Search results for: single valued neutrosophic hesitant fuzzy rough set

Authors: M. Bassoui, M. Ferfra, M. Chrayagne

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This paper presents a qualitative modeling for the nonlinear B-H curve of the saturable magnetic materials for a transformer with shunts used in the power supply for the magnetron. This power supply is composed of a single phase leakage flux transformer supplying a cell composed of a capacitor and a diode, which double the voltage and stabilize the current, and a single magnetron at the output of the cell. A procedure consisting of a fuzzy clustering method and a rule processing algorithm is then employed for processing the constructed fuzzy modeling rules to extract the qualitative properties of the curve.

Keywords: B(H) curve, fuzzy clustering, magnetron, power supply

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Authors: Yasser F. Hassan

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The reduction or removal of noise in a color image is an essential part of image processing, whether the final information is used for human perception or for an automatic inspection and analysis. This paper describes the modeling system based on the rough neural network model to adaptive cellular automata for various image processing tasks and noise remover. In this paper, we consider the problem of object processing in colored image using rough neural networks to help deriving the rules which will be used in cellular automata for noise image. The proposed method is compared with some classical and recent methods. The results demonstrate that the new model is capable of being trained to perform many different tasks, and that the quality of these results is comparable or better than established specialized algorithms.

Keywords: rough sets, rough neural networks, cellular automata, image processing

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Authors: T. Pathinathan, M. Peter

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Fuzzy graphs incorporate concepts from graph theory with fuzzy principles. In this paper, we make a study on the properties of fuzzy graphs which are non-cyclic and are of two-dimensional in structure. In particular, this paper presents 2D structure or the structure of double layer for a non-cyclic fuzzy graph whose underlying crisp graph is non-cyclic. In any graph structure, introducing 2D structure may lead to an inherent cycle. We propose relevant conditions for 2D structured non-cyclic fuzzy graphs. These conditions are extended even to fuzzy graphs of the 3D structure. General theoretical properties that are studied for any fuzzy graph are verified to 2D structured or double layered fuzzy graphs. Concepts like Order, Degree, Strong and Size for a fuzzy graph are studied for 2D structured or double layered non-cyclic fuzzy graphs. Using different types of fuzzy graphs, the proposed concepts relating to 2D structured fuzzy graphs are verified.

Keywords: double layered fuzzy graph, double layered non–cyclic fuzzy graph, order, degree and size

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Authors: Yuguang Gao, Qiang Yang, Yanpeng Zhang, Mingtao Deng

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To enhance the safety, quality and efficiency of healthcare services provided by surgical doctors, we propose a comprehensive approach to the performance evaluation of individual doctors by incorporating insights from performance data as well as views of different stakeholders in the hospital. Exploratory factor analysis was first performed on collective multidimensional performance data of surgical doctors, where key factors were extracted that encompass assessment of professional experience and service performance. A two-level indicator system was then constructed, for which we developed a weighted interval-valued spherical fuzzy analytic hierarchy process to analyze the relative importance of the indicators while handling subjectivity and disparity in the decision-making of multiple parties involved. Our analytical results reveal that, for the key factors identified as instrumental for evaluating surgical doctors’ performance, the overall importance of clinical workload and complexity of service are valued more than capacity of service and professional experience, while the efficiency of resource consumption ranks comparatively the lowest in importance. We also provide a retrospective case study to illustrate the effectiveness and robustness of our quantitative evaluation model by assigning meaningful performance ratings to individual doctors based on the weights developed through our approach.

Keywords: analytic hierarchy processes, factor analysis, fuzzy logic, performance evaluation

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Authors: Nastaran Hajiheydari, Mohammad Soltani Delgosha

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Vendor (supplier) selection is a group decision-making (GDM) process, in which, based on some predetermined criteria, the experts’ preferences are provided in order to rank and choose the most desirable suppliers. In the real business environment, our attitudes or our choices would be made in an uncertain and indecisive situation could not be expressed in a crisp framework. Intuitionistic fuzzy sets (IFSs) could handle such situations in the best way. VIKOR method was developed to solve multi-criteria decision-making (MCDM) problems. This method, which is used to determine the compromised feasible solution with respect to the conflicting criteria, introduces a multi-criteria ranking index based on the particular measure of 'closeness' to the 'ideal solution'. Until now, there has been a little investigation of VIKOR with IFS, therefore we extended the intuitionistic fuzzy (IF) VIKOR to solve vendor selection problem under IF GDM environment. The present study intends to develop an IF VIKOR method in a GDM situation. Therefore, a model is presented to calculate the criterion weights based on entropy measure. Then, the interval-valued intuitionistic fuzzy weighted geometric (IFWG) operator utilized to obtain the total decision matrix. In the next stage, an approach based on the positive idle intuitionistic fuzzy number (PIIFN) and negative idle intuitionistic fuzzy number (NIIFN) was developed. Finally, the application of the proposed method to solve a vendor selection problem illustrated.

Keywords: group decision making, intuitionistic fuzzy set, intuitionistic fuzzy entropy measure, vendor selection, VIKOR

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Authors: Aneta Nitsch-Osuch, Beata Pawlus, Maria Pawlak

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Introduction: Recently, the number of parents who refuse to vaccinate their children or present so-called hesitant behaviors has increased in many developed countries. The study aimed to analyze the completeness and timeliness of vaccinations against hepatitis B and tuberculosis in neonates in a single maternity hospital in Warsaw (Poland). Material and Methods: We analyzed medical records of children born in the hospital between 1st January 2015 and 31st December 2016 and calculated the proportion of newborns not vaccinated on time. Results: The percentage of unvaccinated newborns was similar in the analyzed years: 7.2% in 2015 and 6.7% in 2016. Parental decisions rather than medical contraindications caused non-immunization (4.3% vs. 2.9% in 2015, and 4.7% vs. 2% in 2016). Most parents refused both vaccinations (81%-84%), whereas 7-8% refused only hep B vaccination, and 9-11% refused alone tuberculosis vaccination. The majority of hesitant parents decided to delay both vaccinations (70-80%), while 10-11% of parents chose to delay only one vaccination (hep B). In consecutive years, an increase in the percentage of parents delaying tuberculosis vaccination was reported (10 vs. 19%). Discussion: The increase in the number of newborns who are not correctly vaccinated just after birth due to their parents' decision should be considered non-gradual, both for hepatitis B and tuberculosis. It is necessary to implement effective educational and informative measures targeted at future parents to reinforce positive attitudes towards vaccinations and to dispel doubts about them among parents who are hesitant.

Keywords: hepatitis B, tuberculosis, immunization, new-borns, coverage rate

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Authors: Abdullah M. Almeshal, Mohammad R. Alenezi, Talal H. Alzanki

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This paper presents a hybrid fuzzy logic control strategy for a unicycle trajectory following robot on irregular terrains. In literature, researchers have presented the design of path tracking controllers of mobile robots on non-frictional surface. In this work, the robot is simulated to drive on irregular terrains with contrasting frictional profiles of peat and rough gravel. A hybrid fuzzy logic controller is utilised to stabilise and drive the robot precisely with the predefined trajectory and overcome the frictional impact. The controller gains and scaling factors were optimised using spiral dynamics optimisation algorithm to minimise the mean square error of the linear and angular velocities of the unicycle robot. The robot was simulated on various frictional surfaces and terrains and the controller was able to stabilise the robot with a superior performance that is shown via simulation results.

Keywords: fuzzy logic control, mobile robot, trajectory tracking, spiral dynamic algorithm

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Authors: Iftikhar U. Sikder

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This paper illustrates an application of granular computing approach, namely rough set theory in data mining. The paper outlines the formalism of granular computing and elucidates the mathematical underpinning of rough set theory, which has been widely used by the data mining and the machine learning community. A real-world application is illustrated, and the classification performance is compared with other contending machine learning algorithms. The predictive performance of the rough set rule induction model shows comparative success with respect to other contending algorithms.

Keywords: concept approximation, granular computing, reducts, rough set theory, rule induction

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Authors: Mahnaz Hosseinzadeh, Aliyeh Kazemi

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In this paper, a method is proposed for solving Fuzzy Multi-Objective Linear Programming problems (FMOLPP) with fuzzy right hand side and fuzzy decision variables. To illustrate the proposed method, it is applied to the problem of selecting suppliers for an automotive parts producer company in Iran in order to find the number of optimal orders allocated to each supplier considering the conflicting objectives. Finally, the obtained results are discussed.

Keywords: fuzzy multi-objective linear programming problems, triangular fuzzy numbers, fuzzy ranking, supplier selection problem

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Authors: Jolly Puri, Shiv Prasad Yadav

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Multi-component data envelopment analysis (MC-DEA) is a popular technique for measuring aggregate performance of the decision making units (DMUs) along with their components. However, the conventional MC-DEA is limited to crisp input and output data which may not always be available in exact form. In real life problems, data may be imprecise or fuzzy. Therefore, in this paper, we propose (i) a fuzzy MC-DEA (FMC-DEA) model in which shared and undesirable fuzzy resources are incorporated, (ii) the proposed FMC-DEA model is transformed into a pair of crisp models using cut approach, (iii) fuzzy aggregate performance of a DMU and fuzzy efficiencies of components are defined to be fuzzy numbers, and (iv) a numerical example is illustrated to validate the proposed approach.

Keywords: multi-component DEA, fuzzy multi-component DEA, fuzzy resources, decision making units (DMUs)

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Authors: Aliasghar Baziar, Hassan Masoumi, Alireza Ale Saadi

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The control of the response of electric motors plays a significant role in the damping of transient responses. In this regard, this paper presents a static VAR compensator (SVC) based on a fuzzy logic which is applied to an industrial power network consisting of three phase synchronous, asynchronous and DC motor loads. The speed and acceleration variations of a specific machine are the inputs of the proposed fuzzy logic controller (FLC). In order to verify the effectiveness and proficiency of the proposed Fuzzy Logic based SVC (FLSVC), several non-linear time-domain digital simulation tests are performed. The proposed fuzzy model can properly control the response of electric motors. The results show that the FLSVC is successful to improve the voltage profile significantly over a wide range of operating conditions and disturbances thus improving the overall dynamic performance of the network.

Keywords: fuzzy logic controller, VAR compensator, single cage asynchronous motor, DC motor

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Authors: O. Poleshchuk, E. Komarov

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This paper presents a regression model for interval type-2 fuzzy sets based on the least squares estimation technique. Unknown coefficients are assumed to be triangular fuzzy numbers. The basic idea is to determine aggregation intervals for type-1 fuzzy sets, membership functions of whose are low membership function and upper membership function of interval type-2 fuzzy set. These aggregation intervals were called weighted intervals. Low and upper membership functions of input and output interval type-2 fuzzy sets for developed regression models are considered as piecewise linear functions.

Keywords: interval type-2 fuzzy sets, fuzzy regression, weighted interval

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Authors: H. M. Al-Qassem, L. Cheng, Y. Pan

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In this paper we establish sharp bounds for oscillatory singular integrals with an arbitrary real polynomial phase P. Our kernels are allowed to be rough both on the unit sphere and in the radial direction. We show that the bounds grow no faster than log(deg(P)), which is optimal and was first obtained by Parissis and Papadimitrakis for kernels without any radial roughness. Among key ingredients of our methods are an L¹→L² estimate and extrapolation.

Keywords: oscillatory singular integral, rough kernel, singular integral, Orlicz spaces, Block spaces, extrapolation, L^{p} boundedness

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Authors: Rana Alghamdi

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This study explored teachers’ perceptions of rough-and-tumble (R&T) play in early childhood education in Saudi Arabia. The literature on rough-and-tumble play in Saudi Arabia is limited in scope, and more research is needed to explore teachers’ perceptions on this type of play for early learners. The pertinent literature reveals that R&T play, which includes running, jumping, fighting, wrestling, chasing, pulling, pushing, and climbing, among other rough playful activities, can positively impact learning and development across psychosocial, emotional, and cognitive domains. Teachers’ understanding of R & T play is key, and the attitudes of Saudi early childhood teachers who are responsible for implementing curriculum-based play have not been fully researched. Four early childhood teachers from an urban Saudi preschool participated in the study. The data collected in this study were interpreted through a sociocultural lens. Data sources included in-depth interviews, photo-elicitation interviews, and participant-generated drawings. Three overarching themes emerged: teachers’ concerns about rough-and-tumble play, teachers’ perceptions about the benefits of rough-and-tumble play, and teachers’ expression of gender roles in R & T play as contextualized within Saudi culture. Saudi teachers’ perceptions are discussed in detail, and implications of the findings and recommendations for future research are put forth.

Keywords: rough and tumble play, gender, culture, early childhood, Saudi Arabia

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Authors: Mihai Rebenciuc, Simona Mihaela Bibic

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Branch of modern mathematics, graphs represent instruments for optimization and solving practical applications in various fields such as economic networks, engineering, network optimization, the geometry of social action, generally, complex systems including contemporary urban problems (path or transport efficiencies, biourbanism, & c.). In this paper is studied the interconnection of some urban network, which can lead to a simulation problem of a digraph through another digraph. The simulation is made univoc or more general multivoc. The concepts of fragment and atom are very useful in the study of connectivity in the digraph that is simulation - including an alternative evaluation of k- connectivity. Rough set approach in (bi)digraph which is proposed in premier in this paper contribute to improved significantly the evaluation of k-connectivity. This rough set approach is based on generalized rough sets - basic facts are presented in this paper.

Keywords: (bi)digraphs, rough set theory, systems of interacting agents, complex systems

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Authors: Luiz F. J. Maia

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This paper presents an approach to fuzzy control, with the use of new pertinence functions, applied in the case of an inverted pendulum. Appropriate definitions of pertinence functions to fuzzy sets make possible the implementation of the controller with only one control rule, resulting in a smooth control surface. The fuzzy control system can be implemented with analog devices, affording a true real-time performance.

Keywords: control surface, fuzzy control, Inverted pendulum, pertinence functions

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Authors: R. S. Sheu, H. Usman, M. S. Lawal

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Takagi-Sugeno (T-S) fuzzy model based control of a load frequency deviation in a single machine with limit nonlinearity on power coefficient is presented in the paper. Two T-S fuzzy rules with only rotor angle variable as input in the premise part, and linear state space models in the consequent part involving characteristic matrices determined from limits set on the power coefficient constant are formulated, state feedback control gains for closed loop control was determined from the formulated Linear Matrix Inequality (LMI) with eigenvalue optimization scheme for asymptotic and exponential stability (speed of esponse). Numerical evaluation of the closed loop object was carried out in Matlab. Simulation results generated of both the open and closed loop system showed the effectiveness of the control scheme in maintaining load frequency stability.

Keywords: T-S fuzzy model, state feedback control, linear matrix inequality (LMI), frequency deviation control

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Authors: Tia Claridge

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The aim of this study was to explore whether there are gender differences in how early childhood educators view and facilitate rough and tumble play in England. A qualitative approach was used to carry out semi-structured interviews with female and male early years educators. The key rationale for this study was to examine the significant lack of males working in early years education and the consequent impact this has on pedagogical practice. The findings illustrated that there are some gender differences in educators’ perspectives of rough and tumble play. These include how educators use their own childhood experience to inform their professional practice as well as identifying a need for tailored training to upskill and develop confidence in early years staff with regard to this type of play. The most surprising finding was the influence that urban and rural settings had on educators’ perceptions on weapon play, regardless of gender. Awareness of educator positionality was significant throughout the study for male participants, whereas females rarely commented their own gender. These findings indicate that further research is needed to understand the complex narratives underpinning gender and rough and tumble play.

Keywords: rough and tumble play, educators, gender, early years, pedagogy

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Authors: Behnam Tavakkol

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Uncertain data mining algorithms use different ways to consider uncertainty in data such as by representing a data object as a sample of points or a probability distribution. Fuzzy methods have long been used for clustering traditional (certain) data objects. They are used to produce non-crisp cluster labels. For uncertain data, however, besides some uncertain fuzzy k-medoids algorithms, not many other fuzzy clustering methods have been developed. In this work, we develop a fuzzy kernel k-medoids algorithm for clustering uncertain data objects. The developed fuzzy kernel k-medoids algorithm is superior to existing fuzzy k-medoids algorithms in clustering data sets with non-linearly separable clusters.

Keywords: clustering algorithm, fuzzy methods, kernel k-medoids, uncertain data

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Authors: Tumadhir Fahim M Alsulami

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The concept of this paper builds on connecting between two important notions, fuzzy ideals of BCK-algebras and derivation of BCI-algebras. The result we got is a new concept called derivation fuzzy ideals of BCI-algebras. Followed by various results and important theorems on different types of ideals. In chapter 1: We presented the basic and fundamental concepts of BCK\ BCI- algebras as follows: BCK/BCI-algebras, BCK sub-algebras, bounded BCK-algebras, positive implicative BCK-algebras, commutative BCK-algebras, implicative BCK- algebras. Moreover, we discussed ideals of BCK-algebras, positive implicative ideals, implicative ideals and commutative ideals. In the last section of chapter 1 we proposed the notion of derivation of BCI-algebras, regular derivation of BCI-algebras and basic definitions and properties. In chapter 2: It includes 3 sections as follows: Section 1 contains elementary concepts of fuzzy sets and fuzzy set operations. Section 2 shows O. G. Xi idea, where he applies fuzzy sets concept to BCK-algebras and we studied fuzzy sub-algebras as well. Section 3 contains fuzzy ideals of BCK-algebras basic definitions, closed fuzzy ideals, fuzzy commutative ideals, fuzzy positive implicative ideals, fuzzy implicative ideals, fuzzy H-ideals and fuzzy p-ideals. Moreover, we investigated their concepts in diverse theorems and propositions. In chapter 3: The main concept of our thesis on derivation fuzzy ideals of BCI- algebras is introduced. Chapter 3 splits into 4 sections. We start with General definitions and important theorems on derivation fuzzy ideal theory in section 1. Section 2 and 3 contain derivations fuzzy p-ideals and derivations fuzzy H-ideals of BCI- algebras, several important theorems and propositions were introduced. The last section studied derivations fuzzy implicative ideals of BCI-algebras and it includes new theorems and results. Furthermore, we presented a new theorem that associate derivations fuzzy implicative ideals, derivations fuzzy positive implicative ideals and derivations fuzzy commutative ideals. These concepts and the new results were obtained and introduced in chapter 3 were submitted in two separated articles and accepted for publication.

Keywords: BCK, BCI, algebras, derivation

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Authors: A. M. Benomair, M. O. Tokhi

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This paper presents the investigation on a system model for the stabilization of a Magnetic Levitation System (Maglev’s). The magnetic levitation system is a challenging nonlinear mechatronic system in which an electromagnetic force is required to suspend an object (metal sphere) in air space. The electromagnetic force is very sensitive to the noise which can create acceleration forces on the metal sphere, causing the sphere to move into the unbalanced region. Maglev’s give the contribution in industry and this system has reduce the power consumption, has increase the power efficiency and reduce the cost maintenance. The common applications for Maglev’s Power Generation (e.g. wind turbine), Maglev’s trains and Medical Device (e.g. Magnetically suspended Artificial Heart Pump). This paper presents the comparison between dynamic response and robust characteristic for both conventional PD and Fuzzy PD controller. The main contribution of this paper is the proof of fuzzy PD type stabilization and robustness. By use of a method to tune the scaling factors of the linear PD type fuzzy controller from an equivalent tuned conventional PD.

Keywords: magnetic levitation system, PD controller, Fuzzy Logic Control, Fuzzy PD

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Authors: H. Al-Qassem, L. Cheng, Y. Pan

Abstract:

In this paper, we establish sharp bounds for oscillatory singular integrals with an arbitrary real polynomial phase P. Our kernels are allowed to be rough both on the unit sphere and in the radial direction. We show that the bounds grow no faster than log (deg(P)), which is optimal and was first obtained by Parissis and Papadimitrakis for kernels without any radial roughness. Our results substantially improve many previously known results. Among key ingredients of our methods are an L¹→L² sharp estimate and using extrapolation.

Keywords: oscillatory singular integral, rough kernel, singular integral, orlicz spaces, block spaces, extrapolation, L^{p} boundedness

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Authors: Awais Asif

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This article investigates fixed point theorems of Chatterjea type F-contraction in the setting of F-metric space. We relax the conditions of F-contraction and define modified F-contraction for two mappings. The study provides fixed point results for both single-valued and multivalued mappings. The results are further extended to common fixed point theorems for two mappings. Moreover, to discuss the applicability of our results, an application is provided, which shows the role of our results in finding the solution to functional equations in dynamic programming. Our results generalize and extend the existing results in the literature.

Keywords: Chatterjea type F-contraction, F-cauchy sequence, F-convergent, multi valued mappings

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Authors: Oktay Nusratov, Ramin Rzaev, Aydin Goyushov

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Fuzzy inference method based approach to the forming of modular intellectual system of assessment the quality of communication services is proposed. Developed under this approach the basic fuzzy estimation model takes into account the recommendations of the International Telecommunication Union in respect of the operation of packet switching networks based on IP-protocol. To implement the main features and functions of the fuzzy control system of quality telecommunication services it is used multilayer feedforward neural network.

Keywords: quality of communication, IP-telephony, fuzzy set, fuzzy implication, neural network

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Authors: G. S. Thakur

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This paper presents a Fuzzy Soft Recruitment Model (FSRM) for faculty selection of MHRD technical institutions. The selection criteria are based on 4-tier flexible structure in the institutions. The Advisory Committee on Faculty Recruitment (ACoFAR) suggested nine criteria for faculty in the proposed FSRM. The model Fuzzy Soft is proposed with consultation of ACoFAR based on selection criteria. The Fuzzy Soft distance similarity measures are applied for finding best faculty from the applicant pool.

Keywords: fuzzy soft set, fuzzy sets, fuzzy soft distance, fuzzy soft similarity measures, ACoFAR

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Authors: Jun-Ho Chung, Sung-Hyun Yoo, In-Hwan Choi, Hyun-Kook Lee, Moon-Kyu Song, Choon-Ki Ahn

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The extended finite impulse response (EFIR) filter is addressed to optimize membership functions (MFs) of the fuzzy model that has strong nonlinearity. MFs are important parts of the fuzzy logic system (FLS) and, thus optimizing MFs of FLS is one of approaches to improve the performance of output. We employ the EFIR as an alternative optimization option to nonlinear fuzzy model. The performance of EFIR is demonstrated on a fuzzy cruise control via a numerical example.

Keywords: fuzzy logic system, optimization, membership function, extended FIR filter

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Authors: Walied Hanora

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This paper presents the problem of robust state feedback H∞ for discrete time nonlinear system represented by Takagi-Sugeno fuzzy systems. Based on fuzzy lyapunov function, the condition ,which is represented in the form of Liner Matrix Inequalities (LMI), guarantees the H∞ performance of the T-S fuzzy system with uncertainties. By comparison with recent literature, this approach will be more relaxed condition. Finally, an example is given to illustrate the proposed result.

Keywords: fuzzy lyapunov function, H∞ control , linear matrix inequalities, state feedback, T-S fuzzy systems

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Authors: Purnima Pandit

Abstract:

Malaria remains one of the world’s most deadly infectious disease and arguably, the greatest menace to modern society in terms of morbidity and mortality. To choose the right treatment and to ensure a quality of life suitable for a specific patient condition, early and accurate diagnosis of malaria is essential. It reduces transmission of disease and prevents deaths. Our work focuses on designing an efficient, accurate fuzzy inference system for malaria diagnosis.

Keywords: fuzzy inference system, fuzzy logic, malaria disease, triangular fuzzy number

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Authors: M. Y. Bakeir

Abstract:

Rough set theory is a recent approach for reasoning about data. It has achieved a large amount of applications in various real-life fields. The main idea of rough sets corresponds to the lower and upper set approximations. These two approximations are exactly the interior and the closure of the set with respect to a certain topology on a collection U of imprecise data acquired from any real-life field. The base of the topology is formed by equivalence classes of an equivalence relation E defined on U using the available information about data. The theory of generalized topology was studied by Cs´asz´ar. It is well known that generalized topology in the sense of Cs´asz´ar is a generalization of the topology on a set. On the other hand, many important collections of sets related with the topology on a set form a generalized topology. The notion of Nano topology was introduced by Lellis Thivagar, which was defined in terms of approximations and boundary region of a subset of an universe using an equivalence relation on it. The purpose of this paper is to introduce a new generalized topology in terms of rough set called nano generalized topology

Keywords: rough sets, topological space, generalized topology, nano topology

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Authors: Arindam Chaudhuri

Abstract:

Classification of data has been actively used for most effective and efficient means of conveying knowledge and information to users. The prima face has always been upon techniques for extracting useful knowledge from data such that returns are maximized. With emergence of huge datasets the existing classification techniques often fail to produce desirable results. The challenge lies in analyzing and understanding characteristics of massive data sets by retrieving useful geometric and statistical patterns. We propose a supervised parallel fuzzy rough support vector machine (PFRSVM) for data classification in cloud environment. The classification is performed by PFRSVM using hyperbolic tangent kernel. The fuzzy rough set model takes care of sensitiveness of noisy samples and handles impreciseness in training samples bringing robustness to results. The membership function is function of center and radius of each class in feature space and is represented with kernel. It plays an important role towards sampling the decision surface. The success of PFRSVM is governed by choosing appropriate parameter values. The training samples are either linear or nonlinear separable. The different input points make unique contributions to decision surface. The algorithm is parallelized with a view to reduce training times. The system is built on support vector machine library using Hadoop implementation of MapReduce. The algorithm is tested on large data sets to check its feasibility and convergence. The performance of classifier is also assessed in terms of number of support vectors. The challenges encountered towards implementing big data classification in machine learning frameworks are also discussed. The experiments are done on the cloud environment available at University of Technology and Management, India. The results are illustrated for Gaussian RBF and Bayesian kernels. The effect of variability in prediction and generalization of PFRSVM is examined with respect to values of parameter C. It effectively resolves outliers’ effects, imbalance and overlapping class problems, normalizes to unseen data and relaxes dependency between features and labels. The average classification accuracy for PFRSVM is better than other classifiers for both Gaussian RBF and Bayesian kernels. The experimental results on both synthetic and real data sets clearly demonstrate the superiority of the proposed technique.

Keywords: FRSVM, Hadoop, MapReduce, PFRSVM

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