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## A quadratic optimization problem with bipolar fuzzy relation equation constraints | ||

Iranian Journal of Fuzzy Systems | ||

دوره 19، شماره 6، بهمن و اسفند 2022، صفحه 125-140 اصل مقاله (246.8 K) | ||

نوع مقاله: Research Paper | ||

شناسه دیجیتال (DOI): 10.22111/ijfs.2022.7216 | ||

نویسنده | ||

A. Abbasi Molai^{*}
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^{}School of Mathematics and Computer Sciences,Damghan University, P.O.Box 36715-364, Damghan, Iran | ||

چکیده | ||

This paper studies the quadratic programming problem subject to a system of bipolar fuzzy relation equations with the max-product composition. A characterization of structure of its feasible domain is presented using the lower and upper bound vector on its solution set. A sufficient condition is proposed which under the condition, a component of one of its optimal solutions is the corresponding component of either the lower or upper bound vector. Some sufficient conditions are suggested to reveal one of its optimal solutions without resolution of the problem. Furthermore, some sufficient conditions are then given to determine some components from one of its optimal solutions. Based on these conditions, we can simplify the problem and reduce its dimensions. The simplified problem can be reformulated to an 0-1 mixed integer programming problem. Other unknown variables can be found by solving the current problem. | ||

کلیدواژهها | ||

Bipolar fuzzy relation equation؛ Quadratic programming؛ max-product composition؛ mixed integer programming problem | ||

مراجع | ||

[1] A. Abbasi Molai, The quadratic programming problem with fuzzy relation inequality constraints, Computers and Industrial Engineering, 62 (2012), 256-263.
[2] A. Abbasi Molai, A new algorithm for resolution of the quadratic programming problem with fuzzy relation inequality constraints, Computers and Industrial Engineering, 72 (2014), 306-314.
[3] S. Aliannezhadi, A. Abbasi Molai, Linear fractional programming problem with max-Hamacher FRI, Iranian Journal of Science and Technology, Transactions A: Science, 42 (2018), 693-705.
[4] S. Aliannezhadi, A. Abbasi Molai, Geometric programming with a single-term exponent subject to bipolar maxproduct fuzzy relation equation constraints, Fuzzy Sets and Systems, 397 (2020), 61-83.
[5] S. Aliannezhadi, A. Abbasi Molai, A new algorithm for geometric optimization with a single-term exponent constrained by bipolar fuzzy relation equations, Iranian Journal of Fuzzy Systems, 18 (2021), 137-150.
[6] S. Aliannezhadi, A. Abbasi Molai, B. Hedayatfar, Linear optimization with bipolar max-parametric hamacher fuzzy relation equation Constraints, Kybernetika, 52(4) (2016), 531-557.
[7] S. Aliannezhadi, S. Shahab Ardalan, A. Abbasi Molai, Maximizing a monomial geometric objective function subject to bipolar max-product fuzzy relation constraints, Journal of Intelligent and Fuzzy Systems, 32 (2017), 337-350.
[8] A. Auslender, P. Coutat, Sensitivity analysis for generalized linear-quadratic problems, Journal of Optimization Theory and Applications, 88(3) (1996), 541-559.
[9] J. C. G. Boot, On sensitivity analysis in convex quadratic programming problems, Operations Research, 11(5) (1963), 771-786.
[10] L. Chen, P. P. Wang, Fuzzy relation equations (I): The general and specialized solving algorithms, Soft Computing, 6 (2002), 428-435.
[11] S. C. Fang, G. Li, Solving fuzzy relation equations with a linear objective function, Fuzzy Sets and Systems, 103 (1999), 107-113.
[12] S. Freson, B. De Baets, H. De Meyer, Linear optimization with bipolar max-min constraints, Information Sciences, 234 (2013), 3-15.
[13] A. Ghaffari Hadigheh, K. Mirnia, T. Terlaky, Sensitivity analysis in linear and convex quadratic optimization: Invariant active constraint set and invariant set intervals, INFOR: Information Systems and Operational Research, 44(2) (2006), 129-155.
[14] A. Ghaffari Hadigheh, O. Romanko, T. Terlaky, Sensitivity analysis in convex quadratic optimization: Simultaneous perturbation of the objective and right-hand-side vectors, Algorithmic Operations Research, 2 (2007), 94-111.
[15] A. Ghaffari Hadigheh, T. Terlaky, Sensitivity analysis in convex quadratic optimization: Invariant support set interval, Optimization, 54 (2005), 59-79.
[16] S. M. Guu, Y. K. Wu, Minimizing a linear objective function with fuzzy relation equation constraints, Fuzzy Optimization and Decision Making, 1(4) (2002), 347-360.
[17] R. Hassanzadeh, E. Khorram, I. Mahdavi, N. Mahdavi-Amiri, A genetic algorithm for optimization problems with fuzzy relation constraints using max-product composition, Applied Soft Computing, 11 (2011), 551-560.
[18] B. Kheirfam, J. L. Verdegay, Strict sensitivity analysis in fuzzy quadratic programming, Fuzzy Sets and Systems, 198 (2012), 99-111.
[19] E. Khorram, R. Hassanzadeh, Solving nonlinear optimization problems subjected to fuzzy relation equation constraints with max-average composition using a modified genetic algorithm, Computers and Industrial Engineering, 55 (2008), 1-14.
[20] P. Li, S. C. Fang, 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 (2009), 49-62.
[21] P. Li, Q. Jin, Fuzzy relational equations with min-biimplication composition, Fuzzy Optimization and Decision Making, 11 (2012), 227-240.
[22] P. Li, Y. Liu, Linear optimization with bipolar fuzzy relational equation constraints using the Lukasiewicz triangular norm, Soft Computing, 18 (2014), 1399-1404.
[23] S. Lim, A study on sensitivity analysis for convex quadratic programs, Asia-Pacific Journal of Operational Research, 23(4) (2006), 439-452.
[24] C. C. Liu, Y. Y. Lur, Y. K. Wu, Linear optimization of bipolar fuzzy relational equations with max- Lukasiewicz composition, Information Sciences, 360 (2016), 149-162.
[25] J. Lu, S. C. Fang, Solving nonlinear optimization problems with fuzzy relation equations constraints, Fuzzy Sets and Systems, 119 (2001), 1-20.
[26] P. Patrinos, H. Sarimveis, Convex parametric piecewise quadratic optimization: Theory and algorithms, Automatica, 47 (2011), 1770-1777.
[27] K. Peeva, Y. Kyosev, Fuzzy relational calculus: Theory, applications and software, World Scientific, New Jersey, 2004.
[28] J. Qiu, G. Li, X. P. Yang, Arbitrary-term-absent max-product fuzzy relation inequalities and its lexicographic minimal solution, Information Sciences, 567 (2021), 167-184.
[29] E. Sanchez, Resolution of composite fuzzy relation equations, Information and Control, 30 (1976), 38-48.
[30] J. Skorin-Kapov, Quadratic programming: Quantitative analysis and polynomial runing time algorithms, Ph.D. Thesis, The university of British columbia, 1987.
[31] Y. K. Wu, Optimizing the geometric programming problem with single-term exponents subject to max-min fuzzy relational equation constraints, Mathematical and Computer Modelling, 47 (2008), 352-362.
[32] Y. K. Wu, S. M. Guu A note on fuzzy relation programming problems with max-strict-t-norm composition, Fuzzy Optimization and Decision Making, 3(3) (2004), 271-278.
[33] Y. K. Wu, S. M. Guu, Minimizing a linear function under a fuzzy max-min relational equation constraint, Fuzzy Sets and Systems, 150 (2005), 147-162.
[34] Y. K. Wu, S. M. Guu, J. Y. C. Liu, An accelerated approach for solving fuzzy relation equations with a linear objective function, IEEE Transactions on Fuzzy Systems, 10(4) (2002), 552-558.
[35] Y. K. Wu, S. M. Guu, J. Y. C. Liu, Reducing the search space of a linear fractional programming problem under fuzzy relational equations with max-Archimedean t-norm composition, Fuzzy Sets and Systems, 159 (2008), 3347-3359.
[36] X. P. Yang, Linear programming method for solving semi-latticized fuzzy relation geometric programming with max-min composition, International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems, 23(5) (2015), 781-804.
[37] X. P. Yang, Resolution of bipolar fuzzy relation equations with max- Lukasiewicz composition, Fuzzy Sets and Systems, 397 (2020), 41-60.
[38] X. P. Yang, Random-term-absent addition-min fuzzy relation inequalities and their lexicographic minimum solutions, Fuzzy Sets and Systems, 440 (2022), 42-61.
[39] J. Yang, B. Cao, Monomial geometric programming with fuzzy relation equation constraints, Fuzzy Optimization and Decision Making, 6 (2007), 337-349.
[40] X. P. Yang, H. T. Lin, X. G. Zhou, B. Y. Cao, Addition-min fuzzy relation inequalities with application in BitTorrent-like Peer-to-Peer file sharing system, Fuzzy Sets and Systems, 343 (2018), 126-140.
[41] X. P. Yang, X. G. Zhou, B. Y. Cao, Single-variable term semi-latticized fuzzy relation geometric programming with max-product operator, Information Sciences, 325 (2015), 271-287.
[42] X. P. Yang, X. G. Zhou, B. Y. Cao, Latticized linear programming subject to max-product fuzzy relation inequalities with application in wireless communication, Information Sciences, 358-359 (2016), 44-55.
[43] X. G. Zhou, R. Ahat, Geometric programming problem with single-term exponents subject to max-product fuzzy relational equations, Mathematical and Computer Modelling, 53 (2011), 55-62.
[44] X. G. Zhou, B. Y. Cao, X. P. Yang, The set of optimal solutions of geometric programming problem with maxproduct fuzzy relational equations constraints, International Journal of Fuzzy Systems, 18 (2016), 436-447.
[45] X. G. Zhou, X. P. Yang, B. Y. Cao, Posynomial geometric programming problem subject to max–min fuzzy relation equations, Information Sciences, 328 (2016), 15-25.
[46] J. Zhou, Y. Yu, Y. Liu, Y. Zhang, Solving nonlinear optimization problems with bipolar fuzzy relational equation constraints, Journal of Inequalities and Applications, (2016), DOI:10.1186/s13660-016-1056-6.
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