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

Ravi A. Salim (), Ernastuti, Edi Sukirman, Trini Saptariani and Suryadi Mt ()
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Ravi A. Salim: Department of Information System, Faculty of Computer Science, Universitas Gunadarma, Depok 16424, Indonesia
Ernastuti: Department of Information System, Faculty of Computer Science, Universitas Gunadarma, Depok 16424, Indonesia
Edi Sukirman: Department of Information System, Faculty of Computer Science, Universitas Gunadarma, Depok 16424, Indonesia
Trini Saptariani: Department of Information System, Faculty of Computer Science, Universitas Gunadarma, Depok 16424, Indonesia
Suryadi Mt: Department of Mathematics, Universitas Indonesia, Depok 16424, Indonesia

Mathematics, 2025, vol. 13, issue 15, 1-21

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.

Keywords: pseudo-complemented lattice; differential equation; integral transform; Monte Carlo method; multivalued logic (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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