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Iranian Journal of Fuzzy Systems، جلد ۷، شماره ۲، صفحات ۱-۱۸
عنوان فارسی Exact and approximate solutions of fuzzy LR linear systems: New algorithms using a least squares model and the ABS approach
چکیده فارسی مقاله We present a methodology for characterization and an approach for computing the solutions of fuzzy linear systems with LR fuzzy variables. As solutions, notions of exact and approximate solutions are considered. We transform the fuzzy linear system into a corresponding linear crisp system and a constrained least squares problem. If the corresponding crisp system is incompatible, then the fuzzy LR system lacks exact solutions. 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 solution 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. Also, we characterize solutions by defining an appropriate membership function so that an exact solution is a fuzzy LR vector having the membership function value equal to one and, when an exact solution does not exist, an approximate solution is a fuzzy LR vector with a maximal membership function value. We propose a class of algorithms based on ABS algorithm for solving the LR fuzzy systems. The proposed algorithms can also be used to solve the extended dual fuzzy linear systems. Finally, we show that, when the system has more than one solution, the proposed algorithms are flexible enough to compute special solutions of interest. Several examples are worked out to demonstrate the various possible scenarios for the solutions of fuzzy LR linear systems.
کلیدواژه‌های فارسی مقاله Fuzzy linear system، Fuzzy LR solution، ABS algorithm، Least squares approximation،
عنوان انگلیسی Exact and approximate solutions of fuzzy LR linear systems: New algorithms using a least squares model and the ABS approach
چکیده انگلیسی مقاله We present a methodology for characterization and an approach for computing the solutions of fuzzy linear systems with LR fuzzy variables. As solutions, notions of exact and approximate solutions are considered. We transform the fuzzy linear system into a corresponding linear crisp system and a constrained least squares problem. If the corresponding crisp system is incompatible, then the fuzzy LR system lacks exact solutions. 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 solution 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. Also, we characterize solutions by defining an appropriate membership function so that an exact solution is a fuzzy LR vector having the membership function value equal to one and, when an exact solution does not exist, an approximate solution is a fuzzy LR vector with a maximal membership function value. We propose a class of algorithms based on ABS algorithm for solving the LR fuzzy systems. The proposed algorithms can also be used to solve the extended dual fuzzy linear systems. Finally, we show that, when the system has more than one solution, the proposed algorithms are flexible enough to compute special solutions of interest. Several examples are worked out to demonstrate the various possible scenarios for the solutions of fuzzy LR linear systems.
کلیدواژه‌های انگلیسی مقاله Fuzzy linear system, Fuzzy LR solution, ABS algorithm, Least squares approximation
نویسندگان مقاله رضا قنبری |
department of mathematics, ferdowsi university of mashhad, mashhad, iran
سازمان اصلی تایید شده: دانشگاه فردوسی (Ferdowsi university)

نظام مهدوی امیری | mahdavi amiri
faculty of mathematical sciences, sharif university of technology, tehran, iran
سازمان اصلی تایید شده: دانشگاه صنعتی شریف (Sharif university of technology)

روح اله یوسف پور |
department of mathematics, mazandaran university, babolsar, iran
سازمان اصلی تایید شده: دانشگاه مازندران (Mazandaran university)

نشانی اینترنتی http://ijfs.usb.ac.ir/article_167_fe7dee7c3aebbf868f6740e4d0784901.pdf
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