Bi-level Linear Programming Problem with Neutrosophic Numbers

Authors

  • Surapati Pramanik Department of Mathematics, Nandalal Ghosh B.T. College, Panpur, P.O.-Narayanpur, District –North 24 Parganas, Pin code-743126, West Bengal, India
  • Partha Pratim Dey Department of Mathematics, Patipukur Pallisree Vidyapith, Patipukur, Kolkata-700048, West Bengal, India. E-mail:

Keywords:

Neutrosophic set, Neutrosophic number, bi-level linear programming, goal programming, preference bounds

Abstract

The paper presents a novel strategy for solving bi-level linear programming problem based on goal programming in
neutrosophic numbers environment. Bi-level linear programming problem comprises of two levels namely upper or first level
and lower or second level with one objective at each level. The objective function of each level decision maker and the system
constraints are considered as linear functions with neutrosophic numbers of the form [p + q I], where p, q are real numbers and
I represents indeterminacy. In the decision making situation, we convert neutrosophic numbers into interval numbers and the
original problem transforms into bi-level interval linear programming problem. Using interval programming technique, the target interval of the objective function of each level is identified and the goal achieving function is developed. Since, the objectives of upper and lower level decision makers are generally conflicting in nature, a possible relaxation on the decision variables under the control of each level is taken into account for avoiding decision deadlock. Then, three novel goal programming
models are presented in neutrosophic numbers environment. Finally, a numerical problem is solved to demonstrate the feasibility, applicability and novelty of the proposed strategy.

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Published

2018-09-04

Issue

Section

SI#1,2024: Neutrosophical Advancements And Their Impact on Research

How to Cite

Surapati Pramanik, & Partha Pratim Dey. (2018). Bi-level Linear Programming Problem with Neutrosophic Numbers . Neutrosophic Sets and Systems, 21, 110-121. https://fs.unm.edu/nss8/index.php/111/article/view/311

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