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Algorithms for Solving Fuzzy Linear and Quadratic Problems Directly and Duality Results for Bipolar Fuzzy Optimization Problems

Ghorbani-Moghadam, Khatere | 2019

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  1. Type of Document: Ph.D. Dissertation
  2. Language: Farsi
  3. Document No: 51717 (02)
  4. University: Sharif University of Technology
  5. Department: Mathematical Sciences
  6. Advisor(s): Mahdavi Amiri, Nezameddin; Ghanbari, Reza
  7. Abstract:
  8. There are many linear and nonlinear programming problems with uncertain parameters and variables. These types of linear and nonlinear models are called fuzzy linear and nonlinear programming problems. Solving such problems is important, due to applications and variety of these models. Here, we first review various types of fuzzy linear programming problems based on the models or the solution methods. Next, we revise a method due to Kerre to compare two unipolar LR fuzzy numbers and present some new results on the comparison of LR fuzzy numbers. Then, we solve linear programming problems with unipolar fuzzy numbers by our proposed time varient particle swarm optimization (TV-PSO) algorithm. Next, using a variable neighborhood search algorithm, we solve linear and quadratic programming problems. In our algorithm,local search is defined based on descent directions found by using our modified Kerre’s method. We then define a new ranking function for comparison of two bipolar fuzzy numbers. We make use of this ranking function to present some duality results for linear and nonlinear programming problems with bipolar fuzzy numbers. Next, we extend Kerre’s and modified Kerre’s methods for comparison of two bipolar LR fuzzy numbers. Finally, we provide some illustrative examples to investigate the behavior of the our algorithms and show the effectiveness of their implementations
  9. Keywords:
  10. LR Monopole Fuzzy Numbers ; Kerr's Method ; Modified Kerr's Method ; Particles Swarm Optimization (PSO) ; Quadratic Programming with Fuzzy ; Linear Programming ; Variable Neighborhood Search ; Triangular Bipolar Fuzzy Numbers ; Ranking Function

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