An optimization technique for national income determination model with stability analysis of differential equation in discrete and continuous process under the uncertain environment

Sarkar, Biswajit; Mondal, Sankar Prasad; Hur, Sun; Ahmadian, Ali; Salahshour, Soheil; Guchhait, Rekha; Iqbal, Muhammad Waqas

doi:10.1051/ro/2018071

Cited by 11 publications

(7 citation statements)

References 58 publications

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“…Nonlinear systems may not produce a specific solution for all times but gives a decision maker feature [34,35] of the analyzed system. Through phase portrait analysis and the Lyapunov method, the system stability [36,37] of the designed system definition is feasible. Thus, system design method for nonlinear control systems are application-specific [38].…”

Section: Stability Analysis Of the Non-linear Systemmentioning

confidence: 99%

Nonlinear System Stability and Behavioral Analysis for Effective Implementation of Artificial Lower Limb

et al. 2020

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System performance and efficiency depends on the stability criteria. The lower limb prosthetic model design requires some prerequisites such as hardware design functionality and compatibility of the building block materials. Effective implementation of mathematical model simulation symmetry towards the achievement of hardware design is the focus of the present work. Different postures of lower limb have been considered in this paper to be analyzed for artificial system design of lower limb movement. The generated polynomial equations of the sitting and standing positions of the normal limb are represented with overall system transfer function. The behavioral analysis of the lower limb model shows the nonlinear nature. The Euler-Lagrange method is utilized to describe the nonlinearity in the field of forward dynamics of the artificial system. The stability factor through phase portrait analysis is checked with respect to nonlinear system characteristics of the lower limb. The asymptotic stability has been achieved utilizing the most applicable Lyapunov method for nonlinear systems. The stability checking of the proposed artificial lower extremity is the newer approach needed to take decisions on output implementation in the system design.

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Section: Stability Analysis Of the Non-linear Systemmentioning

confidence: 99%

Nonlinear System Stability and Behavioral Analysis for Effective Implementation of Artificial Lower Limb

et al. 2020

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“…Non-linear interval-valued fuzzy numbers and their relevance to difference equations are shown in [31]. National income determination models with fuzzy stability analysis in a discrete system are elaborately discussed by Sarkar et al [32]. The fuzzy discrete logistic equation is taken and stability situations are found in the literature [33].…”

Section: Difference Equation In An Uncertain Environmentmentioning

confidence: 99%

“…The above equations show that the solution for n is even only. When n is odd, the solutions, which follow from Equation (32), are as follows: Taking the (α, β, γ)-cut of Equation ( 8), we have the following:…”

Section: Solution Of Homogeneous Difference Equation Of Type Imentioning

confidence: 99%

Solution and Interpretation of Neutrosophic Homogeneous Difference Equation

et al. 2020

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In this manuscript, we focus on the brief study of finding the solution to and analyzingthe homogeneous linear difference equation in a neutrosophic environment, i.e., we interpreted the solution of the homogeneous difference equation with initial information, coefficient and both as a neutrosophic number. The idea for solving and analyzing the above using the characterization theorem is demonstrated. The whole theoretical work is followed by numerical examples and an application in actuarial science, which shows the great impact of neutrosophic set theory in mathematical modeling in a discrete system for better understanding the behavior of the system in an elegant manner. It is worthy to mention that symmetry measure of the systems is employed here,which shows important results in neutrosophic arena application in a discrete system.

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“…is the importance degree of the INNs, such (35) In the INDPBM operator, we can only take the correlation among the input arguments and cannot consider the importance degree of input arguments. In what follows, the INWPDBM operator shall be proposed to overcome the shortcoming of the INDPBM operator.…”

Section: Sup In In Sup In In Sup In In Sup In In Sup In In Sup In Inmentioning

confidence: 99%

Some Interval Neutrosophic Dombi Power Bonferroni Mean Operators and Their Application in Multi–Attribute Decision–Making

et al. 2018

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The power Bonferroni mean (PBM) operator is a hybrid structure and can take the advantage of a power average (PA) operator, which can reduce the impact of inappropriate data given by the prejudiced decision makers (DMs) and Bonferroni mean (BM) operator, which can take into account the correlation between two attributes. In recent years, many researchers have extended the PBM operator to handle fuzzy information. The Dombi operations of T-conorm (TCN) and T-norm (TN), proposed by Dombi, have the supremacy of outstanding flexibility with general parameters. However, in the existing literature, PBM and the Dombi operations have not been combined for the above advantages for interval-neutrosophic sets (INSs). In this article, we first define some operational laws for interval neutrosophic numbers (INNs) based on Dombi TN and TCN and discuss several desirable properties of these operational rules. Secondly, we extend the PBM operator based on Dombi operations to develop an interval-neutrosophic Dombi PBM (INDPBM) operator, an interval-neutrosophic weighted Dombi PBM (INWDPBM) operator, an interval-neutrosophic Dombi power geometric Bonferroni mean (INDPGBM) operator and an interval-neutrosophic weighted Dombi power geometric Bonferroni mean (INWDPGBM) operator, and discuss several properties of these aggregation operators. Then we develop a multi-attribute decision-making (MADM) method, based on these proposed aggregation operators, to deal with interval neutrosophic (IN) information. Lastly, an illustrative example is provided to show the usefulness and realism of the proposed MADM method. The developed aggregation operators are very practical for solving MADM problems, as it considers the interaction among two input arguments and removes the influence of awkward data in the decision-making process at the same time. The other advantage of the proposed aggregation operators is that they are flexible due to general parameter.

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An optimization technique for national income determination model with stability analysis of differential equation in discrete and continuous process under the uncertain environment

Cited by 11 publications

References 58 publications

Nonlinear System Stability and Behavioral Analysis for Effective Implementation of Artificial Lower Limb

Nonlinear System Stability and Behavioral Analysis for Effective Implementation of Artificial Lower Limb

Solution and Interpretation of Neutrosophic Homogeneous Difference Equation

Some Interval Neutrosophic Dombi Power Bonferroni Mean Operators and Their Application in Multi–Attribute Decision–Making

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