Parametric Optimization for Fully Fuzzy Linear Programming Problems with Triangular Fuzzy Numbers

This paper presents a new approach for solving FFLP problems using a double parametric form (DPF), which is critical in decision-making scenarios characterized by uncertainty and imprecision. Traditional linear programming methods often fall short in handling the inherent vagueness in real-world pro...

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Published in:Mathematics (Basel) Vol. 12; no. 19; p. 3051
Main Authors: Bhowmick, Aliviya, Chakraverty, Snehashish, Chatterjee, Subhashish
Format: Journal Article
Language:English
Published: Basel MDPI AG 01.10.2024
Subjects:
Decision making
double parametric form
fully fuzzy linear programming
Fuzzy algorithms
Fuzzy logic
Fuzzy sets
Fuzzy systems
Inequality
Linear equations
Linear programming
Mathematical optimization
mathematical programming
Mathematical research
Methods
Numbers
Optimization
Parameter uncertainty
single parametric form
triangular fuzzy number
India
ISSN:2227-7390, 2227-7390
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Abstract This paper presents a new approach for solving FFLP problems using a double parametric form (DPF), which is critical in decision-making scenarios characterized by uncertainty and imprecision. Traditional linear programming methods often fall short in handling the inherent vagueness in real-world problems. To address this gap, an innovative method has been proposed which incorporates fuzzy logic to model the uncertain parameters as TFNs, allowing for a more realistic and flexible representation of the problem space. The proposed method stands out due to its integration of fuzzy arithmetic into the optimization process, enabling the handling of fuzzy constraints and objectives directly. Unlike conventional techniques that rely on crisp approximations or the defuzzification process, the proposed approach maintains the fuzziness throughout the computation, ensuring that the solutions retain their fuzzy characteristics and better reflect the uncertainties present in the input data. In summary, the proposed method has the ability to directly incorporate fuzzy parameters into the optimization framework, providing a more comprehensive solution to FFLP problems. The main findings of this study underscore the method’s effectiveness and its potential for broader application in various fields where decision-making under uncertainty is crucial.
AbstractList This paper presents a new approach for solving FFLP problems using a double parametric form (DPF), which is critical in decision-making scenarios characterized by uncertainty and imprecision. Traditional linear programming methods often fall short in handling the inherent vagueness in real-world problems. To address this gap, an innovative method has been proposed which incorporates fuzzy logic to model the uncertain parameters as TFNs, allowing for a more realistic and flexible representation of the problem space. The proposed method stands out due to its integration of fuzzy arithmetic into the optimization process, enabling the handling of fuzzy constraints and objectives directly. Unlike conventional techniques that rely on crisp approximations or the defuzzification process, the proposed approach maintains the fuzziness throughout the computation, ensuring that the solutions retain their fuzzy characteristics and better reflect the uncertainties present in the input data. In summary, the proposed method has the ability to directly incorporate fuzzy parameters into the optimization framework, providing a more comprehensive solution to FFLP problems. The main findings of this study underscore the method’s effectiveness and its potential for broader application in various fields where decision-making under uncertainty is crucial.
Audience Academic
Author Chatterjee, Subhashish
Bhowmick, Aliviya
Chakraverty, Snehashish
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Snippet This paper presents a new approach for solving FFLP problems using a double parametric form (DPF), which is critical in decision-making scenarios characterized...
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StartPage 3051
SubjectTerms Decision making
double parametric form
fully fuzzy linear programming
Fuzzy algorithms
Fuzzy logic
Fuzzy sets
Fuzzy systems
Inequality
Linear equations
Linear programming
Mathematical optimization
mathematical programming
Mathematical research
Methods
Numbers
Optimization
Parameter uncertainty
single parametric form
triangular fuzzy number
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Title Parametric Optimization for Fully Fuzzy Linear Programming Problems with Triangular Fuzzy Numbers
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https://doaj.org/article/a17d1916236049bab44c3bdec662bd4d
Volume 12
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