Electric systems are getting more complex with time, and primitive protection methods such as traveling wave and impedance-based methods face limitations and shortcomings. This paper incorporates and ...presents the applications of an adaptive neuro-fuzzy inference system and compares it with a back propagation neural network, self-organizing map, and hybrid method of discrete wavelet with adaptive neuro-fuzzy inference system for fault detections, classification, and localization in transmission lines. These methods, in comparison with primitive methods, could be capable of detecting, identifying, and predicting the location of the faults more accurately. The IEEE 9-bus system is utilized to obtain data from one end of the transmission line to develop an ANFIS-based model. This system is simulated in MATLAB/Simulink for different fault cases at various locations. The three-phase voltage and current at one end of IEEE 9-bus number seven are taken for training. Three ANFIS models are developed for fault detection, classification, and localization and compared with other models. For verification of the models, mean square error, mean absolute error, and regression analysis have been computed and compared for all the models. All four techniques have performed well for fault classification, detection, and location. However, the percentage error for the ANFIS-based fault model is less compared to backpropagation, self-organizing map, and discrete wavelet transform with ANFIS. Therefore, the proposed ANFIS models can be implemented for deploying in real-time-based protection systems.
The main goal of this study is to establish common fuzzy fixed points in the context of complete b-metric spaces for a pair of fuzzy mappings that satisfy F-contractions. To strengthen the validity ...of the derived results, non-trivial examples are provided to substantiate the conclusions. Moreover, prior discoveries have been drawn as logical extensions from pertinent literature. Our findings are further reinforced and integrated by the numerous implications that this technique has in the literature. Using fixed point techniques to approximate the solutions of differential and integral equations is very useful. Specifically, in order to enhance the validity of our findings, the existence result of the system of non-linear Fredholm integral equations of second-kind is incorporated as an application.
The main purpose of this research article is to generalize Kannan-type fixed-point (FP) theorems for single-valued mappings and Chatterjea-type FP result for fuzzy mappings (FMs) in the context of ...complete strong b-metric spaces (MSs). Moreover, fuzzy FPs are established for Suzuki-type fuzzy contraction in the setting of complete strong b-MSs. The conclusions are supported by nontrivial examples to enhance the validity of the results obtained in this study. In addition, previous findings have been made as corollaries from the relevant literature. The numerous implications that this technique has across the literature improve and integrate our findings. Applications of some of the results obtained are also incorporated.
In this paper, we have established some fixed point theorems in the context of strong b-metric spaces. For this purpose, Ciric type contraction for single-valued mapping and Nadler’s type Banach and ...Chatterjea contractions for set-valued mappings are applied to obtain fixed point and common fixed points. A simple and different technique has been used to obtain the results. Our results unify, extend and generalize the existence of corresponding present and conventional results existing in the literature of fixed point theory.
The concept of intuitionistic fuzzy b-metric spaces (shortly, IFbMS) has been introduced and studied to generalize both the notion of intuitionistic fuzzy metric spaces and fuzzy b-metric spaces. The ...existence of coincident point and common fixed point for two self-mappings has been established. In order to show the strength of these results, some interesting examples are established as well. Our results generalize many previous results existing in literature. Some nontrivial examples are furnished as well as an application is created to give the strength of our main result.
A wide range of new research articles in artificial intelligence, logic programming, and other applied sciences are based on fixed-point theorems. The aim of this article is to present an ...approximation method for finding the fixed point of generalized Suzuki nonexpansive mappings on hyperbolic spaces. Strong and Δ-convergence theorems are proved using the Noor iterative process for generalized Suzuki nonexpansive mappings (GSNM) on uniform convex hyperbolic spaces. Due to the richness of uniform convex hyperbolic spaces, the results of this paper can be used as an extension and generalization of many famous results in Banach spaces together with CAT(0) spaces.
Clean water is the basic need of every living organism. The field of nanotechnology is one of the utmost wide spread areas for current research and development for the management of discarded water. ...Zinc oxide, iron oxide and copper oxide nanoparticles were synthesized using Punica granatum leave, and pulp extract. These prepared nanoparticles were applied for the removal of anionic toxic dyes from wastewater using batch experiment. Different parameters like pH, dose, initial dye concentration, contact time and temperature were optimized to check the highest removal of selected dye. The effect of presence of electrolytes was also studied. Kinetic models like pseudo-1st-order, pseudo-2nd-order and intraparticle diffusion model were applied to check the rate and order of reaction. Equilibrium models like Freundlich, Langmuir, Temkin and Harkins–Jura were applied to check the nature of adsorption of dye on prepared nanoparticles. Thermodynamics models were also applied to check the enthalpy, entropy and Gibbs free energy of the reaction. Desorption study was conducted to check the reusability of the nanoparticles.
The objective of the present research is to establish and prove some new common fuzzy fixed-point theorems for fuzzy set-valued mappings involving Θ-contractions in a complete metric space. For this ...purpose, a novel integral-type contraction condition is applied to obtain these results. In this way, several useful and classical results have been generalized. Moreover, a concrete example is created to furnish our results. An application to stochastic Volterra integral equations has been given to enhance the validity of our results.
The main purpose of this paper is to establish and prove some new common fixed point theorems for intuitionistic fuzzy maps in the context of (α,β)-cut sets of intuitionistic fuzzy sets on a complete ...metric space in association with the Hausdorff metric. Furthermore, the technique of Meir-Keeler (shortly, M-K) contraction is applied to obtain common fixed point of intuitionistic fuzzy compatible maps and fixed points of Kannan type intuitionistic fuzzy set-valued contractive mappings. Our results generalize M-K type fixed point theorem along with its various generalizations. Some nontrivial examples have been furnished in the support of the main results.
In this manuscript, a novel general class of contractions, called Jaggi–Suzuki-type hybrid (
G
-
α
-
ϕ
)-contraction, is introduced and some fixed point theorems that cannot be deduced from their ...akin in metric spaces are proved. The dominance of this family of contractions is that its contractive inequality can be specialized in various manners, depending on multiple parameters. Nontrivial comparative examples are constructed to validate the assumptions of our obtained theorems. Consequently, a number of corollaries that reduce our result to some prominent results in the literature are highlighted and analyzed. Additionally, we examine Ulam-type stability and well-posedness for the new contraction proposed herein. Finally, one of our obtained corollaries is applied to set up unprecedented existence conditions for solution to a class of integral equations. For future aspects of our results, an open problem is noted concerning the discretized population balance model, whose solution may be analyzed using the techniques established herein.
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