Fuzzy Linear Programming and Optimization Strategies
Summary
Fuzzy linear programming (FLP) extends classical linear programming by admitting imprecision and vagueness in coefficients, constraints and decision variables through fuzzy set theory. This approach enables decision-makers to model real-world uncertainty that arises from incomplete information, subjective judgment and fluctuating environments. A range of optimisation strategies has been developed for FLP, including ranking functions to convert fuzzy parameters into comparable crisp values, α-cut decomposition to handle fuzzy intervals at different confidence levels and multi-objective formulations to balance conflicting goals. Lexicographic and ε-constraint methods offer systematic routes to Pareto-optimal solutions under fuzziness, while more recent treatments employ advanced uncertainty frameworks such as intuitionistic and neutrosophic fuzzy sets, which capture degrees of membership, non-membership and indeterminacy. Algorithmic developments have focused on computational efficiency, convergence properties and the capacity to generate multiple solutions. Practical applications span supply-chain planning, production scheduling, investment portfolios and agricultural resource allocation, demonstrating that fuzzy-based optimisation strategies provide robust decision support where classical models may fail to address the nuances of real-world variability.
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Fuzzy Linear Programming and Optimization Strategies publication trend
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Technical terms
Fuzzy Linear Programming: An extension of linear programming that incorporates fuzzy coefficients or variables to model uncertainty and vagueness in optimisation problems.
Intuitionistic Fuzzy Set: A fuzzy set characterised by a membership degree, a non-membership degree and a hesitation margin, allowing explicit modelling of indeterminacy.
Neutrosophic Fuzzy Set: A generalisation of fuzzy and intuitionistic sets that assigns independent degrees of truth, falsity and indeterminacy to each element.
Triangular Fuzzy Number: A simple fuzzy number described by a triplet (left, mode, right) that defines a triangular membership function for computational tractability.
ε-Constraint Method: A multi-objective optimisation technique that treats one objective as primary and converts other objectives into constraints bounded by specified ε-levels to generate Pareto-optimal solutions.
References
- An ε‐Constraint Method for Multiobjective Linear Programming in Intuitionistic Fuzzy Environment. International Journal of Intelligent Systems (2023).
- Multi-objective optimization model for uncertain crop production under neutrosophic fuzzy environment: A case study. AIMS Mathematics (2023).
- A Novel Approach to Solve Fully Fuzzy Linear Programming Problems with Modified Triangular Fuzzy Numbers. Mathematics (2021).
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