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International Journal of Fuzzy Mathematical Archive
Year : 2023, Volume : 21, Issue : 2
First page : ( 43) Last page : ( 56)
Print ISSN : 2320-3242. Online ISSN : 2320-3250.
Article DOI : 10.22457/ijfma.v21n2a42394

Solving linear programming problems with neutrosophic coefficients

Mondal Suman*

Department of Applied Mathematics, Vidyasagar University, Midnapore-721102, India

*Email: sumanmondal2502002@gmail.com

Online published on 22 November, 2024.

Abstract

In real-world scenarios, both determinate and indeterminate information are present, making it essential to address indeterminate problems in optimization tasks. Neutrosophic numbers (NNs) are particularly effective in representing this mix of information. An NN, expressed as (x+yI), includes a determinate component x and an indeterminate component bI, where x,y∈ℝ, and I symbolizes indeterminacy, with ℝ representing the set of all real numbers. This paper introduces the basic operations of NNs and a corresponding NF, which involves NNs and is termed simply as a NF. While few methods exist for solving neutrosophic linear programming problems (NLPPs), most focus on the three components truth, falsity, and neutrality within the coefficients. Here, we propose a novel approach for solving NLPPs where the coefficients in both the objective function and the constraints are modeled as NNs. To demonstrate the efficacy of our method, we present a numerical example along with an application in production planning, showcasing how NLPPs can be solved and applied in practice. Additionally, we explore the potential ranges for the optimal solution when the indeterminacy I is defined as a possible interval that corresponds to real-world application requirements. This approach provides a more comprehensive framework for addressing uncertainty in optimization problems, particularly in contexts where indeterminate information cannot be ignored.

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Keywords

Fuzzy number, Neutrosophic number, Fuzzy linear programming problem, Neutrosophic linear programming problem.

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