A Short Review on Fuzzy System of Linear Equations

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Köçken H., Albayrak F. İ.

in: Encyclopedia of Information Science and Technology, Third Edition , Mehdi Khosrow-Pour D.B.A., Editor, IGI Global, Pennsylvania, pp.6981-6989, 2015

  • Publication Type: Book Chapter / Chapter Research Book
  • Publication Date: 2015
  • Publisher: IGI Global
  • City: Pennsylvania
  • Page Numbers: pp.6981-6989
  • Editors: Mehdi Khosrow-Pour D.B.A., Editor
  • Yıldız Technical University Affiliated: Yes


Systems of linear equations play a major role in various areas such as operational research, physics, statistics, engineering and social sciences. In many applications, the parameters of linear equation systems are not always exactly known and stable. This imprecision may follow from the lack of exact information, changeable economic conditions, etc.. A frequently used way of expressing the imprecision is to use the fuzzy numbers rather than the crisp numbers. It enables us to consider tolerances for parameters of linear equation systems (the entries of the coefficient matrix and right hand side vector) in a more natural and direct way. Therefore, fuzzy linear equation systems seem to be more realistic and reliable than the crisp case. This study has attempted to provide a short review of notable papers on fuzzy linear equation systems with a basic structural classification. Considering the vast literature, we only aim to present the most cited and leading papers for each classification. Our short review will give a general framework about the progression of the subject and its solution approaches.