Adaptive fuzzy dynamic programming (AFDP) technique for linear programming problems lps with fuzzy constraints

An adaptive fuzzy dynamic programming technique is proposed to solve linear programming problems having fuzzy constraints. Both the left hand sides and the right hand sides of the constraints are fuzzy. Dynamic programming technique ensures the existence of the solution for the Fuzzy Linear Programm...

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Bibliographic Details
Published in:Soft computing (Berlin, Germany) Vol. 27; no. 19; pp. 13931 - 13949
Main Authors: Khan, Izaz Ullah, Aftab, Muhammad
Format: Journal Article
Language:English
Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.10.2023
Springer Nature B.V
Subjects:
Artificial Intelligence
Computational Intelligence
Control
Dynamic programming
Engineering
Fuzzy sets
Linear programming
Mathematical Logic and Foundations
Mechatronics
Optimization
Robotics
Robustness (mathematics)
Simplex method
Variables
Dynamic programming
Fuzzy linear programming (FLP)
Fuzzy mathematical programming
Fuzzy sets and fuzzy modeling
ISSN:1432-7643, 1433-7479
Online Access:Get full text
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Summary:An adaptive fuzzy dynamic programming technique is proposed to solve linear programming problems having fuzzy constraints. Both the left hand sides and the right hand sides of the constraints are fuzzy. Dynamic programming technique ensures the existence of the solution for the Fuzzy Linear Programming FLP problems. Initially, a solution technique is proposed for linear programming problems with both left and right hand sides fuzzy. The dynamic programming technique for the LP’s is then revised to address linear programming problems in which the constraints are fuzzy. The proposed adaptive fuzzy dynamic approach is then implemented on a numerical example. The results obtained showed that the proposed method better optimized the fuzzy linear programming problem. It is shown that the objective function of our fuzzy linear programming improves from 19.5 to 38 by a value of 18.5. Thus a 94.8% improvement is recorded. Thus the proposed technique better optimize the FLP. The proposed approach incorporates fuzzy type uncertainty in modeling the LP problem. It is more practicable, robust and flexible.
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ISSN:1432-7643
1433-7479
DOI:10.1007/s00500-023-08462-9