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Open Access
A study and analysis of Queue models and its applications in communication system
(G.B. Pant University of Agriculture and Technology, Pantnagar - 263145 (Uttarakhand), 2019-08) Agarwal, Rahul; Arun Kumar
Scientists and researchers have been involved over the past few years in the rapid progress in the field of communication via wireless sensor networks. Most of the research on mathematical modeling pa wireless sensor networks has mostly focused on favorable aspects, such as data routing, sensor placement, reliability, etc. A significant amount of delay in study data is actually the effect of queue formation on nodes. It occurs in Therefore, the role of the discreet is very important in wireless sensor network modeling. In this thesis, we study the application of queues implemented in wireless sensor networks and provide insight to the current state of the art and guidelines for the future. The path arrangement is one of the important factors that influence data transmission and processing in wireless sensor networks. This thesis addresses this matter through a path delay examination. We have created a model of wireless sensor network using the open queue network principle and the path delays have been investigated based on the model.
Open Access
Study of simultaneous occurrence of probabilistic and non-probabilistic uncertainties in time series forecasting
(G.B. Pant University of Agriculture and Technology, Pantnagar - 263145 (Uttarakhand), 2019-01) Gupta, Krishna Kumar; Sanjay Kumar
Statistical techniques based conventional time series forecasting models are capable to deal probabilistic uncertainty that is caused by randomness. Fuzzy time series forecasting models can handle the non-probabilistic uncertainty that arises due to vagueness and linguistic representation of time series data. Both probabilistic and non-probabilistic uncertainties arise in time series forecasting but neither probability theory nor fuzzy set theory handles these both types of uncertainty simultaneously. Probabilistic fuzzy set includes prominent characteristics of both fuzzy and probability theory and hence is used to model both uncertainties simultaneously in a single framework. In this research work, probabilistic fuzzy set, probabilistic intuitionistic fuzzy set, hesitant probabilistic fuzzy sets and intuitionistic fuzzy random variables are used to develop six time series forecasting methods to include both kinds of uncertainties and non-determinism. These methods are presented in forms of models. Model-1, Model-2 and Model-3 are based on probabilistic fuzzy set that use probabilistic fuzzy logical relations of different orders and different schemes to partition time series data. Model-4 is was probabilistic intuitionistic fuzzy set based time series forecasting model that includes both types of uncertainties and non-determinism. Model-5 is based on hesitant probabilistic fuzzy set that also includes both types of uncertainties and non-determinism. Model-5 also includes a particular type of non-determinism that arises due to multiple fuzzification of time series data. Model-6 uses intuitionistic fuzzy random variable and handles both types of uncertainties. While Models [1-5] handles non-probabilistic uncertainties associated with membership grades or non-memberships grades, this model includes probabilistic uncertainty due to randomness of time series data. Models [1-6] are implemented to forecast time series data of University of Alabama enrolments, SBI share prices and TAIEX to show their outperformance over others forecasting methods. Performance of the models has been analyzed in terms of RMSE, AFER. Validity, robustness of the models against variations in time series data is also tested using evaluation parameter, performance parameter, tracking signal and statistical test (t-test and Wilcoxon signed rank test) in time series data.
Open Access
Reliability indices and signature analysis of complex networks
(G.B. Pant University of Agriculture and Technology, Pantnagar - 263145 (Uttarakhand), 2018-08) Bisht, Soni; Singh, S.B.
The present research is based on the development of reliability models with the application of UGF, Supplementary variable technique, ANN, and Signature. In this study, six different reliability models have been developed. Model 1 generates an efficient algorithm to compute the reliability indices of complex bridge networks having i.i.d. lifetime components (nodes, edges), with the help of UGF and Owen’s method. Applying reliability structure function, proposed algorithms are used to find the signature and the MTTF. Model 2 assess the reliability characteristics of bridge network and square ladder network on the basis of the flow of information/signals from a source node to a sink node using the universal generating function. The main focus of this model is to estimate the reliability indices, namely, reliability, MTTF, sensitivity assuming failure to be exponentially distributed. Furthermore, for computing the signature of networks with the help of Owens method we have assumed that all components are independent and have identically distributed. Model 3 deals with the reliability and signature analysis of one of the most common multistage interconnection networks, namely, Shuffle exchange networks (SENs).An efficient algorithm has been established to compute the signature and Mean-time-to-failure of shuffle exchange networks with the help of Owen’s method incorporating independent and identically distributed lifetime component. All perspectives of the reliability, viz. terminal, broadcast and network reliability have been analyzed with the help of universal generating function. Model 4 estimates the reliability of Benes network having both independent and identically and non-identically distributed components in three contexts, viz. terminal, broadcast, and network with the help of universal generating function. Subsequently, the signature is computed with the help of Owen’s method using different algorithms. At last, we have computed the mean time to failure with the help of minimal signature. Model 5 focuses on the reliability indices and signature evaluation of all-digital protection system. In this model, firstly, we have computed the reliability of all-digital protection systems using a universal generating function having both independent and identically and non-identically distributed components. Afterwards, the signature is evaluated with the help of Owen’s method using different algorithms where all the system components are coherent. Lastly, we have calculated the mean time to failure with the help of minimal signature. Model 6 [Section 1] introduces the concept of the acyclic transmission network in which numbers of nodes are capable of receiving or sending a signal to the target nodes. The model combined the concepts of Markov processes and minimal cuts incorporating copula to find the various reliability measures. Various reliability characteristics such as transition state probabilities, reliability, MTTF and sensitivity of the proposed network has been evaluated with the help of minimal cuts coupling with Markov processes using Gumbel-Hougaard copula, supplementary variable techniques and Laplace transforms. [Section 2] studies the reliability and profit function of acyclic transmission network with the application of Markov process and artificial neural network. After determining the reliability by Markov process, it is improved with the help of the artificial neural network. All the presented models are demonstrated by appropriate illustrative examples.
Open Access
A study of some nanofluid flow and heat transfer over different geometries
(G.B. Pant University of Agriculture and Technology, Pantnagar - 263145 (Uttarakhand), 2019-01) Mishra, Ashish; Manoj Kumar
The present study is subjected to heat and mass transfer characteristics of nanofluid flow over different geometries. The nanofluid flow saturated in different solid objects, such as cone, stretching cylinder, Riga plate, channel, stretching surfaces, etc., are commonly used in many fields of engineering and manufacturing procedures. The involvement of various physical factors, such as magnetic field, thermal radiation, suction/injection, porous medium, slip effects, chemical reaction, heat generation/absorption, Joule heating, viscous dissipation, volume fraction of different nanoparticles (copper and silver), Brownian motion and thermophoresis effects in nanofluid flow have been discussed. The influences of these parameters are plotted and discussed to examine the variations in velocity profiles, temperature and concentration distributions. Moreover, the factors of engineering interest, such as skin friction coefficient, Nusselt and Sherwood numbers are studied and discussed in details. The introduction section is filled with the essential notions and definitions related to fluid mechanics. The group of similarity transformations has been utilized to convert the principle equations into non-dimensional set and the Runge-Kutta-Fehlberg method of fourth-fifth order along with shooting technique is used to solve them with the help of computing tools. For validation of present numerical codes, we have compared our results with previously published works. The outcome involving to the related work may be helpful to explore various aspects of nanofluid flow problems over other objects. The obtained results have huge significances in different fields of applied science and different branches of engineering and applied mathematics.
Open Access
A study of some micro-polar fluid flow problems
(G.B. Pant University of Agriculture and Technology, Pantnagar - 263145 (Uttarakhand), 2018-12) Singh, Khilap; Manoj Kumar
In the recent decades, the importance of non-Newtonian fluids has significantly increased because of their relation with applied sciences. The flow of these fluids takes vital role not only in hypothesis but also in several industrial processes. Among the various non-Newtonian fluids, the micro-polar fluids have achieve the special attention in recent years due to their applications in biotechnology, chemical engineering, geophysics, materials processing and polymeric fabrication and so on. Micro-polar fluids correspond to the many industrial important fluids for example, bio-fluids, body fluids, colloidal suspensions, human and animal blood, lubricants, polymers, liquid crystals, paints etc. Because of wide range of utilizations of these fluids present work is done to examine the impact of different parameters on the flow behaviors of micro-polar fluid. In the present work, author has studied different problems of micro-polar fluid flow in various shaped bodies. The governing equations of flows of micro-polar fluid are non-linear in nature and solved by using both analytical and numerical methods. Different numerical methods for example Finite element method, Finite difference method, Quasilinearization, Keller-box method, Runge-Kutta-Fehlberg fourth fifth order method and Shooting method etc. can be applied for handling these problems. In the present thesis author has used Keller-box method, Runge-Kutta-Fehlberg fourth fifth order method, shooting method together with an analytic method known as differential transformation method. The work incorporated in the present research is divided into five chapters. Author has formulated eight problems out of which seven are for steady flow and one is for unsteady flow. One problem is solved by applying differential transformation method, two problems are solved by applying Keller box method, while six problems are solved by applying shooting technique along with Runge-Kutta-Fehlberg fourth fifth order method. To approve of results obtained from all these problems with particular conditions, author compare results with results of previously published literature. Excellent agreement between the results is obtained. The impact of various pertinent parameters on velocity, micro-rotation, temperature and concentration profiles is studied comprehensively and is portrayed graphically. The skin-friction coefficient, the couple stress coefficient, the Nusselt and Sherwood numbers have also been computed and depicted using graphs and tables. It is hoped that the results obtained from the present study will give important data to group of audience.
Open Access
Interval-valued intuitionistic hesitant fuzzy and uncertain linguistic based multi-criteria group decision making methods
(G.B. Pant University of Agriculture and Technology, Pantnagar - 263145 (Uttarakhand), 2018-01) Joshi, Dheeraj Kumar; Sanjay Kumar
Multi-criteria group decision making (MCGDM) has various applications in many real life problems of banking, data mining, water resource location, human resource development, resource allocation and portfolio selection. The present research work mainly focus on development and implementation of MCGDM/MCDM models in the environment of uncertainty and hesitation. In this study, 6 different models of MCGDM methods are developed in interval-valued intuitionistic hesitant fuzzy (IVIHF), probabilistic hesitant fuzzy (PHF) and interval-valued intuitionistic hesitant fuzzy linguistic and uncertain linguistic environment. These models are based on entropy measure, distance and similarity measures. Cloud model based TOPSIS method and Choquet integral based TOPSIS methods are also developed to consider both randomness, fuzziness and interaction phenomenon in MCGDM problems. Model [1] is IVIHF entropy based MCGDM method. In this model criterion weights are determined using IVIHF entropy. Model [2] is probabilistic intuitionistic fuzzy information based TOPSIS method. In Model [3], a series of distance and similarity measures for probabilistic hesitant fuzzy set is defined and used in MCDM problem. In Model [4], a new class of fuzzy set called probabilistic hesitant fuzzy linguistic set is defined and used in MCGDM problem. In Model [2], Model [3] and Model [4] a real case study of stock selection problem has been taken for MCGDM methods. Model [5] is trapezium cloud based TOPSIS method for MCGDM and is used to rank different stocks on the basis of some financial criteria. Model [6] is Choquet integral based TOPSIS method in interval-valued intuitionistic hesitant fuzzy uncertain linguistic environment and deals with the situations where decision makers have hesitation in providing their preferences over objects in decision making. All developed models (Model [1-6]) are implemented on real life problems of stock selection problem, candidate selection problem and ranking of the organizations. To examine the validity of ranking results validity test of all models (Model [1-6]) under certain test criteria are also done along with comparative analysis. Simulation study of Model [2], Model [3] and Model [4] with similar real data set of seven organizations provides their different ranking. To further compare rankings of the organizations: Model [2-4] are implemented in portfolio selection problems to analyze portfolio risk and return.
Open Access
Interval-valued intuitionistic hesitant fuzzy and uncertain linguistic based multi-criteria group decision making methods
(G.B. Pant University of Agriculture and Technology, Pantnagar - 263145 (Uttarakhand), 2018-01) Joshi, Dheeraj; Sanjay Kumar
Multi-criteria group decision making (MCGDM) has various applications in many real life problems of banking, data mining, water resource location, human resource development, resource allocation and portfolio selection. The present research work mainly focus on development and implementation of MCGDM/MCDM models in the environment of uncertainty and hesitation. In this study, 6 different models of MCGDM methods are developed in interval-valued intuitionistic hesitant fuzzy (IVIHF), probabilistic hesitant fuzzy (PHF) and interval-valued intuitionistic hesitant fuzzy linguistic and uncertain linguistic environment. These models are based on entropy measure, distance and similarity measures. Cloud model based TOPSIS method and Choquet integral based TOPSIS methods are also developed to consider both randomness, fuzziness and interaction phenomenon in MCGDM problems. Model [1] is IVIHF entropy based MCGDM method. In this model criterion weights are determined using IVIHF entropy. Model [2] is probabilistic intuitionistic fuzzy information based TOPSIS method. In Model [3], a series of distance and similarity measures for probabilistic hesitant fuzzy set is defined and used in MCDM problem. In Model [4], a new class of fuzzy set called probabilistic hesitant fuzzy linguistic set is defined and used in MCGDM problem. In Model [2], Model [3] and Model [4] a real case study of stock selection problem has been taken for MCGDM methods. Model [5] is trapezium cloud based TOPSIS method for MCGDM and is used to rank different stocks on the basis of some financial criteria. Model [6] is Choquet integral based TOPSIS method in interval-valued intuitionistic hesitant fuzzy uncertain linguistic environment and deals with the situations where decision makers have hesitation in providing their preferences over objects in decision making. All developed models (Model [1-6]) are implemented on real life problems of stock selection problem, candidate selection problem and ranking of the organizations. To examine the validity of ranking results validity test of all models (Model [1-6]) under certain test criteria are also done along with comparative analysis. Simulation study of Model [2], Model [3] and Model [4] with similar real data set of seven organizations provides their different ranking. To further compare rankings of the organizations: Model [2-4] are implemented in portfolio selection problems to analyze portfolio risk and return.
Open Access
Intuitionistic fuzzy and hesitant fuzzy sets based time series forecasting methods
(G.B. Pant University of Agriculture and Technology, Pantnagar - 263145 (Uttarakhand), 2017-12) Bisht, Kamlesh; Sanjay Kumar
In the present research work, various time series forecasting methods using intuitionistic fuzzy, hesitant fuzzy and dual hesitant fuzzy sets are developed to address issue of non stochastic uncertainty and non-stochastic hesitation. These methods are presented in form of various models. Model [1] and Model [4] are computational algorithm based higher order fuzzy time series forecasting models which are based on intuitionistic fuzzy and hesitant fuzzy respectively. Model [2] and Model [3] use hesitant fuzzy set to handle hesitancy in fuzzy time series forecasting. In the present research work, methodology of hesitant fuzzy time series forecasting method is also developed and presented in Model [5]. Model [6] is intuitionistic fuzzy time series forecasting model which is based on dual hesitant fuzzy set. Model [2], Model [3], Model [5] and Model [6] use max-min composition operation. Performance of these developed models over existing fuzzy time series and intuitionistic fuzzy time series forecasting methods is verified by implementing them on two time series data of University of Alabama and SBI share price. The outperformance of all models is tested using RMSE and AFER error measures. Validity of the developed models id tested using correlation coefficients, tracking signal, evaluation parameter and performance parameters. Superiority of developed models is also tested using two tailed t-test at the confidence level 1% and 5%. In forecasting enrollments of University of Alabama, the performance of Model [4] in terms of both RMSE and AFER is found better than model [1], Model [2], Model [3], Model [5] and Model [6]. In forecasting share prices of SBI, the performance of Model [6] in terms of both RMSE and AFER is found better than Model [1], Model [2], Model [3], Model [4] and Model [5]. In forecasting enrollments of University of Alabama, Model [1] outperforms over Model [2] but its performance is equally good as of Model [3], Model [4], Model [5] and Model [6]. Model [2] outperforms over Model [4] and Model [5] but its performance is good as Model [3] and Model [6]. Model [3] performs equally good as Model [4], Model [5] and Model [6]. Model [4] outperforms over Model [6] but its performance is good as Model [5]. Model [5] is equally good in performance as the Model [6]. In forecasting SBI share prices, Model [1] outperforms over Model [2], Model [3] but its performance is good as Model [4], Model [5]. Model [2] outperforms over Model [4], Model [5] and Model [6] but its performance is good as Model [3]. Model [3] outperforms over Model [4], Model [5] and Model [6]. Model [4] performed equally good as Model [5] and Model [6]. Model [5] outperforms over Model [6]. All developed models not only handle the non-stochastic uncertainty and hesitation but also enhance the accuracy in forecasted enrollments and financial time series data of SBI share price.
Open Access
On reliability modeling of complex systems: signature and fuzzy based expressions
(G.B. Pant University of Agriculture and Technology, Pantnagar - 263145 (Uttarakhand), 2017-07) Akshay Kumar; Singh, S.B.
The present research study is based on the development of reliability models with the help of UGF and fuzzy sets. In this study, eight different reliability models have been developed. Model-1 studies the reliability characteristic of sliding window coherent system which consists of n number of components connected in parallel configuration using UGF. Model-2 discusses the signature reliability of complex and k-out-of-n coherent system with the help of reliability functions. Model-3 focuses on reliability metrics of a sliding window coherent system in case of multiple failures. Model-4 deals with a linear multi-state sliding window coherent system which generalizes the consecutive k-out-of-r-from-n:F system in multi-state case. All the aforesaid models evaluated the signature, MTTF, Barlow-Proschan index and expected cost etc. Model-5 studies the reliability of two states consecutive sliding window system consisting of generalized linear multi-state sliding window system having m consecutive independent and identically distributed components. Model-6 introduces and studies the intervalvalued reliability of to 2-out-of-4 system with the help of reliability function using UGF. The considered system consists of 2 numbers of components connected in series. Model7 investigates the intuitionistic fuzzy reliability measure of a linear (circular) consecutive k-out-of-n:F system of non-identical elements with the Weibull lifetime distribution and Markov process. Model-8 deals with series, parallel and consecutive k-out-of-n: F systems, using triangular hesitant fuzzy number and Weibull distribution.

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