Solution for a System of First-Order Linear Fuzzy Boundary Value Problems

Nagalakshmi, S.; Kumar, G. Suresh; Madhavi, B.

doi:10.28924/2291-8639-21-2023-4

Cited by 3 publications

(4 citation statements)

References 13 publications

(14 reference statements)

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“…The granular difference and granular division operations properties have been presented in [30,31] . The existence and uniqueness of solutions for homogeneous and non-homogeneous system of first order linear fuzzy boundary value problems under granular differentiability has been discussed in [32] . Moreover, the solution of second-order fuzzy homogeneous differential equations with fuzzy coefficients have been studied in [33] .…”

Section: Some Of the Applications Of Granular Derivativementioning

confidence: 99%

Tracking Control of a Class of Fuzzy Dynamical Systems under the Concept of Granular Differentiability

Abbasi¹,

Jalali²

2023

Fuzzy Information and Engineering

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In this work, the tracking control of a class of uncertain linear dynamical systems is investigated. The uncertainty is considered to be represented as fuzzy numbers, and hence, these uncertain dynamical systems are referred to as fuzzy linear dynamical systems, which are presented in the form of fuzzy differential equations (FDEs). The solution of an FDE is found using an approach called relative-distance-measure fuzzy interval arithmetic and under the granular differentiability concept. The control objective is to provide a control law such that the output of the system tracks a desired reference input in the presence of uncertainties. To this end, a theorem is proposed, which suggests that the control law should take the form of a feedback of fuzzy states with fuzzy gains and a fuzzy pre-compensator. However, since the fuzzy states of the system may not always be measurable, a fuzzy observer is designed for the estimation of such fuzzy states. It is also clearly shown that the generalized Hukuhara differentiability concept is unable for solving the problem examined in this study. Finally, the efficiency of the approach is examined for a plane landing control problem.

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Section: Some Of the Applications Of Granular Derivativementioning

confidence: 99%

Tracking Control of a Class of Fuzzy Dynamical Systems under the Concept of Granular Differentiability

Abbasi¹,

Jalali²

2023

Fuzzy Information and Engineering

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“…Refer to [8] first-order gr-derivative, and gr-integration for n-dimensional fuzzy valued function. Now, we define second order gr-differentiability for n-dimensional fuzzy valued function.…”

Section: And Write It Asmentioning

confidence: 99%

“…Najariyan and Zhao [9] offered a solution to the fuzzy dynamical system under gr-differentiability. Nagalakshmi et al [8] generalized the concept of fuzzy numbers to n-dimensional fuzzy numbers and developed an algorithm to solve system of first-order FBVPs under the concept of gr-differentability.…”

Section: Introductionmentioning

confidence: 99%

An Algorithm for the Solution of Second Order Linear Fuzzy System With Mechanical Applications

Nagalakshmi¹,

Kumar²,

Agarwal³

et al. 2023

Int. J. Anal. Appl.

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In this paper, we consider homogeneous and non-homogeneous second order linear fuzzy systems under granular differentiability. The concept of continuous n-dimensional fuzzy functions on the space of n-dimensional fuzzy numbers are introduced. Developed an algorithm for the solution of a non-homogeneous second order linear fuzzy system under granular differentiability. The proposed algorithm is applied to solve some well-known mechanical problems with fuzzy uncertainty.

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“…Najariyan et al [23,24] investigated the solution of singular FDEs with the concept of gr-differentiability. Soma et al [25,26] established conditions for the existence and uniqueness of solutions for fuzzy initial value problems and system of fuzzy boundary value problems under gr-differentiability. These results were obtained by studying FDEs under the gr-differentiability to overcome all of the shortcomings discussed previously.…”

Section: Articlementioning

confidence: 99%

Existence and Uniqueness of Solutions for Fuzzy Boundary Value Problems Under Granular Differentiability

Soma,

Suresh Kumar,

Agarwal

et al. 2023

Fuzzy Information and Engineering

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This paper considers fuzzy boundary value problems associated with second-order fuzzy differential equations under granular differentiability. Using a horizontal membership function, we present the notion of second-order granular differentiability for fuzzy functions. Using the granular differentiability concept, we interpret two kinds of two-point boundary value problems for second-order fuzzy differential equations. Sufficient conditions are established for the existence and uniqueness of solutions to these fuzzy boundary value problems. An algorithm is presented for solving non-linear fuzzy boundary value problems under granular differentiability. We provide one example and two engineering applications to demonstrate the algorithm's effectiveness and results.

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Solution for a System of First-Order Linear Fuzzy Boundary Value Problems

Cited by 3 publications

References 13 publications

Tracking Control of a Class of Fuzzy Dynamical Systems under the Concept of Granular Differentiability

Tracking Control of a Class of Fuzzy Dynamical Systems under the Concept of Granular Differentiability

An Algorithm for the Solution of Second Order Linear Fuzzy System With Mechanical Applications

Existence and Uniqueness of Solutions for Fuzzy Boundary Value Problems Under Granular Differentiability

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