A New Approach to Solve Fuzzy System of Linear Equations

Volume 7, Issue 3, pp 205-212 http://dx.doi.org/10.22436/jmcs.07.03.06

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Authors

S. Nayak - Department of Mathematics, National Institute of Technology, Rourkela, Odisha -769008, India. S. Chakraverty - Department of Mathematics, National Institute of Technology, Rourkela, Odisha -769008, India.

Abstract

System of linear equations is a common mathematical phenomenon which occurs in science and engineering problems. But fuzzy systems of linear equations are obtained when we deal with uncertain problems. Various methods are proposed by different authors to solve linear equations for both fuzzy and fully fuzzy systems. Here we have developed an alternative and straight forward arithmetic to handle uncertain interval and fuzzy values. In this arithmetic we write the interval into crisp form by some transformation and used the mathematical limit concept. Fuzzy values are converted into \(\alpha\)-cut form and then the monotonic functions are operated through the proposed method. Two algorithms have proposed to solve Fully Fuzzy Linear System (FFLS) of equations. Finally some example problems are considered for both fuzzy and fully fuzzy system of linear equations and the obtained results are compared, which are found to be in good argument.

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Keywords

• Uncertainty
• Triangular Fuzzy Number (TFN)
• Trapezoidal Fuzzy Number (TRFN)
• Fuzzy linear system of equations

MSC

•  15A06
•  03E72

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