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Optimal solution of multi-objective linear programming with \(\inf\)-\(\to\) fuzzy relation equations constraint. (English) Zbl 1341.90150

Summary: This paper aims to solve the problem of multiple-objective linear optimization model subject to a system of \(\inf\)-\(\to\) composition fuzzy relation equations, where \(\to\) is \( R\)-, \( S\)- or \( QL\)-implications generated by continuous Archimedean \(t\)-norm (\(s\)-norm). Since the feasible domain of \(\inf\)-\(\to\) relation equations constraint is nonconvex, these traditional mathematical programming techniques may have difficulty in computing efficient solutions for this problem. Therefore, we firstly investigate the solution sets of a system of \(\inf\)-\(\to\) composition fuzzy relation equations in order to characterize the feasible domain of this problem. And then employing the smallest solution of constraint equation, we yield the optimal values of linear objective functions subject to a system of \(\inf\)-\(\to\) composition fuzzy relation equations. Secondly, the two-phase approach is applied to generate an efficient solution for the problem of multiple-objective linear optimization model subject to a system of \(\inf\)-\(\to\) composition fuzzy relation equations. Finally, a procedure is represented to compute the optimal solution of multiple-objective linear programming with \(\inf\)-\(\to\) composition fuzzy relation equations constraint. In addition, three numerical examples are provided to illustrate the proposed procedure.

MSC:

90C70 Fuzzy and other nonstochastic uncertainty mathematical programming
90C05 Linear programming
90C29 Multi-objective and goal programming
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