%0 Journal Article
%T LP problems constrained with D-FRIs
%J Journal of Algorithms and Computation
%I University of Tehran
%Z 2476-2776
%A Ghodousian, A.
%A Jafarpour, M.
%D 2018
%\ 12/30/2018
%V 50
%N issue 2
%P 59-79
%! LP problems constrained with D-FRIs
%K Fuzzy relation
%K fuzzy relational inequality
%K linear optimization
%K fuzzy compositions and t-norms
%R 10.22059/jac.2018.69778
%X In this paper, optimization of a linear objective function with fuzzy relational inequality constraints is investigated where the feasible region is formed as the intersection of two inequality fuzzy systems and Dombi family of t-norms is considered as fuzzy composition. Dombi family of t-norms includes a parametric family of continuous strict t-norms, whose members are increasing functions of the parameter. This family of t-norms covers the whole spectrum of t-norms when the parameter is changed from zero to infinity. The resolution of the feasible region of the problem is firstly investigated when it is defined with max-Dombi composition. Based on some theoretical results, a necessary and sufficient condition and three other necessary conditions are derived for determining the feasibility. Moreover, in order to simplify the problem, some procedures are presented. It is shown that a lower bound is always attainable for the optimal objective value. Also, it is proved that the optimal solution of the problem is always resulted from the unique maximum solution and a minimal solution of the feasible region. A method is proposed to generate random feasible max-Dombi fuzzy relational inequalities and an algorithm is presented to solve the problem. Finally, an example is described to illustrate these algorithms.
%U https://jac.ut.ac.ir/article_69778_67019cccd3ae9e759e6e2c4861660c90.pdf