LP problems constrained with D-FRIs

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Article Type:
Research/Original Article (دارای رتبه معتبر)
Abstract:
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.
Language:
English
Published:
Journal of Algorithms and Computation, Volume:50 Issue: 2, Dec 2018
Pages:
59 to 79
https://www.magiran.com/p2116061  
سامانه نویسندگان
  • Maryam Jafarpour
    Author (2)
    Phd Student Department of Algorithms and Computation, University of Tehran, Tehran, Iran
    Jafarpour، Maryam
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