Browsing by Author "Haque, Rakibul"

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Citation Count: 0
The Existence and Uniqueness Conditions for Solving Neutrosophic Differential Equations and Its Consequence on Optimal Order Quantity Strategy
(Mdpi, 2024) Momena, Alaa Fouad; Salahshour, Soheıl; Rahaman, Mostafijur; Salahshour, Soheil; Mondal, Sankar Prasad
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.
Citation Count: 1
Solvability Criteria for Uncertain Differential Equations and Their Applicability in an Economic Lot-Size Model with a Type-2 Interval Phenomenon
(Mdpi, 2023) Rahaman, Mostafijur; Salahshour, Soheıl; Alam, Shariful; Zupok, Sebastian; Salahshour, Soheil; Azizzadeh, Fariba; Mondal, Sankar Prasad
Interval numbers comprise potential fields of application and describe the imprecision brought on by the flexible nature of data between boundaries. The recently added type-2 interval number allows a more thorough understanding of interval numbers. Differential equations are commonly employed in mathematical models to handle dynamic problems. It is essential to provide theories of differential equations to describe these models in an ambiguous environment controlled by type-2 interval numbers. This study proposes the type-2 interval context solvability requirements for the initial-valued first differential equation. The conditions for the solution's existence and uniqueness must be met before a brief manifestation of the solution under generalized Hukuhara differentiation occurs. An economic order quantity model analysis in a type-2 interval scenario uses a generalized Hukuhara differentiation approach.