A New Perspective on Neutrosophic Differential Equation

Sumathi, I. R.; Priya, V.Mohana

doi:10.14419/ijet.v7i4.10.21031

Cited by 10 publications

(10 citation statements)

References 3 publications

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“…In the recent time, researcher is also working on neutrosophic differential equation. Sumanthi et al [12] proposed a method to solve differential equation involving neutrosophic numbers with an application in the field of bacteria culture model. Thereafter, Sumanthi et al [13] discuss about the solution a neutrosophic differential equation where they have taken trapezoidal neutrosophic number as boundary conditions.…”

Section: Neutrosophic Differential Equationmentioning

confidence: 99%

“…Smarandache [5][6][7] gives the concept of neutrosophic set theory to explain more complex system than fuzzy where the falsity-membership value is not the complement of truth membership value and an indeterminacy in play about the assignment of values of truth membership and falsity-membership function. After the invention of neutrosophic set, a new branch came in the field of fuzzy mathematics, which needs further development of the different fields of neutrosophic mathematics like Neutrosophic Vector Space [8], Neutrosophic Topological Space [9], Neutrosophic Group Theory [10], Neutrosophic Ring Theory [11], and Neutrosophic Differential Equation [12,13], etc. In the recent time, many researchers are still working on the development of neutrosophic set theory and its various types of applications.…”

Section: Introductionmentioning

confidence: 99%

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Second-order neutrosophic boundary-value problem

Moi

Biswas²,

Pal

2021

Complex Intell. Syst.

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In this article, some properties of neutrosophic derivative and neutrosophic numbers have been presented. This properties have been used to develop the neutrosophic differential calculus. By considering different types of first- and second-order derivatives, different kind of systems of derivatives have been developed. This is the first time where a second-order neutrosophic boundary-value problem has been introduced with different types of first- and second-order derivatives. Some numerical examples have been examined to explain different systems of neutrosophic differential equation.

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Section: Neutrosophic Differential Equationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Second-order neutrosophic boundary-value problem

Moi

Biswas²,

Pal

2021

Complex Intell. Syst.

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“…As a result, neutrosophic set theory emerged as a new concept within the domain of fuzzy systems. Several researchers have worked on neutrosophic mathematics, such as neutrosophic topological space [6], neutrosophic calculus [7], neutrosophic vector spaces [8], and neutrosophic differential equations [9], etc. In this article, we establish a theorem that demonstrates both the existence and uniqueness of a solution to the neutrosophic differential equation y ′ (x) = f (x, y(x)) with y(x 0 ) = y 0 , where f : I × N n → N n is levelwise continuous neutrosophic function and satisfies a generalized Lipschitz condition.…”

Section: Introductionmentioning

confidence: 99%

The Existence and Uniqueness Conditions for Solving Neutrosophic Differential Equations and Its Consequence on Optimal Order Quantity Strategy

Momena,

Haque,

Rahaman

et al. 2024

Logistics

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Background: Neutrosophic logic explicitly quantifies indeterminacy while also maintaining the independence of truth, indeterminacy, and falsity membership functions. This characteristic assumes an imperative part in circumstances, where dealing with contradictory or insufficient data is a necessity. The exploration of differential equations within the context of uncertainty has emerged as an evolving area of research. Methods: the solvability conditions for the first-order linear neutrosophic differential equation are proposed in this study. This study also demonstrates both the existence and uniqueness of a solution to the neutrosophic differential equation, followed by a concise expression of the solution using generalized neutrosophic derivative. As an application of the first-order neutrosophic differential equation, we discussed an economic lot sizing model in a neutrosophic environment. Results: This study finds the conditions for the existing solution of a first-order neutrosophic differential equation. Through the numerical simulation, this study also finds that the neutrosophic differential equation approach is much better for handling uncertainty involved in inventory control problems. Conclusions: This article serves as an introductory exploration of differential equation principles and their application within a neutrosophic environment. This approach can be used in any operation research or decision-making scenarios to remove uncertainty and attain better outcomes.

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“…The added dimension allows better representation where the boundary between membership and non-membership is poorly defined. Similarly, different neutrosophic numbers [ [28], [29], [30], [31], [32], [33]], [34], [35], [36], [37], [38]] were developed to approach MCDM problems systematically. Various arithmetic operations are required to deal with decision-making problems systematically.…”

Section: Introductionmentioning

confidence: 99%

The Theoretical Framework on Approximations of Neutrosophic Numbers and its Application

Kurian,

2023

Preprint

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Neutrosophic sets are effectual logic represented to understand ambiguous and inconsistent information. They are frequently used to explain many types of partial or incomplete information. Researchers have given much attention to the decision-making theory and its associated methodologies based on uncertain linguistic factors. This article emphasizes the novel neutrosophic number approximations to handle linguistic variables and their application in multiple-attribute decision-making. Different approximation techniques are introduced in neutrosophic sets, but substantial data loss may occur. Hence hexagonal neutrosophic number was proposed to deal with information loss during approximation. Also, the comparisons study with existing techniques is explored to show the effectiveness of proposed approximation. The expected interval criterion was retained although approximation was made to give more desirable features. An MCDM (Multi-Criteria Decision Making) problem is presented to demonstrate efficiency and simplicity with uncertain parameters.

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A New Perspective on Neutrosophic Differential Equation

Cited by 10 publications

References 3 publications

Second-order neutrosophic boundary-value problem

Second-order neutrosophic boundary-value problem

The Existence and Uniqueness Conditions for Solving Neutrosophic Differential Equations and Its Consequence on Optimal Order Quantity Strategy

The Theoretical Framework on Approximations of Neutrosophic Numbers and its Application

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