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Mathematics
Volume 13
Issue 15
10.3390/math13152534
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This is an early access version, the complete PDF, HTML, and XML versions will be available soon.
Article

Using Pseudo-Complemented Truth Values of Calculation Errors in Integral Transforms and Differential Equations Through Monte Carlo Algorithms

by
Ravi A. Salim
1,*,
Ernastuti
1,
Edi Sukirman
1,
Trini Saptariani
1 and
Suryadi MT
2,*
1
Department of Information System, Faculty of Computer Science, Universitas Gunadarma, Depok 16424, Indonesia
2
Department of Mathematics, Universitas Indonesia, Depok 16424, Indonesia
*
Authors to whom correspondence should be addressed.
Mathematics 2025, 13(15), 2534; https://doi.org/10.3390/math13152534 (registering DOI)
Submission received: 9 July 2025 / Revised: 29 July 2025 / Accepted: 4 August 2025 / Published: 6 August 2025
Versions Notes

Abstract

This study aims to demonstrate how mathematics, especially calculus concepts, can be expanded to include semi-entities and how these can be applied to sampling activities. Here, the multivalued logic uses pseudo-complemented lattices, instead of Boolean algebras. Truth values can express the intensity of a property: for example, the property of being heavy intensifies as weight increases. They can also express the state-of-the-art knowledge of an individual about a certain thing. To express that a number 𝑥 approaches 𝑎 is to say that the statement “𝑥 = 𝑏” is not fully true but approaches the full-true value as 𝑏 − 𝑎 approaches zero. This approach generalizes the concept of a limit and the concepts derived from it, such as differentiation and integration. A Monte Carlo algorithm replaces one function with another with finite domain, preferably its finite part, by sampling the domain and calculating its map. The discussion extends to integration over an unbounded interval, integral transforms, and differential equations. This study then covers strategies for producing Monte Carlo estimates of respective problems and determining their crucial truth values. In the discussion, a topic related to axiomatizing set theory is also suggested.

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MDPI and ACS Style

Salim, R.A.; Ernastuti; Sukirman, E.; Saptariani, T.; MT, S. Using Pseudo-Complemented Truth Values of Calculation Errors in Integral Transforms and Differential Equations Through Monte Carlo Algorithms. Mathematics 2025, 13, 2534. https://doi.org/10.3390/math13152534

AMA Style

Salim RA, Ernastuti, Sukirman E, Saptariani T, MT S. Using Pseudo-Complemented Truth Values of Calculation Errors in Integral Transforms and Differential Equations Through Monte Carlo Algorithms. Mathematics. 2025; 13(15):2534. https://doi.org/10.3390/math13152534

Chicago/Turabian Style

Salim, Ravi A., Ernastuti, Edi Sukirman, Trini Saptariani, and Suryadi MT. 2025. "Using Pseudo-Complemented Truth Values of Calculation Errors in Integral Transforms and Differential Equations Through Monte Carlo Algorithms" Mathematics 13, no. 15: 2534. https://doi.org/10.3390/math13152534

APA Style

Salim, R. A., Ernastuti, Sukirman, E., Saptariani, T., & MT, S. (2025). Using Pseudo-Complemented Truth Values of Calculation Errors in Integral Transforms and Differential Equations Through Monte Carlo Algorithms. Mathematics, 13(15), 2534. https://doi.org/10.3390/math13152534

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