Epistemic uncertainty based linear programming problem and its solution

Epistemic uncertainty such as fuzzy based linear programming problem with equality constraints has been considered here. Fuzziness presents in system parameters are modelled using Trapezoidal Fuzzy Number (TrFN). In the considered problem the coefficients are defined as crisp while the decision vari...

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Bibliographic Details
Published in:International journal of machine learning and cybernetics Vol. 15; no. 6; pp. 2337 - 2346
Main Authors: Behera, Diptiranjan, Thomas, Romane
Format: Journal Article
Language:English
Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.06.2024
Springer Nature B.V
Subjects:
Artificial Intelligence
Complex Systems
Computational Intelligence
Control
Decision making
Engineering
Equality
Fuzzy sets
Fuzzy systems
Linear programming
Mechatronics
Methods
Optimization
Original Article
Pattern Recognition
Production planning
Robotics
Systems Biology
Uncertainty
Fuzzy radius
cut
Fuzzy feasible solution
Fuzzy objective function
Fuzzy linear programming problem
Fuzzy optimization
Trapezoidal fuzzy number
Fuzzy centre
ISSN:1868-8071, 1868-808X
Online Access:Get full text
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Summary:Epistemic uncertainty such as fuzzy based linear programming problem with equality constraints has been considered here. Fuzziness presents in system parameters are modelled using Trapezoidal Fuzzy Number (TrFN). In the considered problem the coefficients are defined as crisp while the decision variables as well as the right-hand side of the constraints are taken as fuzzy. Accordingly, a new method to solve the problem based on the fuzzy centre and radius has been proposed here. First the problem is solved for fuzzy centre and next the bounds of the fuzzy variable are replaced in terms of fuzzy centre and radius. Then using the obtained fuzzy centre solution there one can have the radius of the solution. Finally using the results for centre and radius one can get the final solution. For the implementation of this proposed methodology LINGO 18.0 software has been used. Consequently, optimal fuzzy feasible solution has been obtained to get the optimal value (maximum/minimum) of the fuzzy objective function. Moreover, various numerical examples have been solved using the proposed method and the obtained solutions are compared with the solution of existing methods for validation. Moreover, it has been observed that present methods overcome the limitations of Maleki (Maleki in Far East J Math Sci 4:283–301, 2002), Nasseri (Nasseri in Appl Math Sci 2:2473–2480, 2008), Mahdavi-Amiri and Nasseri (Mahdavi-Amiri and Nasseri in Fuzzy Sets Syst 158:1961–1978, 2007) and Saati et al. (Saati et al. in Int J Inf Decis Sci 7:312–333, 2015), and clearly the advantages of the proposed method are discussed in conclusion section.
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ISSN:1868-8071
1868-808X
DOI:10.1007/s13042-023-02033-y