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New Approaches for Solving Fuzzy LR Linear Systems and a Class of Fuzzy Location Problems

Ghanbari, Reza | 2010

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  1. Type of Document: Ph.D. Dissertation
  2. Language: Farsi
  3. Document No: 40144 (02)
  4. University: Sharif University of Technology
  5. Department: Mathematical Sciences
  6. Advisor(s): Mahdavi Amiri, Nezamoddin
  7. Abstract:
  8. By increasing complexity of systems, soft computing including fuzzy computing, evolutionary computing and intelligent computing, have been developing in recent years. Here, we focus on two subjects making use of soft computing. Firstly, we study fuzzy LR linear systems.
    We transform the fuzzy linear system into a corresponding linear crisp system and a constrained least squares model. We show that the fuzzy LR system has an exact solution if and only if the corresponding crisp system is compatible (has a solution) and the optimal value of the corresponding least squares problem is equal to zero. In this case, the exact solution is determined by the solutions of the two corresponding problems. On the other hand, if the corresponding crisp system is compatible and the optimal value of the corresponding constrained least squares problem is nonzero, then we characterize approximate solutions of the fuzzy system by solution of the least squares problem.Comparison results of our approach with the ones due to other existing algorithms show the efficincy of our proposed approch. Secondly, we propose a compromised solution of an LR fuzzy linear system by use of a ranking function. Also, when the ranking function is a member of a certain class of ranking functions, we propose a class of algorithms, based on ABS class of algorithms, to compute the general compromised solution. In the second part of our work, we propose a new approach for hybridization of genetic algorithms with some neighborhood search based metaheuristic algorithms. In our hybrid algorithms, we consider gradually increasing probability for the application of the neighborhood search procedure on the best individuals as the number of iterations of the genetic algorithm grows. We test the programs on a variety of randomly generated large scale fuzzy bus terminal location problems. The computational xperiments demonstrate the efficiency of the proposed approaches
  9. Keywords:
  10. Combinatorial Optimization ; Evolutionary Algorithm ; Genetic Algorithm ; Hybrid Algorithm ; Abaffy-Broyden-Spedicato (ABS)Method ; Soft Computation ; Least Squares Approximation ; Fuzzy Linear System ; Exact and Approximate Solution

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