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Geometric Programming Problems with Triangular and Trapezoidal Twofold Uncertainty Distributions.

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Title: Geometric Programming Problems with Triangular and Trapezoidal Twofold Uncertainty Distributions.
Authors: Mondal, Tapas1 (AUTHOR) tm19@iitbbs.ac.in, Ojha, Akshay Kumar1 (AUTHOR), Pani, Sabyasachi1 (AUTHOR)
Source: Journal of Optimization Theory & Applications. Mar2024, Vol. 200 Issue 3, p978-1016. 39p.
Subjects: Geometric programming
Abstract: Geometric programming is a well-known optimization tool for dealing with a wide range of nonlinear optimization and engineering problems. In general, it is assumed that the parameters of a geometric programming problem are deterministic and accurate. However, in the real-world geometric programming problem, the parameters are frequently inaccurate and ambiguous. To tackle the ambiguity, this paper investigates the geometric programming problem in an uncertain environment, with the coefficients as triangular and trapezoidal twofold uncertain variables. In this paper, we introduce uncertain measures in a generalized version and focus on more complicated twofold uncertainties to propose triangular and trapezoidal twofold uncertain variables within the context of uncertainty theory. We develop three reduction methods to convert triangular and trapezoidal twofold uncertain variables into singlefold uncertain variables using optimistic, pessimistic, and expected value criteria. Reduction methods are used to convert the geometric programming problem with twofold uncertainty into the geometric programming problem with singlefold uncertainty. Furthermore, the chance-constrained uncertain-based framework is used to solve the reduced singlefold uncertain geometric programming problem. Finally, a numerical example is provided to demonstrate the effectiveness of the procedures. [ABSTRACT FROM AUTHOR]
Copyright of Journal of Optimization Theory & Applications is the property of Springer Nature and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
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  Data: <searchLink fieldCode="JN" term="%22Journal+of+Optimization+Theory+%26+Applications%22">Journal of Optimization Theory & Applications</searchLink>. Mar2024, Vol. 200 Issue 3, p978-1016. 39p.
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  Data: Geometric programming is a well-known optimization tool for dealing with a wide range of nonlinear optimization and engineering problems. In general, it is assumed that the parameters of a geometric programming problem are deterministic and accurate. However, in the real-world geometric programming problem, the parameters are frequently inaccurate and ambiguous. To tackle the ambiguity, this paper investigates the geometric programming problem in an uncertain environment, with the coefficients as triangular and trapezoidal twofold uncertain variables. In this paper, we introduce uncertain measures in a generalized version and focus on more complicated twofold uncertainties to propose triangular and trapezoidal twofold uncertain variables within the context of uncertainty theory. We develop three reduction methods to convert triangular and trapezoidal twofold uncertain variables into singlefold uncertain variables using optimistic, pessimistic, and expected value criteria. Reduction methods are used to convert the geometric programming problem with twofold uncertainty into the geometric programming problem with singlefold uncertainty. Furthermore, the chance-constrained uncertain-based framework is used to solve the reduced singlefold uncertain geometric programming problem. Finally, a numerical example is provided to demonstrate the effectiveness of the procedures. [ABSTRACT FROM AUTHOR]
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  Data: <i>Copyright of Journal of Optimization Theory & Applications is the property of Springer Nature and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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        Value: 10.1007/s10957-023-02347-5
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      – TitleFull: Geometric Programming Problems with Triangular and Trapezoidal Twofold Uncertainty Distributions.
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              Text: Mar2024
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