A new approach to evaluate linear programming problem in pentagonal neutrosophic environment.

Area of Science:

• Operations Research
• Fuzzy Mathematics
• Decision Sciences

Background:

• Linear programming (LP) is a fundamental optimization technique.
• Neutrosophic theory extends fuzzy sets, offering a more robust framework for uncertainty.
• Existing methods do not address linear programming problems with pentagonal neutrosophic numbers.

Purpose of the Study:

• To introduce the first approach for solving pentagonal neutrosophic linear programming (PNLP) problems.
• To develop a method for handling objectives and constraints defined by pentagonal neutrosophic numbers (PNNs).
• To establish a framework for decision-making under uncertainty using PNNs in LP.

Main Methods:

• Defined arithmetic operation laws and mathematical computations for pentagonal neutrosophic numbers (PNNs).
• Developed a ranking function to convert PNLP problems into equivalent crisp linear programming (CrLP) problems.
• Utilized standard LP solvers to find solutions for the transformed crisp problems.

Main Results:

• Successfully converted PNLP problems into solvable crisp LP (CrLP) problems.
• Demonstrated the conversion process using defined PNN arithmetic and ranking functions.
• Validated the proposed method's adequacy through numerical examples.

Conclusions:

• The proposed pentagonal neutrosophic approach provides a viable method for solving PNLP problems.
• This novel technique extends the applicability of linear programming to complex uncertain environments.
• The method offers a practical way to address decision-making problems involving pentagonal neutrosophic uncertainty.