• INTERACTIVE APPROACH FOR SOLVING A BI-LEVEL MULTI-OBJECTIVE QUADRATIC PROGRAMMING PROBLEM WITH NEUTROSOPHIC PARAMETERS IN THE OBJECTIVE FUNCTION

O. E. EMAM, A. ABDO, A. M. YOUSSEF*

Abstract


In this paper we investigate a hierarchical structure problem that consist from two stages, first stage decision maker and second stage decision maker. Each level has multiple objectives need to reach and achieve them under same constrains. All problems that people faced did not contain clear information most of these problems has vague information and uncertainty, so we introduce in this paper a solution algorithm for the bi-level problem with multiple objective function and with neutrosophic parameter in these objective functions. Our algorithm starts with converting the trapezoidal neutrosophic parameter to crisp then we will use first order taylor method to convert the quadratic form to linear form. After that we will use the weight method to make the problem single objective function at each level and in the final step, we will use the interactive approach to solve the bi-level linear programming problem.


Keywords


Bi-level programming; linear programming; Neutrosophic set; Trapezoidal neutrosophic number; Multi-objective; Quadratic programming; Interactive approach.

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