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A new method for solving an arbitrary fully fuzzy linear system

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Abstract

In this paper, We propose a simple and practical method (that works only for triangular fuzzy numbers) to solve an arbitrary fully fuzzy linear system (FFLS) in the form \(\widetilde{A}\otimes \widetilde{x}=\widetilde{b},\) where \(\widetilde{A}_{n \times n}\) is a fuzzy matrix, \(\widetilde{x}\) and \(\widetilde{b}\) are n × 1 fuzzy vectors. The idea of the presented method is constructed based on the extending 0-cut and 1-cut solution of original fully fuzzy linear systems (FFLS). We also define a fuzzy solution of FFLS and establish the necessary and sufficient conditions for the uniqueness of a fuzzy solution.

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Authors and Affiliations

  1. Department of Mathematics, Science and Research Branch, Islamic Azad university, Tehran, Iran

    S. Moloudzadeh & P. Darabi

  2. Department of Industrial engineering, Faculty of engineering, Izmir university, Gursel Aksel Blv. No. 14, 35350, Uckuyular, Izmir, Turkey

    T. Allahviranloo

Authors
  1. S. Moloudzadeh
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  2. T. Allahviranloo
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  3. P. Darabi
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Corresponding author

Correspondence to S. Moloudzadeh.

Additional information

Communicated by V. Loia.

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Moloudzadeh, S., Allahviranloo, T. & Darabi, P. A new method for solving an arbitrary fully fuzzy linear system. Soft Comput 17, 1725–1731 (2013). https://doi.org/10.1007/s00500-013-0986-x

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