/S0019-9958(65)90241-X
  • Ammar EE, Youness EA. Study on multi objective transportation problem with fuzzy numbers. Appl Math Comput. 2005;166:241–253.
  • Ebrahimnejad A. Fuzzy linear programming approach for solving transportation problems with interval-valued trapezoidal fuzzy numbers. Acad Proc Eng Sci. 2016;41:299–316.
  • Kaur A, Kumar A. A new approach for solving fuzzy transportation problem using generalized trapezoidal fuzzy numbers. Appl Soft Comput. 2012;12:1201–1213. doi: 10.1016/j.asoc.2011.10.014
  • Kumar Das S, Mandal T. A new approach for solving fully fuzzy linear fractional programming problem. RAIRO Oper Res. doi:10.1051/ro/2016022.
  • Gupta A, Kumar A, Kaur A. Mehar's method to find exact fuzzy optimal solution of unbalanced fully fuzzy multi-objective transportation problems. Optim Lett. 2012;6:1737–1751. doi: 10.1007/s11590-011-0367-2
  • Kerre EE. The use of fuzzy set theory in electro-cardiological diagnostics. In: Gupta MM, Sanchez E, editors. Approximate reasoning decision analysis. North-Holland Publishing, Amsterdam, the Netherlands, Vol. 166. 1982. p. 277–282.
  • Charnes A, Cooper WW. Programming with linear fractional functionals. Nav Res Logist Quart. 1962;9:181–186. doi: 10.1002/nav.3800090303
  • Patkal VN, Stancu-Minasian IM. On disjunctive linear fractional programming. Eur J Oper Res. 1985;21:101–105. doi: 10.1016/0377-2217(85)90093-1
  • Stancu-Minasian IM. Stochastic programming with multiple-objective functions. Dordrecht: D. Reidel Publishing Company; 1984.