Fully Fuzzy Linear Systems

Authors

  • . Fallah Jelodar,
  • F. Hoseinzadeh Lotfi,
  • N. Mikaeilvand,
  • T. Allahviranloo,
Abstract:

As can be seen from the definition of extended operations on fuzzy numbers, subtraction and division of fuzzy numbers are not the inverse operations to addition and multiplication . Hence, to solve the fuzzy equations or a fuzzy system of linear equations analytically, we must use methods without using inverse operators. In this paper, a novel method to find the solutions in which 0 is not the inner point of supports, of fully fuzzy linear systems (shown as FFLS ) is proposed, if they exist by an analytic approach. The system's parameters were splitted into two groups of nonpositive and nonnegative by solving a multi objective linear programming problem, MOLP , and employing an embedding method to transform n× n FFLS to 2n× 2n parametric form linear system and hence, transforming operations on fuzzy numbers to operations on functions. And finally, numerical examples are used to illustrate this approach. Keywords: Fuzzy Numbers, Fully Fuzzy Linear System, Systems of Fuzzy Linear Equations, Embedding Method, Splitting Method.

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Journal title

volume 1  issue None

pages  35- 49

publication date 2011-10

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