A New Method for Solving Interval and Fuzzy Quadratic Equations of Dual Form

  • Kamal Mamehrashi Department of Mathematics, School of Science and Engineering, University of Kurdistan Hewler, Erbil, KRI, Iraq http://orcid.org/0000-0003-3663-2424
Keywords: Extended zero, Dual equation, Interval arithmetic.


In this paper, we present a numerical method for solving a quadratic interval equation in its dual form. The method is based on the generalized procedure of interval extension called” interval extended zero” method. It is shown that the solution of interval quadratic equation based on the proposed method may be naturally treated as a fuzzy number. An important advantage of the proposed method is that it substantially decreases the excess width defect. Several numerical examples are included to demonstrate the applicability and validity of the proposed method.


Download data is not yet available.

Author Biography

Kamal Mamehrashi, Department of Mathematics, School of Science and Engineering, University of Kurdistan Hewler, Erbil, KRI, Iraq

Kamal received his PhD in Applied Mathematics (Optimal Control & Optimization) in 2016, MSc in Applied Mathematics (Dynamical Systems) in 2003 and BSc in Pure Mathematics in 2000. He joined the Mathematics unit at UKH as a lecturer in February, 2017. Before joining UKH, he has taught as an Assistant Professor and Lecturer for 15 years from 2002 at different Universities in Iran. Kamal has worked as the head of mathematics and engineering department for more than 10 years. He is currently working on 2D optimal control problems and fractional optimal control problems by using the numerical methods and also has published several journal papers.


Abbasbandy, S. & Ezzati, R. (2006). Newton’s method for solving a system of fuzzy nonlinear equations. Appl. Math. Comput., 175(2), 1189-1199.
Abbasbandy, S. & Otadi, M. (2006). Numerical solution of fuzzy polynomials by fuzzy neural network, Appl. Math. Comput., 181(2), 1084-1089.
Alefeld, G. & Herzberger, J. (1983). Introduction to Interval Computations, Academic Press, New York.
Allahviranloo, T., Otadi, M. & Mosleh, M. (2007). Iterative method for fuzzy equations. Soft Comput., 12(10), 935-939.
Buckley, J.J. (1992). Solving fuzzy equations in economics and finance. Fuzzy Sets and Systems, 48(3),
Buckley, J.J. (1987). The fuzzy mathematics of finance. Fuzzy Sets and Systems, 21(3), 257-273.
Calzi, M. Li. (1990). Towards a general setting for the fuzzy mathematics of finance. Fuzzy Sets and
Systems, 35(3), 265-280.
Chalco-Cano, Y., Roma ́n-Flores, H., Rojas-Medar, M., Saavedra, O.R. and Jime ́nez-Gamero, M.D. (2007). The extension principle and a decomposition of fuzzy sets. Information Sciences, 177(23), 5394-5403.
Chen, S.H. & Yang, X.W. (2000). Interval finite element method for beam structures. Finite Elements
in Analysis and Design, 34(1), 75-88.
Dehghan, M., Hashemi, B. &. Ghatee, M. (2007). Solution of the fully fuzzy linear systems using iterative techniques. Chaos Solitons and Fractals, 34(2), 316-336.
Dubois, D. & Prade, H. (1978). Operations on fuzzy numbers. J. Systems Sci., 9(6), 613-626.
Ferreira, J.A., Patricio, F. & Oliveira, F. (2005). On the computation of solutions of systems of interval polynomial equations. Journal of Computational and Applied Mathematics, 173(2), 295-302.
Kaufmann, A. & Gupta, M.M. (1985). Introduction Fuzzy Arithmetic, Van Nostrand Reinhold, New York.
Lai, Y.J. & Hwang, C.L. (1992). Fuzzy Mathematical programming theory and applications. Springer, Berlin.
Mosleh, M. & Otadi, M. (2010). A New Approach to the Numerical Solution of Dual Fully Fuzzy Polynomial Equations. Int. J. Industrial Mathematics, 2(2), 129-142.
Mosleh, M., Otadi, M. & Vafaee Varmazabadi, Sh. (2008). General Dual Fuzzy Linear Systems, Int. J. Contemp. Math. Sciences, 3(28), 1385 - 1394.
Movahedian, M., Salahshour, S., Haji Ghasemi, S., Khezerloo, S., Khezerloo, M. & Khorasany, S.M. (2009). Duality in linear interval equations. Int. J. Industrial Mathematics, 1(1), 41-45.
Muzzioli, S. & Reynaerts, H. (2006). Fuzzy linear systems of the form A1x+b1 = A2x+b2. Fuzzy Sets and Systems, 157(7), 939-951.
Sevastjanov, P. & Dymova, L. (2009). A new method for solving interval and fuzzy equations: linear case. Information sciences, 179(7), 925-937.
Shieh, B.-S. (2008), Infinite fuzzy relation equations with continuous t-norms. Information Sciences, 178(8), 1961-1967.
Wu, C.C. & Chang, N.B. (2003). Grey input-output analysis and its application for environmental cost
allocation. European Journal of Operational Research, 145(1), 175-201.
Zadeh, L.A. (1965). Fuzzy sets. Information and Control, 8(3), 338-353.
Zadeh, L.A. (1975). The concept of a linguistic variable and its application to approximate reasoning. Information Sciences, 8(3), 199-249.
How to Cite
Mamehrashi, K. (2021, December 28). A New Method for Solving Interval and Fuzzy Quadratic Equations of Dual Form. UKH Journal of Science and Engineering, 5(2), 81-89. https://doi.org/https://doi.org/10.25079/ukhjse.v5n2y2021.pp81-89
Research Articles
Share |