SOLVING FUZZY LINEAR PROGRAMMING PROBLEMS USING RANKING FUNCTIONS
Abstract
Fuzzy Linear Programming Problems (FLPP) extend classical linear programming by
incorporating uncertainty and imprecision in model parameters. In many real‑world
optimization problems, coefficients such as cost, profit, resource availability, and
technological parameters cannot be expressed as exact values. Instead, they are often vague
or uncertain. Fuzzy set theory provides an effective mathematical framework to represent
such uncertainty using fuzzy numbers.
One of the most widely used techniques for solving fuzzy linear programming problems is
the ranking function method. Ranking functions convert fuzzy numbers into crisp values
so that fuzzy optimization models can be transformed into classical linear programming
models. These models can then be solved using conventional optimization techniques such
as the simplex method.
This research paper presents the theoretical foundations of fuzzy linear programming and
explains the role of ranking functions in solving these problems. A mathematical modeling
framework is presented, followed by two numerical examples that illustrate the solution
process. The paper also reviews existing ranking methods and summarizes twenty relevant
research contributions in this field.
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