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20173
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Subject: Mathematics × End date: 2017 × Start date: 2017 × Type: Thesis × Thesis Type: Ph.D ×
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    ThesisItemOpen 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.
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    ThesisItemOpen 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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    ThesisItemOpen Access
    Numerical study of some flow problems in nanofluid
    (G.B. Pant University of Agriculture and Technology, Pantnagar - 263145 (Uttarakhand), 2017-04) Pandey, Alok Kumar; Manoj Kumar
    In the present study numerical scheme have been employed to analyze the boundary layer flow, heat and mass transfer flow past a nanofluid due to various geometries. The flow around immersed bodies in Newtonian and Non-Newtonian fluid streams are commonly encountered in many studies in medical arena, geophysics, mechanical engineering, hydrodynamics, chemical engineering and ocean engineering etc. The boundary layer flow of nanofluid around bodies of various geometries such as wedge, stretching cylinder, stretching surface, parallel plate and divergent/convergent channel have been discussed. The different flow conditions involve various physical phenomenon such as magnetic effect, velocity slip effect, thermal slip effect, suction/injection, Brownian motion and thermophoresis effects, porosity, buoyancy effect, heat generation/absorption, thermal radiation, chemical reaction, viscous dissipation, Ohmic dissipation and nanoparticle volume fraction etc., have been investigate their impact on profiles of nanofluid for velocity, temperature and concentration. Further, their effects on skin friction coefficient, Nusselt and Sherwood number are studied and discussed in details. The pre requisites of essential concepts have been involved in introduction section. The Lie group transformation and similarity transformation have been employed to altered the fundamental equations into similar dimensionless form and then after Runge-KuttaFehlberg scheme of fourth fifth order together with shooting technique is applied to solve them with the aid of standard MATLAB package. To check the validity of our code we have contrasted our results with those reported in previous literature. This investigation declared that boundary layer flow and heat transfer analysis may be performed in large industrial significance including industrial cooling applications as smart fluids, in nuclear reactors, automotive applications, electronic applications and biomedical applications. The MHD nanofluid flow in electrical conducting fluid can manage the rate of cooling and the required class of products can be obtained. The present study may support in the fields of applied science and also for the researchers working in the field of miniaturized technology, medical science and mechanical engineering etc.