Analysis of illegal drug transmission model using fractional delay differential equations
AIMS Mathematics
The global burden of illegal drug-related death and disability continues to be a public health th... more The global burden of illegal drug-related death and disability continues to be a public health threat in developed and developing countries. Hence, a fractional-order mathematical modeling approach is presented in this study to examine the consequences of illegal drug usage in the community. Based on epidemiological principles, the transmission mechanism is the social interaction between susceptible and illegal drug users. A pandemic threshold value ($ \Lambda $) is provided for the illegal drug-using profession, which determines the stability of the model. The Lyapunov function is employed to determine the stability conditions of illegal drug addiction equilibrium point of society. Finally, the proposed model has been extended to include time lag in the delayed illegal drug transmission model. The characteristic equation of the endemic equilibrium establishes a set of appropriate conditions for ensuring local stability and the development of a Hopf bifurcation of the model. Finally...
The quality of the public transport sector affects the economy and the daily livelihoods of passe... more The quality of the public transport sector affects the economy and the daily livelihoods of passengers. One of the most important objectives of policymakers is to choose the influencing criteria for performance evaluations. A variety of factors are crucial for raising the standards of public transportation services. In this investigation, we used a decision-based model with uncertainty in order to identify significant criteria in the public transport sector. We also performed a comparative analysis to rank the Rajasthan State Road Transport Corporation (RSRTC) bus depots based on their performance using hybrid multi-criteria decision-making (MCDM) techniques such as TOPSIS, VIKOR, and ELECTRE. To handle judgement ambiguities, in this work we incorporated the Delphi method (DM) and the analytic hierarchy process (AHP), along with fuzzy set theory. The fuzzy Delphi method was used to filter the important criteria. Using a fuzzy AHP approach, the screening criterion weights and ranking...
This study aims to build a framework for measuring the productivity in the public transport secto... more This study aims to build a framework for measuring the productivity in the public transport sector through a data envelopment analysis (DEA) technique. This paper extends the Malmquist productivity index (MP1) and Luenberger productivity indicator (I.P1) evaluation with the concept of an input-oriented new slack model (NSM). NSM model measures the efficiency with the effect of slacks and satisfies unit invariance, radial and translation invariance properties. In particular, the purpose of the proposed extension is to obtain the overall productivity change in terms of technical change (Frontier Shift) and technical efficiency change (Catch-up Effect) for Rajasthan State Road Transport Corporation (RSRTC) bus depots from 2008 to 2019. For this purpose, the number of buses, number of employers, fuel consumption and route distance arc are considered input variables, while passenger-kilometres occupied and vehicle utilisation are output variables. Finally, the result demonstrates that th...
New fractional PID-controller to mitigate frequency variations in power systems
Journal | MESA, 2020
In recent decades, the response of a Fractional Order Proportional Integral Derivative (FOPID) co... more In recent decades, the response of a Fractional Order Proportional Integral Derivative (FOPID) controller has become subject of interest for many researchers. From literature, it is observed that numerous studies are conducted to understand the behavior of FOPID under various operational configurations. Although promising results have been attained using the FOPID controller, it is observed that the dimensional aspects associated with it have been overlooked so far. In this regard, the present study is emphasized to develop a new FOPID controller which is dimensionally balanced. It is introduced as a Dimensionally balanced fractional order proportional integral derivative controller (DBFOPID). The proposed controller has been tested on an isolated power system. Furthermore, the optimized parametric values of the variables affecting overshoot, settling time and rise time are estimated using Particle Swarm Optimization. To evaluate the optimum values of these parameters, integral of t...
Hierarchy of Sectors in BSE SENSEX for Optimal Equity Investments Using Fuzzy AHP
Advances in Intelligent Systems and Computing, 2019
The stock market is considered as one of the most vital components of a free-market economy. The ... more The stock market is considered as one of the most vital components of a free-market economy. The investments of the stock market are associated with a greater amount of risk. Due to the uncertainty associated with stocks, there is a great need to understand the trend in rising and fall of stocks corresponding to a particular sector or an industry to invest profitably. In view of this, authors have taken up a study to identify the best sector in BSE SENSEX for investments. Fuzzy Analytical Hierarchy Process is used to evaluate and study the dominance of various sectors including Automobile, Finance, Information technology, Oil, Pharmaceuticals, and Power. Four crucial derivatives criteria’s Return on equity, Book value per share, Price-earnings ratio, Price to book ratio are considered to study the dominance of each sector. The results of this study help in prioritizing the sectors for future investments.
DEA Model for Exogenously Fixed Variables Under Fuzzy Environment
Advances in Intelligent Systems and Computing, 2019
Data Envelopment Analysis (DEA) is developed to estimate the performance of Decision-Making Units... more Data Envelopment Analysis (DEA) is developed to estimate the performance of Decision-Making Units (DMUs) and it is a nonparametric approach based on linear programming. In the real world, some inputs and outputs are not precisely known which are dealt by fuzzy DEA, where these variables could be expressed as fuzzy numbers. In addition, exogenously fixed inputs and outputs are also involved in efficiency measurement, which are not under the control of management. DEA can deal these situations with crisp variables. This paper proposed a DEA model with exogenously fixed fuzzy inputs and outputs to estimate the performance of DMUs having exogenously fixed variables in a fuzzy environment. A numerical example is also presented.
Fuzzy Slack Based Measure (SBM) of Data Envelopment Analysis
Slack based measure (SBM) model of Data Envelopment Analysis (DEA) is very effective to evaluate ... more Slack based measure (SBM) model of Data Envelopment Analysis (DEA) is very effective to evaluate the relative efficiency of decision making units (DMUs). It deals with the directly input excess and output shortfall to assess the effect of slacks on efficiency with common crisp inputs and outputs. In some cases, input and output data of DMUs cant be precisely measured, so, the uncertain theory has played an important role in DEA. In these cases, the data can be represented as linguistic variable characterized by fuzzy numbers. This paper attempts to extend the traditional DEA model to a fuzzy framework, thus proposing a fuzzy SBM DEA model based on Alpha-cut approach to deal with the efficiency measuring problem with the given fuzzy input and output data. Finally, a numerical example is presented to illustrate the fuzzy SBM model. Since the efficiency measures are expressed by membership functions rather than by crisp values, more information is provided for management. By extending ...
An Efficient Portfolio Management for Trading Under Uncertain Environment
This study presents a framework for efficient portfolio management for trading under uncertain en... more This study presents a framework for efficient portfolio management for trading under uncertain environment. The proposed framework can be used to determine the dominance of various sectors among the chosen set of alternatives. The dominance of these sectors are analyzed by considering various aspects such as Return on equity, Book value per share, Price earnings ratio, and Price to book ratio. For illustration, the dominance of various sectors is evaluated using the proposed framework. The historical stats of various sectors, corresponding to the aforementioned criteria's are collected from various sources and the dominance is studied using the proposed framework. The findings of this study facilitate novice users in understanding the relative dominance of each sector.
Data Envelopment Analysis (DEA) is a multi-criteria technique based on linear programming to deal... more Data Envelopment Analysis (DEA) is a multi-criteria technique based on linear programming to deal with many real-life problems, mostly in nonprofit organizations. The slacks-based measure (SBM) model is one of the DEA model used to assess the relative efficiencies of decision-making units (DMUs). The SBM DEA model directly used input slacks and output slacks to determine the relative efficiency of DMUs. In order to deal with qualitative or uncertain data, a fuzzy SBM DEA model is used to assess the performance of DMUs in this study. The credibility measure approach, transform the fuzzy SBM DEA model into a crisp linear programming model at different credibility levels is used. The results came from the fuzzy DEA model are more rational to the real-world situation than the conventional DEA model. In the end, the data of Indian oil refineries is collected, and the efficiency behavior of the companies obtained by applying the proposed model for its numerical illustration.
The slack-based measure (SBM) DEA model is a non-radial model used to calculate the relative effi... more The slack-based measure (SBM) DEA model is a non-radial model used to calculate the relative efficiency, input, and output targets of the different decision-making units (DMUs) based on their best peers or efficient frontier. The conventional SBM DEA model used crisp inputs and outputs. But, it can be observed in real-life problems that sometimes the available data is in linguistic forms such as “few”, “many”, “small”, or missing data. The DEA technique is frontier based, and therefore, imprecise data may lead to untenable results. Fuzzy theory, which is already established to handle uncertain data, can overcome this problem. Furthermore, the sensitivity and stability analysis have been checked the robustness of fuzzy DEA models. In this study, sensitivity and stability analysis of the fuzzy SBM DEA has been performed. The lower and upper sensitive bounds for inputs and outputs variables have been obtained for both the inefficient and efficient DMUs to calculate the input and output...
Underlying dynamics of crime transmission with memory
Chaos, Solitons & Fractals, 2021
Abstract Various studies suggest different mathematical models of integer order differential equa... more Abstract Various studies suggest different mathematical models of integer order differential equations predict crime. But these models do not inherit non-local property, which depicts behavior changes due to contact with criminals for a long period. To overcome this, a fractional-order mathematical model of crime transmission is proposed in this study. The proposed model considers the previous effects of the input while predicting the crime growth rate. A mathematical model of crime transmission inherited with memory property is proposed in this study to analyze crime congestion. Abstract compartmental parameters of fractional crime transmission equation, which illustrates various stages of criminal activity, were employed to analyze crime contagion in the society. The present study demonstrates the progression of the flow of population by classifying into three systems based on involvement in crime and imprisonment by considering the criminal history of an individual. Subsequently, the equilibria of the three-dimensional fractional crime transmission model are evaluated using phase-plane analysis. The Lyapunov function is employed to determine threshold conditions to achieve a crime-free society.
Dynamics of Crime Transmission Using Fractional Order Differential Equations
Fractals, 2021
Due to the alarming rise in types of crime committed and the number of criminal activities across... more Due to the alarming rise in types of crime committed and the number of criminal activities across the world, there is a great need to amend the existing policies and models adopted by jurisdictional institutes. The majority of the mathematical models have not included the history of the crime committed by the individual, which is vital to control crime transmission in stipulated time. Further, due to various external factors and policies, a considerable number of criminals have not been imprisoned. To address the aforementioned issues prevailing in society, this research proposes a fractional-order crime transmission model by categorizing the existing population into four clusters. These clusters include law-abiding citizens, criminally active individuals who have not been imprisoned, prisoners, and prisoners who completed the prison tenure. The well-posedness and stability of the proposed fractional model are discussed in this work. Furthermore, the proposed model is extended to th...
International Journal of Business and Systems Research, 2017
This paper measures the scale efficiency of decision-making units (DMUs) with fuzzy input and out... more This paper measures the scale efficiency of decision-making units (DMUs) with fuzzy input and output data using fuzzy data envelopment analysis (FDEA) model. FDEA is used to measure the relative efficiencies of a set of DMUs under fuzzy environment in which the input and output data can be represented as linguistic variable characterised by fuzzy variables. The FDEA is solved using the concept of chance-constrained programming and credibility approach. In a special case, when fuzzy inputs and fuzzy outputs are independent trapezoidal or triangular fuzzy variables, the model can be transformed into crisp linear programming. Finally, numerical illustration is presented to illustrate the FDEA model to measure the scale efficiency of DMUs with fuzzy data as well as the effectiveness of the presented method.
DEA-neural networks approach to assess the performance of public transport sector of India
OPSEARCH, 2015
This paper proposes the integrated Data Envelopment Analysis-Neural Networks approach to measures... more This paper proposes the integrated Data Envelopment Analysis-Neural Networks approach to measures the efficiency of public transport sector of India. Data have been collected for 30 State Road Transport Undertakings (STUs) for the year 2011–2012. Efficiency of the STUs is measured with the use of three inputs and single output. Fleet Size, Total Staff and Fuel Consumption are considered as inputs and Passenger Kilometers as output. On the basis of the status of efficiency, it is concluded that efficiency of the STUs are not good and very far from the optimal level. In order to check the robustness of the results, regression and correlation analysis are also conducted which reveal that the efficiency scores measured by all the models having the common trends. The most efficient and the lowest efficient STUs are found same by all the models. The results also demonstrate that the proposed models are highly flexible and don’t require any prior assumptions about the functional form between inputs and outputs. The models also handle the problem of the presence of the outliers and statistical noise in the data points.
Uploads
Papers by Shivi Agarwal