
Linear Fractional Multi-Objective Optimization Problems Subject to Fuzzy Relational Equations with the Max-Average Composition
Z. Valizadeh-Gh, Department of Mathematics, Roudehen Branch, Islamic Azad University, Roudehen, Iran
E. Khorram, Faculty of Mathematics and Computer Science, Amirkabir University of Technology, Tehran, Iran
E. Khorram, Faculty of Mathematics and Computer Science, Amirkabir University of Technology, Tehran, Iran
Received: Dec. 21, 2014;
Accepted: Jan. 19, 2015;
Published: Feb. 8, 2015
DOI: 10.11648/j.acm.s.2015040102.15 View 3577 Downloads 258
Abstract
In this paper, linear fractional multi-objective optimization problems subject to a system of fuzzy relational equations (FRE) using the max-average composition are considered. First, some theorems and results are presented to thoroughly identify and reduce the feasible set of the fuzzy relation equations. Next, the linear fractional multi-objective optimization problem is converted to a linear one using Nykowski and Zolkiewski's approach. Then, the efficient solutions are obtained by applying the improved ε-constraint method. Finally, the proposed method is effectively tested by solving a consistent test problem.
Keywords
Fuzzy Relational Equation, The Max-Average Composition, Linear Fractional Multi-Objective Optimization Problems, The Improved ε-Constraint Method
To cite this article
Z. Valizadeh-Gh,
E. Khorram,
Linear Fractional Multi-Objective Optimization Problems Subject to Fuzzy Relational Equations with the Max-Average Composition, Applied and Computational Mathematics. Special Issue: New Advances in Fuzzy Mathematics: Theory, Algorithms, and Applications.
Vol. 4, No. 1-2,
2015, pp. 20-30.
doi: 10.11648/j.acm.s.2015040102.15
Reference
[1]
Abbasi Molai, A., A new algorithm for resolution of the quadratic programming problem with fuzzy relation inequality constraints, Computers & Industrial Engineering, 72, 306-314 (2014)
[2]
Abbasi Molai, A., Resolution of a system of the max-product fuzzy relation equations using L○U-factorization, Information Sciences, 234, 86--96 (2013)
[3]
Abbasi Molai, A., The quadratic programming problem with fuzzy relation inequality constraints, Computers & Industrial Engineering, 62(1), 256--263 (2012)
[4]
Brouwer, R.K., A method of relational fuzzy clustering based on producing feature vectors using Fast Map, Information Sciences, 179(20), 3561-3582 (2009)
[5]
Di Martino, F., & Sessa, S., Digital watermarking in coding/decoding processes with fuzzy relation equations, Soft Computing, 10, 238--243 (2006)
[6]
Ehrgott, M., Multicriteria Optimization, Springer, Berlin (2005)
[7]
Ehrgott, M., & Ruzika, S., Improved ε-Constraint Method for Multiobjective Programming, Journal of Optimization Theory and Applications, 138, 375--396 (2008)
[8]
Friedrich, T., Kroeger, T., & Neumann, F., Weighted preferences in evolutionary multi-objective optimization, International Journal of Machine Learning and Cybernetics, 4(2), 139--148 (2013)
[9]
Ghodousian, A., & Khorram, E., Linear optimization with an arbitrary fuzzy relational inequality, Fuzzy Sets and Systems, 206, 89--102 (2012)
[10]
Guo, F.F., Pang, L.P., Meng, D., & Xia, Z.Q., An algorithm for solving optimization problems with fuzzy relational inequality constraints, Information Sciences, 252, 20-31 (2013)
[11]
Guu, S.M., Wu, Y.K., & Lee, E.S., Multi-objective optimization with a max-t-norm fuzzy relational equation constraint, Computers and Mathematics with Applications, 61, 1559--1566 (2011)
[12]
Khorram, E., & Ghodousian, A., Linear objective function optimization with fuzzy relation equation constraints regarding max-average composition, Applied Mathematics and Computation, 173, 872--886 (2006)
[13]
Khorram, E., & Hassanzadeh, R., Solving nonlinear optimization problems subjected to fuzzy relation equation constraints with max-average composition using a modified genetic algorithm, Computers & Industrial Engineering, 55, 1--14 (2008)
[14]
Khorram, E., & Zarei, H., Multi-objective optimization problems with fuzzy relation equation constraints regarding max-average composition, Mathematical and Computer Modelling, 49, 856--867 (2009)
[15]
Klir, G.J., & Folger, T.A., Fuzzy Sets, Uncertainty and information, Prentice-Hall, NJ (1988)
[16]
Loetamonphong, J., Fang, S.C., & Young, R.E., Multi-objective optimization problems with fuzzy relation equation constraints, Fuzzy Sets and Systems, 127, 141--164 (2002)
[17]
Li, P., & Fang, S.C., Minimizing a linear fractional function subject to a system of sup-T equations with a continuous Archimedean triangular norm, Journal of Systems Science and Complexity, 22, 49--62 (2009)
[18]
Li, D.-C., & Geng, S.-L., Optimal solution of multi-objective linear programming with inf-→ fuzzy relation equations constraint, Information Sciences, 271, 159-178 (2014)
[19]
Nykowski, I., & Zolkiewski, Z., A compromise procedure for the multiple objective linear fractional programming problem, European Journal of Operational research, 19(1), 91--97 (1985)
[20]
Peeva, K., Resolution of fuzzy relational equations -- Method, algorithm and software with applications, Information Sciences, 234, 44--63 (2013)
[21]
Sanchez, E., Resolution of composite fuzzy relation equations, Information and Control, 30, 38--48 (1976)
[22]
Sandri, S., & Martins-Bedê, F.T., A method for deriving order compatible fuzzy relations from convex fuzzy partitions, Fuzzy Sets and Systems, 239, 91-103 (2014)
[23]
Wang, H.F., A multi-objective mathematical programming problem with fuzzy relation constraints, Journal of Multi-Criteria Decision Analysis, 4, 23--35 (1995)
[24]
Wang, X., Cao, X., Wu, C., & Chen, J., Indicators of fuzzy relations, Fuzzy Sets and Systems, 216, 91-107 (2013)
[25]
Wang, X., & Xue, Y., Traces and property indicators of fuzzy relations, Fuzzy Sets and Systems, 246, 78-90 (2014)
[26]
Zhou, X.G., & Ahat, R., Geometric programming problem with single-term exponents subject to max-product fuzzy relational equations, Mathematical and Computer Modelling, 53(1--2), 55--62 (2011)