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New approach to solve fully fuzzy system of linear equations using single and double parametric form of fuzzy numbers

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Abstract

This paper proposes two new methods to solve fully fuzzy system of linear equations. The fuzzy system has been converted to a crisp system of linear equations by using single and double parametric form of fuzzy numbers to obtain the non-negative solution. Double parametric form of fuzzy numbers is defined and applied for the first time in this paper for the present analysis. Using single parametric form, the n × n fully fuzzy system of linear equations have been converted to a 2n × 2n crisp system of linear equations. On the other hand, double parametric form of fuzzy numbers converts the n × n fully fuzzy system of linear equations to a crisp system of same order. Triangular and trapezoidal convex normalized fuzzy sets are used for the present analysis. Known example problems are solved to illustrate the efficacy and reliability of the proposed methods.

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Acknowledgements

This work was financially supported by the Board of Research in Nuclear Sciences (Department of Atomic Energy), Government of India. We would also like to thank the anonymous referees and the editor for various valuable comments and suggestions to improve the quality of the paper.

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  1. Department of Mathematics, National Institute of Technology Rourkela, Odisha, 769 008, India

    DIPTIRANJAN BEHERA & S CHAKRAVERTY

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  1. DIPTIRANJAN BEHERA
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  2. S CHAKRAVERTY
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Correspondence to S CHAKRAVERTY.

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BEHERA, D., CHAKRAVERTY, S. New approach to solve fully fuzzy system of linear equations using single and double parametric form of fuzzy numbers. Sadhana 40, 35–49 (2015). https://doi.org/10.1007/s12046-014-0295-9

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  • DOI: https://doi.org/10.1007/s12046-014-0295-9

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