Search results for: fuzzy mathematics

Authors: Javad Rahimipour Anaraki, Saeed Samet, Mahdi Eftekhari, Chang Wook Ahn

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Feature selection and attribute reduction are crucial problems, and widely used techniques in the field of machine learning, data mining and pattern recognition to overcome the well-known phenomenon of the Curse of Dimensionality. This paper presents a feature selection method that efficiently carries out attribute reduction, thereby selecting the most informative features of a dataset. It consists of two components: 1) a measure for feature subset evaluation, and 2) a search strategy. For the evaluation measure, we have employed the fuzzy-rough dependency degree (FRFDD) of the lower approximation-based fuzzy-rough feature selection (L-FRFS) due to its effectiveness in feature selection. As for the search strategy, a modified version of a binary shuffled frog leaping algorithm is proposed (B-SFLA). The proposed feature selection method is obtained by hybridizing the B-SFLA with the FRDD. Nine classifiers have been employed to compare the proposed approach with several existing methods over twenty two datasets, including nine high dimensional and large ones, from the UCI repository. The experimental results demonstrate that the B-SFLA approach significantly outperforms other metaheuristic methods in terms of the number of selected features and the classification accuracy.

Keywords: binary shuffled frog leaping algorithm, feature selection, fuzzy-rough set, minimal reduct

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Authors: Abhimanyu Kumar, Chirag Gupta

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This work presents a comprehensive study on the employment of Model Predictive Control (MPC) for a three-phase voltage-source inverter to regulate the output voltage efficiently. The inverter is modeled via the Clarke Transformation, considering a scenario where the load is unknown. An LC filter model is developed, demonstrating its efficacy in Total Harmonic Distortion (THD) reduction. The system, when implemented with fault-tolerant multilevel inverter topologies, ensures reliable operation even under fault conditions, a requirement that is paramount with the increasing dependence on renewable energy sources. The research also integrates a Fuzzy Logic based fault tolerance system which identifies and manages faults, ensuring consistent inverter performance. The efficacy of the proposed methodology is substantiated through rigorous simulations and comparative results, shedding light on the voltage prediction efficiency and the robustness of the model even under fault conditions.

Keywords: total harmonic distortion, fuzzy logic, renewable energy sources, MLI

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Authors: Asadullah Sheikh, Kerry Barnett, Paul Ayres

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Despite significant progress in access, equity and public examination success, poor student performance in mathematics in secondary schools has become a major concern in Bangladesh. A substantial body of research has emphasised the important contribution of teaching practices to student achievement. However, this has not been investigated in Bangladesh. Therefore, the study sought to find out the effectiveness of mathematics teaching practices as a means of improving secondary school mathematics in Dhaka Municipality City (DMC) area, Bangladesh. The purpose of this study was twofold, first, to identify the 20 highest performing secondary schools in mathematics in DMC, and second, to investigate the teaching practices of mathematics teachers in these schools. A two-phase mixed method approach was adopted. In the first phase, secondary source data were obtained from the Board of Intermediate and Secondary Education (BISE), Dhaka and value-added measures used to identify the 20 highest performing secondary schools in mathematics. In the second phase, a concurrent mixed method design, where qualitative methods were embedded within a dominant quantitative approach was utilised. A purposive sampling strategy was used to select fifteen teachers from the 20 highest performing secondary schools. The main sources of data were classroom teaching observations, and teacher interviews. The data from teacher observations were analysed with descriptive and nonparametric statistics. The interview data were analysed qualitatively. The main findings showed teachers adopt a direct teaching approach which incorporates orientation, structuring, modelling, practice, questioning and teacher-student interaction that creates an individualistic learning environment. The variation in developmental levels of teaching skill indicate that teachers do not necessarily use the qualitative (i.e., focus, stage, quality and differentiation) aspects of teaching behaviours effectively. This is the first study to investigate teaching behaviours of effective secondary mathematics teachers within Dhaka, Bangladesh. It contributes in an international dimension to the field of educational effectiveness and raise questions about existing constructivist approaches. Further, it contributes to important insights about teaching behaviours that can be used to inform the development of evidence-based policy and practice on quality teaching in Bangladesh.

Keywords: effective teaching, mathematics, secondary schools, student achievement, value-added measures

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Authors: Theresa Marie Miller, Ma. Nympha Joaquin

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The aim of this study was to check the predictive power of social-oriented and individual-oriented achievement motivation on student engagement and collaborative problem-solving skills in mathematics. A sample of 277 fourth year high school students from the Philippines were selected. Surveys and videos of collaborative problem solving activity were used to collect data from respondents. The mathematics teachers of the participants were interviewed to provide qualitative support on the data. Systemaitc correlation and regression analysis were employed. Results of the study showed that achievement motivations−SOAM and IOAM− linearly predicted student engagement but was not significantly associated to the collaborative problem-solving skills in mathematics. Student engagement correlated positively with collaborative problem-solving skills in mathematics. The results contribute to theorizing about the predictive power of achievement motivations, SOAM and IOAM on the realm of academic behaviors and outcomes as well as extend the understanding of collaborative problem-solving skills of 21st century learners.

Keywords: achievement motivation, collaborative problem-solving skills, individual-oriented achievement motivation, social-oriented achievement motivation, student engagement

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Authors: Ali Taher Othman Ali

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The aim of this research is to provide a draft proposal for the professional development of mathematics teachers in accordance with the orientation of science, technology, engineering and mathematics which is known by the abbreviation STEM, as a modern and contemporary orientation in the teaching and learning of mathematics and in order to achieve the objective of the research, the researcher used the theoretical descriptive method through the induction of the literature of education and the previous studies and experiments related to the topic. The researcher concluded by providing the proposal according to five basic axes, the first axe: professional development as a system, and its requirements include: development of educational systems, and allocate sufficient budgets to support the requirements of teaching STEM, identifying mechanisms for incentives and rewards for teachers attending professional development programs based on STEM; the second: development of in-depth knowledge content and its requirements include: basic sciences content development for STEM, linking the scientific understanding of teachers with real-world issues and problems, to provide the necessary resources to expand teachers' knowledge in this area; the third: the necessary pedagogical skills of teachers in the field of STEM, and its requirements include: identification of the required training and development needs and the mechanism of determining these needs, the types of professional development programs and the mechanism of designing it, the mechanisms and places of execution, evaluation and follow-up; the fourth: professional development strategies and mechanisms in the field of STEM, and its requirements include: using a variety of strategies to enable teachers to design and transfer effective educational experiences which reflect their scientific mastery in the fields of STEM, provide learning opportunities, and developing the skills of procedural research to generate new knowledge about the STEM; the fifth: to support professional development in the area of STEM, and its requirements include: support leadership within the school, provide a clear and appropriate opportunities for professional development for teachers within the school through professional learning communities, building partnerships between the Ministry of education and the local and international community institutions. The proposal includes other factors that should be considered when implementing professional development programs for mathematics teachers in the field of STEM.

Keywords: professional development, mathematics teachers, the orientation of science, technology, engineering and mathematics (STEM)

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Authors: Tanveer Hussain, Khan Muhammad, Amin Ullah, Mi Young Lee, Sung Wook Baik

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The Big Data generated from distributed vision sensors installed on large scale in smart cities create hurdles in its efficient and beneficial exploration for browsing, retrieval, and indexing. This paper presents a three-folded framework for effective video summarization of such data and provide a compact and representative format of Big Video Data. In the first fold, the paper acquires input video data from the installed cameras and collect clues such as type and count of objects and clarity of the view from a chunk of pre-defined number of frames of each view. The decision of representative view selection for a particular interval is based on fuzzy inference system, acquiring a precise and human resembling decision, reinforced by the known clues as a part of the second fold. In the third fold, the paper forwards the selected view frames to the summary generation mechanism that is supported by a saliency-aware convolution neural network (CNN) model. The new trend of fuzzy rules for view selection followed by CNN architecture for saliency computation makes the multi-view video summarization (MVS) framework a suitable candidate for real-world practice in smart cities.

Keywords: big video data analysis, fuzzy logic, multi-view video summarization, saliency detection

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Authors: Juanita Morris

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The purpose of this study will examine the mediating relationships between the theories of intelligence, mathematics anxiety, gender stereotype threat, meta-cognition and math performance through the use of eye tracking technology, affecting student perception and problem-solving abilities. The participants will consist of (N=80) female graduate students. Test administered were the Abbreviated Math Anxiety Scale, Tobii Eye Tracking software, gender stereotype threat through Google images, and they will be asked to describe their problem-solving approach allowed to measure metacognition. Participants will be administered mathematics problems while having gender stereotype threat shown to them through online images while being directed to look at the eye tracking software Tobii. We will explore this by asking ‘Is mathematics anxiety associated with the theories of intelligence and gender stereotype threat and how does metacognition and math performance place a role in mediating those perspectives?’. It is hypothesized that math-anxious students are more likely affected by the gender stereotype threat and that may play a role in their performance? Furthermore, we also want to explore whether math anxious students are more likely to be an entity theorist than incremental theorist and whether those who are math anxious will be more likely to be fixated on variables associated with coefficients? Path analysis and independent samples t-test will be used to generate results for this study. We hope to conclude that both the theories of intelligence and metacognition mediate the relationship between mathematics anxiety and gender stereotype threat.

Keywords: math anxiety, emotions, affective domains fo learning, cognitive underlinings

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Authors: Ezeamagu M.U, Madu B.C

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This study was designed to investigate the efficacy of 5Es constructivist-based instructional model on students’ retention in primary Mathematics. 5Es stands for Engagement, Exploration, Explanation, Elaboration and Evaluation. The study adopted the pre test post test non-equivalent control group quasi-experimental research design. The sample size for the study was one hundred and thirty four pupils (134), seventy six male (76) and fifty eight female (58) from two primary schools in Nsukka education zone. Two intact classes in each of the sampled schools comprising all the primary four pupils were used. Each of the schools was given the opportunity of being assigned randomly to either experimental or control group. The Experimental group was taught using 5Es model while the control group was taught using the conventional method. Two research questions were formulated to guide the study and three hypotheses were tested at p ≤ 0. 05. A Fraction Achievement Test (FAT) of ten (10) questions were used to obtain data on pupils’ retention. Research questions were answered using mean and standard deviation while hypotheses were tested using analysis of covariance (ANCOVA). The result revealed that the 5Es model was more effective than the conventional method of teaching in enhancing pupils’ performance and retention in mathematics, secondly there is no significant difference in the mean retention scores of male and female students taught using 5Es instructional model. Based on the findings, it was recommended among other things, that the 5Es instructional model should be adopted in the teaching of mathematics in primary level of the educational system. Seminar, workshops and conferences should be mounted by professional bodies, federal and state ministries of education on the use of 5Es model. This will enable the mathematics educator, serving teachers, students and all to benefit from the approach.

Keywords: constructivist, education, mathematics, primary, retention

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Authors: Early Sol A. Gadong, Lourdes C. Zamora, Jonny B. Pornel, Aurora Fe C. Bautista

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Various research has shown that writing allows students to engage in metacognition and provides them with a venue to communicate their disposition towards what they are learning. However, few studies have explored students’ feelings about the incorporation of such writing activities in their mathematics classes. Through reflection sheets, group discussions, and interviews, this mixed-methods study explored students’ perceptions and insights on supplementary writing activities in their Elementary Algebra class. Findings revealed that while students generally have a positive regard for writing activities, they have conflicting views about how writing activities can help them in their learning. A big majority contend that writing activities can enhance the learning of mathematical content and attitudes towards mathematics if they allow students to explore and synthesize what they have learned and reflected on their emotional disposition towards mathematics. Also, gender does not appear to play a significant role in students’ reactions to writing activities.

Keywords: writing in math, metacognition, affective factors in learning, elementary algebra classroom

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Authors: DoHyeung Kim, DaeHee Seo, ByungDoo Kim, ByungGil Lee

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As many recent researches being implemented in aviation and maritime aspects, strong doubts have been raised concerning the reliability of the estimation of collision risk. It is shown that using position and velocity of objects can lead to imprecise results. In this paper, therefore, a new approach to the estimation of collision risks using pose and shape of objects is proposed. Simulation results are presented validating the accuracy of the new criterion to adapt to collision risk algorithm based on fuzzy logic.

Keywords: collision risk, pose, shape, fuzzy logic

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Authors: Oveis Abedinia, Noradin Ghadimi, Nasser Mikaeilvand, Roza Poursoleiman, Asghar Poorfaraj

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In this paper a robust Fuzzy Proportional Integral Differential (PID) controller is applied to multi-machine power system based on Modified Shuffled Frog Leaping (MSFL) algorithm. This newly proposed controller is more efficient because it copes with oscillations and different operating points. In this strategy the gains of the PID controller is optimized using the proposed technique. The nonlinear problem is formulated as an optimization problem for wide ranges of operating conditions using the MSFL algorithm. The simulation results demonstrate the effectiveness, good robustness and validity of the proposed method through some performance indices such as ITAE and FD under wide ranges operating conditions in comparison with TS and GSA techniques. The single-machine infinite bus system and New England 10-unit 39-bus standard power system are employed to illustrate the performance of the proposed method.

Keywords: fuzzy PID, MSFL, multi-machine, low frequency oscillation

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Authors: Ali Rashash Alzahrani, Elizabeth Stojanovski

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Data on various aspects of education are collected at the institutional and government level regularly. In Australia, for example, students at various levels of schooling undertake examinations in numeracy and literacy as part of NAPLAN testing, enabling longitudinal assessment of such data as well as comparisons between schools and states within Australia. Another source of educational data collected internationally is via the PISA study which collects data from several countries when students are approximately 15 years of age and enables comparisons in the performance of science, mathematics and English between countries as well as ranking of countries based on performance in these standardised tests. As well as student and school outcomes based on the tests taken as part of the PISA study, there is a wealth of other data collected in the study including parental demographics data and data related to teaching strategies used by educators. Overall, an abundance of educational data is available which has the potential to be used to help improve educational attainment and teaching of content in order to improve learning outcomes. A multivariate assessment of such data enables multiple variables to be considered simultaneously and will be used in the present study to help develop profiles of students based on performance in mathematics using data obtained from the PISA study.

Keywords: cluster analysis, education, mathematics, profiles

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Authors: Vahid Anari, Mina Bakhshi

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Visual search and identification of immunohistochemically stained tissue of meningioma was performed manually in pathologic laboratories to detect and diagnose the cancers type of meningioma. This task is very tedious and time-consuming. Moreover, because of cell's complex nature, it still remains a challenging task to segment cells from its background and analyze them automatically. In this paper, we develop and test a computerized scheme that can automatically identify cells in microscopic images of meningioma and classify them into positive (proliferative) and negative (normal) cells. Dataset including 150 images are used to test the scheme. The scheme uses Fuzzy C-means algorithm as a color clustering method based on perceptually uniform hue, saturation, value (HSV) color space. Since the cells are distinguishable by the human eye, the accuracy and stability of the algorithm are quantitatively compared through application to a wide variety of real images.

Keywords: positive cell, color segmentation, HSV color space, immunohistochemistry, meningioma, thresholding, fuzzy c-means

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Authors: Emmanuel Iyamuremye, Irenee Ndayambaje

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This study investigated the influence of Concrete Pictorial Abstract (CPA) teaching approach on mathematics achievement based on a sample of eighth-grade students (N = 10,345) from the Rwandan Lower Secondary School quasi-experimental study with pre-test and post-test control group of 2019 (RLSQES19). Key aspects studied included mathematics concept understanding and mathematics concept retention and how these are influenced by teacher's teaching approach. Specifically, the study aimed to a.) investigate students' concept understanding and concept retention in mathematics when exposed to CPA approach and to those exposed to non-CPA approach before and after the intervention, and b.) ascertain the significant difference between the performance of the students exposed to CPA approach and those exposed to non-CPA approach in terms of post-test scores and retention test scores. Two groups (control and experimental) undergone pre-test, post-test, and retention test. The assignment of control and experimental group among senior two classes from 10 schools was done randomly. The materials used to determine the performance of the students is a teacher-made test. Descriptive statistics and ANCOVA were used for the analysis of the study. For determining the improvement in concept understanding of mathematics, Hakes methods of calculating gain were used to analyze the pre-test and post test score. The level of performance of the two groups in the pre-test is below average level. During the post-test and retention test, the performance of students in non-CPA group is on average level, and students in CPA group are on above average level. Hakes methods of calculating gain revealed higher significant performance in the post-test and retention test of CPA group of students than non-CPA group of students.

Keywords: concept understanding, concept retention, performance, teaching approach

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Authors: Hemad Zareiforoush, Saeed Minaei, Ahmad Banakar, Mohammad Reza Alizadeh

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The quality inspection of rice (Oryza sativa L.) during its various processing stages is very important. In this research, an artificial intelligence-based model coupled with computer vision techniques was developed as a decision support system for qualitative grading of rice grains. For conducting the experiments, first, 25 samples of rice grains with different levels of percentage of broken kernels (PBK) and degree of milling (DOM) were prepared and their qualitative grade was assessed by experienced experts. Then, the quality parameters of the same samples examined by experts were determined using a machine vision system. A grading model was developed based on fuzzy logic theory in MATLAB software for making a relationship between the qualitative characteristics of the product and its quality. Totally, 25 rules were used for qualitative grading based on AND operator and Mamdani inference system. The fuzzy inference system was consisted of two input linguistic variables namely, DOM and PBK, which were obtained by the machine vision system, and one output variable (quality of the product). The model output was finally defuzzified using Center of Maximum (COM) method. In order to evaluate the developed model, the output of the fuzzy system was compared with experts’ assessments. It was revealed that the developed model can estimate the qualitative grade of the product with an accuracy of 95.74%.

Keywords: machine vision, fuzzy logic, rice, quality

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Authors: Ben Khayut, Lina Fabri, Maya Avikhana

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The models of the modern Artificial Narrow Intelligence (ANI) cannot: a) independently and continuously function without of human intelligence, used for retraining and reprogramming the ANI’s models, and b) think, understand, be conscious, cognize, infer, and more in state of Uncertainty, and changes in situations, and environmental objects. To eliminate these shortcomings and build a new generation of Artificial Intelligence systems, the paper proposes a Conception, Model, and Method of Computational Psycholinguistic Cognitive Situational-Fuzzy Self-Controlled Brain and Mind System (CPCSFSCBMSUU) using a neural network as its computational memory, operating under uncertainty, and activating its functions by perception, identification of real objects, fuzzy situational control, forming images of these objects, modeling their psychological, linguistic, cognitive, and neural values of properties and features, the meanings of which are identified, interpreted, generated, and formed taking into account the identified subject area, using the data, information, knowledge, and images, accumulated in the Memory. The functioning of the CPCSFSCBMSUU is carried out by its subsystems of the: fuzzy situational control of all processes, computational perception, identifying of reactions and actions, Psycholinguistic Cognitive Fuzzy Logical Inference, Decision making, Reasoning, Systems Thinking, Planning, Awareness, Consciousness, Cognition, Intuition, Wisdom, analysis and processing of the psycholinguistic, subject, visual, signal, sound and other objects, accumulation and using the data, information and knowledge in the Memory, communication, and interaction with other computing systems, robots and humans in order of solving the joint tasks. To investigate the functional processes of the proposed system, the principles of Situational Control, Fuzzy Logic, Psycholinguistics, Informatics, and modern possibilities of Data Science were applied. The proposed self-controlled System of Brain and Mind is oriented on use as a plug-in in multilingual subject Applications.

Keywords: computational brain, mind, psycholinguistic, system, under uncertainty

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Authors: Sadık Ata, Kevser Dincer

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In this study, the performance of proton exchange membrane (PEM) fuel cell was experimentally investigated and modelled with Rule-Based Mamdani-Type Fuzzy (RBMTF) modelling technique. Coating on the anode side of the PEM fuel cell was accomplished with the spin method by using Yttria-stabilized zirconia (YSZ). Input-output parameters were described by RBMTF if-then rules. Numerical parameters of input and output variables were fuzzificated as linguistic variables: Very Very Low (L1), Very Low (L2), Low (L3), Negative Medium (L4), Medium (L5), Positive Medium (L6),High (L7), Very High (L8) and Very Very High (L9) linguistic classes. The comparison between experimental data and RBMTF is done by using statistical methods like absolute fraction of variance (R2). The actual values and RBMTF results indicated that RBMTF can be successfully used for the analysis of performance PEM fuel cell.

Keywords: proton exchange membrane (PEM), fuel cell, rule-based mamdani-type fuzzy (RMBTF) modelling, Yttria-stabilized zirconia (YSZ)

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Authors: J. Al-Dmour, A. Sagahyroon, A. Al-Ali, S. Abusnana

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Radio Frequency Based Identification Systems have emerged as one of the possible valuable solutions that can be utilized in healthcare systems. Nowadays, RFID tags are available with built-in human vital signs sensors such as Body Temperature, Blood Pressure, Heart Rate, Blood Sugar level and Oxygen Saturation in Blood. This work proposes the design, implementation, and testing of an integrated mobile RFID-based health care system. The system consists of a wireless mobile vital signs data acquisition unit (RFID-DAQ) integrated with a fuzzy-logic–based software algorithm to monitor and assess patients conditions. The system is implemented and tested in ‘Rashid Center for Diabetes and Research’, Ajman, UAE. System testing results are compared with the Modified Early Warning System (MEWS) that is currently used in practice. We demonstrate that the proposed and implemented system exhibits an accuracy level that is comparable and sometimes better than the widely adopted MEWS system.

Keywords: healthcare, fuzzy logic, MEWS, RFID

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Authors: Abderrahim Siam, Ramdane Maamri, Zaidi Sahnoun

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The development of adaptive user interfaces (UI) presents for a long time an important research area in which researcher attempt to call upon the full resources and skills of several disciplines. The adaptive UI community holds a thorough knowledge regarding the adaptation of UIs with users and with contexts of use. Several solutions, models, formalisms, techniques, and mechanisms were proposed to develop adaptive UI. In this paper, we propose an approach based on the fuzzy set theory for modeling the concept of the appropriateness of different solutions of UI adaptation with different situations for which interactive systems have to adapt their UIs.

Keywords: adaptive user interfaces, adaptation solution’s appropriateness, fuzzy sets

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Authors: H. Naseh, M. Mirshams, M. Mirdamadian, H. R. Fazeley

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This paper presents an extension of fuzzy-genetic algorithm multi-objective optimization methodology that could effectively be used to find the overall satisfaction of objective functions (selecting the design variables) in the early stages of design process. The coupling of objective functions due to design variables in an engineering design process will result in difficulties in design optimization problems. In many cases, decision making on design variables conflicts with more than one discipline in system design. In space launch system conceptual design, decision making on some design variable (e.g. oxidizer to fuel mass flow rate O/F) in early stages of the design process is related to objective of liquid propellant engine (specific impulse) and Tanks (structure weight). Then, the primary application of this methodology is the design of a liquid propellant engine with the maximum specific impulse and cylindrical stiffened tank with the minimum weight. To this end, the design problem is established the fuzzy rule set based on designer's expert knowledge with a holistic approach. The independent design variables in this model are oxidizer to fuel mass flow rate, thickness of stringers, thickness of rings, shell thickness. To handle the mentioned problems, a fuzzy-genetic algorithm multi-objective optimization methodology is developed based on Pareto optimal set. Consequently, this methodology is modeled with the one stage of space launch system to illustrate accuracy and efficiency of proposed methodology.

Keywords: cylindrical stiffened tanks, multi-objective, genetic algorithm, fuzzy approach

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Authors: Carol Okigbo

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Mathematical problem solving has long been accorded an important place in mathematics curricula at every education level in both advanced and emerging economies. Its classroom approaches have varied, such as teaching for problem-solving, teaching about problem-solving, and teaching mathematics through problem-solving. It requires engaging in tasks for which the solution methods are not eminent, making sense of problems and persevering in solving them by exhibiting processes, strategies, appropriate attitude, and adequate exposure. Teachers play important roles in helping students acquire competency in problem-solving; thus, they are expected to be good problem-solvers and have proper conceptions of problem-solving. Studies show that teachers’ conceptions influence their decisions about what to teach and how to teach. Therefore, how teachers view their roles in teaching problem-solving will depend on their pedagogical conceptions of problem-solving. If teaching problem-solving is a major component of secondary school mathematics instruction, as recommended by researchers and mathematics educators, then it is necessary to establish teachers’ conceptions, what they do, and how they approach problem-solving. This study is designed to determine secondary school teachers’ conceptions regarding mathematical problem solving, its current situation, how teachers’ conceptions relate to their demographics, as well as the interaction patterns in the mathematics classroom. There have been many studies of mathematics problem solving, some of which addressed teachers’ conceptions using single-method approaches, thereby presenting only limited views of this important phenomenon. To address the problem more holistically, this study adopted an integrated mixed methods approach which involved a quantitative survey, qualitative analysis of open-ended responses, and ethnographic observations of teachers in class. Data for the analysis came from a random sample of 327 secondary school mathematics teachers in two Nigerian states - Anambra State and Enugu State who completed a 45-item questionnaire. Ten of the items elicited demographic information, 11 items were open-ended questions, and 25 items were Likert-type questions. Of the 327 teachers who responded to the questionnaires, 37 were randomly selected and observed in their classes. Data analysis using ANOVA, t-tests, chi-square tests, and open coding showed that the teachers had different conceptions about problem-solving, which fall into three main themes: practice on exercises and word application problems, a process of solving mathematical problems, and a way of teaching mathematics. Teachers reported that no period is set aside for problem-solving; typically, teachers solve problems on the board, teach problem-solving strategies, and allow students time to struggle with problems on their own. The result shows a significant difference between male and female teachers’ conception of problems solving, a significant relationship among teachers’ conceptions and academic qualifications, and teachers who have spent ten years or more teaching mathematics were significantly different from the group with seven to nine years of experience in terms of their conceptions of problem-solving.

Keywords: conceptions, education, mathematics, problem solving, teacher

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Authors: Mohamed A. Moustafa Hassan, Omnia S .S. Hussian, Hany M. Elsaved

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This paper introduces the application of Fuzzy Logic Controller (FLC) to extract the Maximum Power Point Tracking (MPPT) from the PV panel. In addition, the proportional integral (PI) controller is used to be the strategy for battery charge control according to acceptable performance criteria. The parameters of the PI controller have been tuned via Modified Adaptive Accelerated Coefficient Particle Swarm Optimization (MAACPSO) technique. The simulation results, using MATLAB/Simulink tools, show that the FLC technique has advantages for use in the MPPT problem, as it provides a fast response under changes in environmental conditions such as radiation and temperature. In addition, the use of PI controller based on MAACPSO results in a good performance in terms of controlling battery charging with constant voltage and current to execute rapid charging.

Keywords: battery charging, fuzzy logic control, maximum power point tracking, PV system, PI controller, evolutionary technique

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Authors: Ayşegül Çabuk, Mine Işıksal

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Mathematics is a sense-making activity so that it requires meaningful learning. Hence based on this idea, meaningful mathematical connections are necessary to learn mathematics. At that point, the major question has become that which educational methods can provide opportunities to provide mathematical connections and to understand mathematics. The amalgam of reasoning and proof can be the one of the methods that creates opportunities to learn mathematics in a meaningful way. However, even if reasoning and proof should be included from prekindergarten to grade 12, studies in literature generally include secondary school students and pre-service mathematics teachers. With the light of the idea that the amalgam of reasoning and proof has significant effect on middle school students' mathematical learning, this study aims to investigate middle grade students' tendencies while reasoning the correctness of statements related to numbers. The sample included 272 middle grade students, specifically 69 of them were sixth grade students (25.4%), 101 of them were seventh grade students (37.1%) and 102 of them were eighth grade students (37.5%). Data was gathered through an achievement test including 2 essay types of problems about algebra. The answers of two items were analyzed both quantitatively and qualitatively in terms of students' solutions strategies while reasoning the correctness of the statements. Similar on the findings in the literature, most of the students, in all grade levels, used numerical examples to judge the statements. Moreover the results also showed that the majority of these students appear to believe that providing one or more selected examples is sufficient to show the correctness of the statement. Hence based on the findings of the study, even students in earlier ages have proving and reasoning abilities their reasoning's generally based on the empirical evidences. Therefore, it is suggested that examples and example-based reasoning can be a fundamental role on to generate systematical reasoning and proof insight in earlier ages.

Keywords: reasoning, mathematics learning, middle grade students

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Authors: Danielle Sandler dos Passos, Helder Coelho, Flávia Mori Sarti

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Analysing the world banking sector, we realize that traditional risk measurement methodologies no longer reflect the actual scenario with uncertainty and leave out events that can change the dynamics of markets. Considering this, regulators and financial institutions began to search more realistic models. The aim is to include external influences and interdependencies between agents, to describe and measure the operationalization of these complex systems and their risks in a more coherent and credible way. Within this context, X-Events are more frequent than assumed and, with uncertainties and constant changes, the concept of antifragility starts to gain great prominence in comparison to others methodologies of risk management. It is very useful to analyse whether a system succumbs (fragile), resists (robust) or gets benefits (antifragile) from disorder and stress. Thus, this work proposes the creation of the Banking Antifragility Index (BAI), which is based on the calculation of a triangular fuzzy number – to "quantify" qualitative criteria linked to antifragility.

Keywords: adaptive complex systems, X-Events, risk management, antifragility, banking antifragility index, triangular fuzzy number

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Authors: Zahid Ullah, Atlas Khan

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In today's data-driven world, the role of mathematics in bridging the gap between theory and applications is becoming increasingly vital. This abstract highlights the significance of mathematics as a powerful tool for analyzing, interpreting, and extracting meaningful insights from vast amounts of data. By integrating mathematical principles with real-world applications, researchers can unlock the full potential of data-driven decision-making processes. This abstract delves into the various ways mathematics acts as a bridge connecting theoretical frameworks to practical applications. It explores the utilization of mathematical models, algorithms, and statistical techniques to uncover hidden patterns, trends, and correlations within complex datasets. Furthermore, it investigates the role of mathematics in enhancing predictive modeling, optimization, and risk assessment methodologies for improved decision-making in diverse fields such as finance, healthcare, engineering, and social sciences. The abstract also emphasizes the need for interdisciplinary collaboration between mathematicians, statisticians, computer scientists, and domain experts to tackle the challenges posed by the data-driven landscape. By fostering synergies between these disciplines, novel approaches can be developed to address complex problems and make data-driven insights accessible and actionable. Moreover, this abstract underscores the importance of robust mathematical foundations for ensuring the reliability and validity of data analysis. Rigorous mathematical frameworks not only provide a solid basis for understanding and interpreting results but also contribute to the development of innovative methodologies and techniques. In summary, this abstract advocates for the pivotal role of mathematics in bridging theory and applications in a data-driven world. By harnessing mathematical principles, researchers can unlock the transformative potential of data analysis, paving the way for evidence-based decision-making, optimized processes, and innovative solutions to the challenges of our rapidly evolving society.

Keywords: mathematics, bridging theory and applications, data-driven world, mathematical models

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Authors: Mehrdad Abkenari, Mehmet Kunt, Mahdi Nourollahi

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Evaluating the environmental risk factors is a combination of analysis of transportation effects. Various definitions for risk can be found in different scientific sources. Each definition depends on a specific and particular perspective or dimension. The effects of potential risks present along the new proposed routes and existing infrastructures of large transportation projects like railways should be studied under comprehensive engineering frameworks. Despite various definitions provided for ‘risk’, all include a uniform concept. Two obvious aspects, loss and unreliability, have always been pointed in all definitions of this term. But, selection as the third aspect is usually implied and means how one notices it. Currently, conducting engineering studies on the environmental effects of railway projects have become obligatory according to the Environmental Assessment Act in developing countries. Considering the longitudinal nature of these projects and probable passage of railways through various ecosystems, scientific research on the environmental risk of these projects have become of great interest. Although many areas of expertise such as road construction in developing countries have not seriously committed to these studies yet, attention to these subjects in establishment or implementation of different systems have become an inseparable part of this wave of research. The present study used environmental risks identified and existing in previous studies and stations to use in next step. The second step proposes a new hybrid approach of analytical network process (ANP) and DEMATEL in fuzzy conditions for assessment of determined risks. Since evaluation of identified risks was not an easy touch, mesh structure was an appropriate approach for analyzing complex systems which were accordingly employed for problem description and modeling. Researchers faced the shortage of real space data and also due to the ambiguity of experts’ opinions and judgments, they were declared in language variables instead of numerical ones. Since fuzzy logic is appropriate for ambiguity and uncertainty, formulation of experts’ opinions in the form of fuzzy numbers seemed an appropriate approach. Fuzzy DEMATEL method was used to extract the relations between major and minor risk factors. Considering the internal relations of risk major factors and its sub-factors in the analysis of fuzzy network, the weight of risk’s main factors and sub-factors were determined. In general, findings of the present study, in which effective railway environmental risk indicators were theoretically identified and rated through the first usage of combined model of DEMATEL and fuzzy network analysis, indicate that environmental risks can be evaluated more accurately and also employed in railway projects.

Keywords: DEMATEL, ANP, fuzzy, risk

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Authors: Liping Yang, Curran Crawford, Jr. Ren, Zhengyi Ren

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Considering the cost evaluation and the stress analysis, a fuzzy satisfactory optimization (FSO) method has been developed for a hybrid composite flywheel. To evaluate the cost, the cost coefficients of the flywheel components are obtained through calculating the weighted sum of the scores of the material manufacturability, the structure character, and the material price. To express the satisfactory degree of the energy, the cost, and the mass, the satisfactory functions are proposed by using the decline function and introducing a satisfactory coefficient. To imply the different significance of the objectives, the object weight coefficients are defined. Based on the stress analysis of composite material, the circumferential and radial stresses are considered into the optimization formulation. The simulations of the FSO method with different weight coefficients and storage energy density optimization (SEDO) method of a flywheel are contrasted. The analysis results show that the FSO method can satisfy different requirements of the designer and the FSO method with suitable weight coefficients can replace the SEDO method.

Keywords: flywheel energy storage, fuzzy, optimization, stress analysis

Procedia PDF Downloads 348

Authors: Thor Alexis Sazon, Alexander Guzman-Urbina, Yasuhiro Fukushima

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This study outlines the method of how to develop a surrogate life cycle model based on fuzzy logic using three fuzzy inference methods: (1) the conventional Fuzzy Inference System (FIS), (2) the hybrid system of Data Analytics and Fuzzy Inference (DAFIS), which uses data clustering for defining the membership functions, and (3) the Adaptive-Neuro Fuzzy Inference System (ANFIS), a combination of fuzzy inference and artificial neural network. These methods were demonstrated with a case study where the Global Warming Potential (GWP) and the Levelized Cost of Energy (LCOE) of solar photovoltaic (PV) were estimated using Solar Irradiation, Module Efficiency, and Performance Ratio as inputs. The effects of using different fuzzy inference types, either Sugeno- or Mamdani-type, and of changing the number of input membership functions to the error between the calibration data and the model-generated outputs were also illustrated. The solution spaces of the three methods were consequently examined with a sensitivity analysis. ANFIS exhibited the lowest error while DAFIS gave slightly lower errors compared to FIS. Increasing the number of input membership functions helped with error reduction in some cases but, at times, resulted in the opposite. Sugeno-type models gave errors that are slightly lower than those of the Mamdani-type. While ANFIS is superior in terms of error minimization, it could generate solutions that are questionable, i.e. the negative GWP values of the Solar PV system when the inputs were all at the upper end of their range. This shows that the applicability of the ANFIS models highly depends on the range of cases at which it was calibrated. FIS and DAFIS generated more intuitive trends in the sensitivity runs. DAFIS demonstrated an optimal design point wherein increasing the input values does not improve the GWP and LCOE anymore. In the absence of data that could be used for calibration, conventional FIS presents a knowledge-based model that could be used for prediction. In the PV case study, conventional FIS generated errors that are just slightly higher than those of DAFIS. The inherent complexity of a Life Cycle study often hinders its widespread use in the industry and policy-making sectors. While the methodology does not guarantee a more accurate result compared to those generated by the Life Cycle Methodology, it does provide a relatively simpler way of generating knowledge- and data-based estimates that could be used during the initial design of a system.

Keywords: solar photovoltaic, fuzzy logic, inference system, artificial neural networks

Procedia PDF Downloads 167

Authors: T. Ganesan, M. S. Aris, I. Elamvazuthi, Momen Kamal Tageldeen

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Terms set in power purchase agreements (PPA) challenge power utility companies in balancing between the returns (from maximizing power production) and securing long term supply contracts at capped production. The production limitation set in the PPA has driven efforts to maximize profits through efficient and economic power production. In this paper, a combined industrial-scale gas turbine (GT) - absorption chiller (AC) system is considered to cool the GT air intake for reducing the plant’s heat rate (HR). This GT-AC system is optimized while considering power output limitations imposed by the PPA. In addition, the proposed formulation accounts for uncertainties in the ambient temperature using Type-2 fuzzy programming. Using the enhanced chaotic differential evolution (CEDE), the Pareto frontier was constructed and the optimization results are analyzed in detail.

Keywords: absorption chillers (AC), turbine inlet air cooling (TIC), power purchase agreement (PPA), multiobjective optimization, type-2 fuzzy programming, chaotic differential evolution (CDDE)

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Authors: Ahmet Erdoğan, Şahin Kesici, Mustafa Baloğlu

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Information technologies have lead to changes in the areas of communication, learning, and teaching. Besides offering many opportunities to the learners, these technologies have changed the teaching methods and beliefs of teachers. What the Technological Pedagogical Content Knowledge (TPACK) means to the teachers is considerably important to integrate technology successfully into teaching processes. It is necessary to understand how to plan and apply teacher training programs in order to balance students’ pedagogical and technological knowledge. Because of many inefficient teacher training programs, teachers have difficulties in relating technology, pedagogy and content knowledge each other. While providing an efficient training supported with technology, understanding the three main components (technology, pedagogy and content knowledge) and their relationship are very crucial. The purpose of this study is to determine whether motivational beliefs and self-regulated learning strategies are significant predictors of mathematics teacher candidates' TPACK perceptions. A hundred seventy five Turkish mathematics teachers candidates responded to the Motivated Strategies for Learning Questionnaire (MSLQ) and the Technological Pedagogical And Content Knowledge (TPACK) Scale. Of the group, 129 (73.7%) were women and 46 (26.3%) were men. Participants' ages ranged from 20 to 31 years with a mean of 23.04 years (SD = 2.001). In this study, a multiple linear regression analysis was used. In multiple linear regression analysis, the relationship between the predictor variables, mathematics teacher candidates' motivational beliefs, and self-regulated learning strategies, and the dependent variable, TPACK perceptions, were tested. It was determined that self-efficacy for learning and performance and intrinsic goal orientation are significant predictors of mathematics teacher candidates' TPACK perceptions. Additionally, mathematics teacher candidates' critical thinking, metacognitive self-regulation, organisation, time and study environment management, and help-seeking were found to be significant predictors for their TPACK perceptions.

Keywords: candidate mathematics teachers, motivational beliefs, self-regulated learning strategies, technological and pedagogical knowledge, content knowledge

Procedia PDF Downloads 482