Computer-Based Fuzzy Numerical Method for Solving Engineering and Real-World Applications

Rafiq, Naila; Yaqoob, Naveed; Kausar, Nasreen; Shams, Mudassir; Mir, Nazir Ahmad; Gaba, Yaé Ulrich; Khan, Naveed Jeelani

doi:10.1155/2021/6916282

Cited by 7 publications

(3 citation statements)

References 25 publications

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“…Here, we present some examples to illustrate the performance and efficiency of MBHPM to solve TLDFSEs. CAS-Maple 18 with stopping criteria are used to terminate the computer program [42][43][44] :…”

Section: Numerical Outcomesmentioning

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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Section: Numerical Outcomesmentioning

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

Self Cite

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“…Example 1: Mechanical Engineering Problem: Consider a mechanical system 30,32,33 that consist of two masses, m1 and m2, each of which is free to slide along a horizontal surface with no fraction. Three springs are used to bind the masses to each other as well as to two stiff walls.…”

Section: Engineering Applicationsmentioning

confidence: 99%

Computationally semi-numerical technique for solving system of intuitionistic fuzzy differential equations with engineering applications

Shams

Kausar

Kousar

et al. 2022

Advances in Mechanical Engineering

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Some complex problems in science and engineering are modeled using fuzzy differential equations. Many fuzzy differential equations cannot be solved by using exact techniques because of the complexity of the problems mentioned. We utilize analytical techniques to solve a system of fuzzy differential equations because they are simple to use and frequently result in closed-form solutions. The Generalized Modified Adomian Decomposition Method is developed in this article to compute the analytical solution to the linear system of intuitionistic triangular fuzzy initial value problems. The starting values in this case are thought of as intuitionistic triangular fuzzy numbers. Engineering examples, such as the Brine Tanks Problem, are used to demonstrate the proposed approach and show how the series solution converges to the exact solution in closed form or in series. The corresponding graphs at different levels of uncertainty show the example’s numerical outcomes. The graphical representations further demonstrate the effectiveness and accuracy of the proposed method in comparison to Taylor’s approaches and the classical Decomposition method.

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“…In addition, some important fuzzy numbers such as trapezoidal fuzzy and triangular fuzzy numbers have many applications. In [70], Rafiq et al proposed an efficient numerical iterative method for estimating roots of fuzzy nonlinear equations, which are based on the special type of fuzzy number called triangular fuzzy number. Furthermore, some real-life applications were also considered as numerical test problems from engineering, which contain fuzzy quantities in the parametric form.…”

Section: Introductionmentioning

confidence: 99%

Almost periodic fractional fuzzy dynamic equations on timescales: A survey

Wang,

Tan,

Agarwal

2023

Math Methods in App Sciences

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In this paper, we systematically present some main results of the fractional calculus, almost periodic functions, fuzzy functions, fuzzy fractional calculus, and almost periodic generalized fuzzy dynamic equations on timescales. Moreover, the potential future research of almost periodic fractional fuzzy dynamic equations on timescales is discussed. The results presented in this survey can be applied to study the qualitative theory of almost periodic fractional fuzzy dynamic equations and fuzzy fractional calculus on timescales.

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Computer-Based Fuzzy Numerical Method for Solving Engineering and Real-World Applications

Cited by 7 publications

References 25 publications

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

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

Computationally semi-numerical technique for solving system of intuitionistic fuzzy differential equations with engineering applications

Almost periodic fractional fuzzy dynamic equations on timescales: A survey

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