University of Sistan and BaluchestanIranian Journal of Fuzzy Systems1735-065419620221201A quadratic optimization problem with bipolar fuzzy relation equation constraints125140721610.22111/ijfs.2022.7216ENA.Abbasi MolaiSchool of Mathematics and Computer Sciences,Damghan University, P.O.Box 36715-364, Damghan, IranJournal Article20221107This paper studies the quadratic programming problem subject to a<br />system of bipolar fuzzy relation equations with the max-product<br />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.https://ijfs.usb.ac.ir/article_7216_f729f77e33fb3186ce5979c7669851b7.pdf