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Approximate Symmetric Solution of Dual Fuzzy Systems Regarding Two Different Fuzzy Multiplications


Affiliations
1 Department of Mathematics, Roudehen Branch, Islamic Azad University, Roudehen, Iran, Islamic Republic of
2 Department of Mathematics, Karaj Branch, Islamic Azad University, Karaj, Iran, Islamic Republic of
3 Department of Mathematics, Karaj Branch, Islamic Azad University, Karaj
 

We consider two types of dual fuzzy systems with respect to two different fuzzy multiplications and propose an approach for computing an approximate nonnegative symmetric solution of some dual fuzzy linear system of equations. We convert the m × n dual fuzzy linear system to two m × n real linear systems by considering equality of the median intervals of the left and right sides of the dual fuzzy system. Then, the real systems are solved, when the solutions does not satisfy nonnegative fuzziness conditions, an appropriate constrained least squares problem is solved. We finally present some computational algorithms and illustrate their effectiveness by solving some randomly generated consistent as well as inconsistent systems.

Keywords

LR Fuzzy Numbers, Triangular Fuzzy Numbers, Dual Fuzzy Systems, Median Interval Defuzzification
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  • Approximate Symmetric Solution of Dual Fuzzy Systems Regarding Two Different Fuzzy Multiplications

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Authors

Z. Valizadeh
Department of Mathematics, Roudehen Branch, Islamic Azad University, Roudehen, Iran, Islamic Republic of
R. Ezzati
Department of Mathematics, Karaj Branch, Islamic Azad University, Karaj, Iran, Islamic Republic of
S. Khezerloo
Department of Mathematics, Karaj Branch, Islamic Azad University, Karaj

Abstract


We consider two types of dual fuzzy systems with respect to two different fuzzy multiplications and propose an approach for computing an approximate nonnegative symmetric solution of some dual fuzzy linear system of equations. We convert the m × n dual fuzzy linear system to two m × n real linear systems by considering equality of the median intervals of the left and right sides of the dual fuzzy system. Then, the real systems are solved, when the solutions does not satisfy nonnegative fuzziness conditions, an appropriate constrained least squares problem is solved. We finally present some computational algorithms and illustrate their effectiveness by solving some randomly generated consistent as well as inconsistent systems.

Keywords


LR Fuzzy Numbers, Triangular Fuzzy Numbers, Dual Fuzzy Systems, Median Interval Defuzzification

References





DOI: https://doi.org/10.17485/ijst%2F2012%2Fv5i2%2F30349