The solution techniques for linear and quadratic equations with coefficients as Cauchy neutrosphic numbers

Rahaman, Mostafijur; Mondal, Sankar Prasad; Chatterjee, Banashree; Alam, Shariful

doi:10.1007/s41066-021-00276-0

Cited by 6 publications

(3 citation statements)

References 36 publications

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“…The notion of neutrosophic Riemann integration is established by Biswas et al [38]. Rahaman et al [39] established the approach for solving linear and quadratic equations using Cauchy neutrosophic coefficients. Salama et al [40] discussed an NDE by using a neutrosophic thick function.…”

Section: Neutrosophic Calculus and Differential Equationmentioning

confidence: 99%

“…It has come to our attention that the majority of studies [9,[34][35][36][37][38][39][41][42][43][44][45][46][47]49,50] in neutrosophic set theory have focused on applying neutrosophic sets in various scientific disciplines. However, there has been minimal effort directed towards the comprehensive development of neutrosophic differential equations and their manifestation within the neutrosophic context.…”

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confidence: 99%

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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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Section: Neutrosophic Calculus and Differential Equationmentioning

confidence: 99%

mentioning

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

Self Cite

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“…Different researchers used various fuzzy numbers to solve fuzzy linear systems of equations. For example, Akram et al 30–32 used the LR-bipolar fuzzy number to solve the bipolar fuzzy linear system of equation, Rehaman et al 33 used the neutrosphic fuzzy number, Nasseri and Zahmatkesh 34 used triangular fuzzy number to solve fully fuzzy linaer system of equations, Akram et al 35 linear system of equations in m-polar fuzzy environment, Matinfar et al 36 used Householder Decomposition method, Muzzioli and Reynaerts 37 used triangular fuzzy number to solve A 1 x + b 1 = A 2 x + b 2 , Abbasbandy et al 38 find minimal solution of general dual fuzzy linear systems, Lodwick and Dubois 39 used interval linear systems as a necessary step in fuzzy linear systems of equations, Nasseri et al 40 trapezoidal fuzzy numbers to solve fuzzy linear system of equations, and many others.…”

Section: Introductionmentioning

confidence: 99%

Modified Block Homotopy Perturbation Method for solving triangular linear Diophantine fuzzy system of equations

Shams

Kausar

Khan

et al. 2023

Advances in Mechanical Engineering

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Numerous real-world applications can be solved using the broadly adopted notions of intuitionistic fuzzy sets, Pythagorean fuzzy sets, and q-rung orthopair fuzzy sets. These theories, however, have their own restrictions in terms of membership and non-membership levels. Because it utilizes benchmark or control parameters relating to membership and non-membership levels, this theory is particularly valuable for modeling uncertainty in real-world problems. We propose the unique concept of linear Diophantine fuzzy set with benchmark parameters to overcome these restrictions. Different numerical, analytical, and semi-analytical techniques are used to solve linear systems of equations with several fuzzy numbers, such as intuitionistic fuzzy number, triangular fuzzy number, bipolar fuzzy number, trapezoidal fuzzy number, and hexagon fuzzy number. The purpose of this research is to solve a fuzzy linear system of equations with the most generalized fuzzy number, such as Triangular linear Diophantine fuzzy number, using an analytical technique called Homotopy Perturbation Method. The linear systems co-efficient are crisp when the right hand side vector is a triangular linear Diophantine fuzzy number. A numerical test examples demonstrates how our newly improved analytical technique surpasses other existing methods in terms of accuracy and CPU time. The triangular linear Diophantine fuzzy systems of equations’ strong and weak visual representations are explored.

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Generalized neutrosophic Laplace transform and its application in an EOQ model with price and deterioration-dependent demand

Haque,

Rahaman,

Alam

et al. 2024

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The solution techniques for linear and quadratic equations with coefficients as Cauchy neutrosphic numbers

Cited by 6 publications

References 36 publications

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

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

Modified Block Homotopy Perturbation Method for solving triangular linear Diophantine fuzzy system of equations

Generalized neutrosophic Laplace transform and its application in an EOQ model with price and deterioration-dependent demand

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