Fully fuzzified linear programming, solution and duality

  • Authors:

  • S. M. Hashemi;M. Modarres;E. Nasrabadi;M. M. Nasrabadi

  • Affiliations:

  • Department of Computer Science, Amirkabir University of Technology, Tehran, Iran;Department of Industrial Engineering, Sharif University of Technology, Tehran, Iran;Department of Computer Science, Amirkabir University of Technology, Tehran, Iran;Department of Mathematics, Payam Noor University of Birjand, Birjand, Iran

  • Venue:
  • Journal of Intelligent & Fuzzy Systems: Applications in Engineering and Technology
  • Year:
  • 2006

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Abstract

In this paper, we propose a two-phase approach to find the optimal solutions of a class of fuzzy linear programming problems called fully fuzzified linear programming (FFLP), where all decision parameters and variables are fuzzy numbers. Our approach is constructed on the basis of comparison of mean and standard deviation of fuzzy numbers. In this approach, the first phase maximizes the possibilistic mean value of fuzzy objective function and obtains a set of feasible solutions. The second phase minimizes the standard deviation of the original fuzzy objective function, by considering all basic feasible solutions obtained at the end of the first phase. The advantage of the proposed approach is its simplicity in programming and computation. Moreover, we also generalize the concept of linear programming duality and extend the duality as well as the weak duality theory to FFLP.