A Fuzzy Linear Programming Problem with Fuzzy Convergent Equality Constraints

퍼지 융합 등식 제약식을 갖는 퍼지 선형계획법 문제

  • Oh, Se-Ho (Dept. of Industrial Engineering, Cheongju University)
  • 오세호 (청주대학교 산업공학과)
  • Received : 2015.07.20
  • Accepted : 2015.10.20
  • Published : 2015.10.31


The fuzzy linear programming(FLP) is the useful approach to many real world problems under uncertainty. This paper deals with a FLP whose objective value is fuzzy. And the right hand sides of convergent equality constraints are fuzzy numbers. We assume that the membership function of the objective value is piecewise linear and those of the right hand side are trapezoidal. Each of these trapezoidal functions can be algebraically replaced with three linear functions. Then the FLP problem is transformed into the Zimmermann's symmetric model. The fuzzy solution based on the max-min rule can be obtained by solving the crisp linear programming problem derived from the symmetric model. A numerical example has illustrated our approach. The application of our approach to the inconsistent linear system can enable generate us to get define the useful and flexible inexact solutions within acceptable tolerance. Further research is required to generalize the membership function.


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