Search results for: fuzzy mathematics

Authors: S. Rawashdi, D. Bshouty

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This paper aimed at discussing how to urge middle and high school Arab students in Israel to be aware of the importance of and investing in learning mathematics. In the first phase of the study, three questionnaires were passed to two nine-grade classes, one on Awareness, one on Awakeness and one on Learning. One of the two classes was an outstanding class from a public school (PUBS) of 31 students, and the other a heterogeneous class from a private school (PRIS) with 31 students. The Learning questionnaire which was administrated to the Awareness and Awareness topics was passed to PRIS and the Awareness and Awareness Questionnaires were passed to the PUBS class After two months we passed the post-questionnaire to both classes to validate the long-term impact of the study. The findings of the study show that awakeness and awareness processes have an effect on the math learning process, on its context in students' daily lives and their growing interest in learning math.

Keywords: awakeness, awareness, learning mathematics, pupils

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Authors: A. Buruzs, M. F. Hatwágner, L. T. Kóczy

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The aim of the present paper is to develop an integrated method that may provide assistance to decision makers during system planning, design, operation and evaluation. In order to support the realization of Circular Economy (CE), it is essential to evaluate local needs and conditions which help to select the most appropriate system components and resource needs. Each of these activities requires careful planning, however, the model of CE offers a comprehensive interdisciplinary framework. The aim of this research was to develop and to introduce a practical methodology for evaluation of local and regional opportunities to promote CE.

Keywords: circular economy, factors, fuzzy cognitive map, model reduction, sustainability

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Authors: Hassan Naseh, Javad Roozgard

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This paper represents the methodology based on Artificial Intelligent (AI) applied to Liquid Propellant Engine (LPE) optimization. The AI methodology utilized from Adaptive neural Fuzzy Inference System (ANFIS). In this methodology, the optimum objective function means to achieve maximum performance (specific impulse). The independent design variables in ANFIS modeling are combustion chamber pressure and temperature and oxidizer to fuel ratio and output of this modeling are specific impulse that can be applied with other objective functions in LPE design optimization. To this end, the LPE’s parameter has been modeled in ANFIS methodology based on generating fuzzy inference system structure by using grid partitioning, subtractive clustering and Fuzzy C-Means (FCM) clustering for both inferences (Mamdani and Sugeno) and various types of membership functions. The final comparing optimization results shown accuracy and processing run time of the Gaussian ANFIS Methodology between all methods.

Keywords: ANFIS methodology, artificial intelligent, liquid propellant engine, optimization

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Authors: Jay-R. Hosana Leonidas, Jayson A. Lucilo

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The K-12 Curriculum in the Philippines shed light to mathematics education as it recognizes the use of smartphones/mobile phones as appropriate tools necessary in teaching mathematics. However, there were limited pieces of evidence on the use of these devices in teaching and learning process. This descriptive study developed lessons integrating the use of mobile phone applications with basis on low-level competencies of students in Precalculus and determined its effects on students’ conceptual understanding, procedural skills, and attitudes towards Precalculus. Employing Bring Your Own Device (BYOD) scheme in the study, lessons developed were conducted among Grade 11 Science, Technology, Engineering, and Mathematics (STEM) students at Central Bicol State University of Agriculture for the academic year 2018-2019. This study found that there is a significant difference between the competency levels of students along conceptual understanding and procedural skills prior to and after the conduct of lessons developed. Also, it disclosed that the use of mobile phone applications had positive effects on students’ attitudes towards Precalculus. Thus, the use of mobile phone applications in teaching Precalculus can enrich students’ understanding of concepts and procedural skills (solving and graphing skills) and can increase students’ motivation, self-confidence, and enjoyment in dealing with Precalculus.

Keywords: bring your own device, mathematics education, mobile phone applications, senior high school

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Authors: Elmahdi Elgharbaoui, Tamou Nasser, Ahmed Essadki

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In the era of sustainable development, photovoltaic (PV) technology has shown significant potential as a renewable energy source. Photovoltaic generators (GPV) have a non-linear current-voltage characteristic, with a maximum power point (MPP) characterized by an optimal voltage, and depends on environmental factors such as temperature and irradiation. To extract each time the maximum power available at the terminals of the GPV and transfer it to the load, an adaptation stage is used, consisting of a boost chopper controlled by a maximum power point tracking technique (MPPT) through a stage of pulse width modulation (PWM). Our choice has focused on three techniques which are: the perturbation and observation method (P&O), the incremental conductance method (InCond) and the last is that of control using the fuzzy logic. The implementation and simulation of the system (photovoltaic generator, chopper boost, PWM and MPPT techniques) are then performed in the Matlab/Simulink environment.

Keywords: photovoltaic generator, technique MPPT, boost chopper, PWM, fuzzy logic, P&O, InCond

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Authors: A. Giannakopoulos, S. B. Buckley

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Problem solving in any field is recognised as a prerequisite for any advancement in knowledge. For example in South Africa it is one of the seven critical outcomes of education together with critical thinking. As a systematic way to problem solving was initiated in mathematics by the great mathematician George Polya (the father of problem solving), more detailed and comprehensive ways in problem solving have been developed. This paper is based on the findings by the author and subsequent recommendations for further research in problem solving and critical thinking. Although the study was done in mathematics, there is no doubt by now in almost anyone’s mind that mathematics is involved to a greater or a lesser extent in all fields, from symbols, to variables, to equations, to logic, to critical thinking. Therefore it stands to reason that mathematical principles and learning cannot be divorced from any field. In management of knowledge situations, the types of problems are similar to mathematics problems varying from simple to analogical to complex; from well-structured to ill-structured problems. While simple problems could be solved by employees by adhering to prescribed sequential steps (the process), analogical and complex problems cannot be proceduralised and that diminishes the capacity of the organisation of knowledge creation and innovation. The low efficiency in some organisations and the low pass rates in mathematics prompted the author to view problem solving as a product. The authors argue that using mathematical approaches to knowledge management problem solving and treating problem solving as a product will empower the employee through further training to tackle analogical and complex problems. The question the authors asked was: If it is true that problem solving and critical thinking are indeed basic skills necessary for advancement of knowledge why is there so little literature of knowledge management (KM) about them and how they are connected and advance KM?This paper concludes with a conceptual model which is based on general accepted principles of knowledge acquisition (developing a learning organisation), knowledge creation, sharing, disseminating and storing thereof, the five pillars of knowledge management (KM). This model, also expands on Gray’s framework on KM practices and problem solving and opens the doors to a new approach to training employees in general and domain specific areas problems which can be adapted in any type of organisation.

Keywords: critical thinking, knowledge management, mathematics, problem solving

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Authors: Idha Novianti, Suci Nurhayati, Puryati, Elang Krisnadi

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Community service activities are activities of the academic community in practicing and cultivating science, knowledge, and technology to advance the general welfare and educate the nation's life as described in the Higher Education Law. Training activities on the use of GeoGebra software are an option because GeoGebra software is software that is easy to operate and complete in the presentation of graphic design. The training activity was held for 3 hours online via teams and 3 hours offline. Involving 15 junior high school mathematics teachers located around south Tangerang. As a result, all teachers were satisfied with the activity, and they had additional new knowledge and skills to teach mathematics in the topic of geometry and algebra. The existence of new knowledge made the participants increase their confidence in developing mathematical science for students at school.

Keywords: geogebra, Ms. teams, junior high school teacher, mathematics

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Authors: Mohab Magdy Mostafa Mohamed

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The objective of this paper is to introduce a vertical handover (VHO) algorithm between wireless LANs (WLANs) and LTE mobile networks. The proposed algorithm is based on the fuzzy control theory and takes into consideration power level, subscriber velocity, and target cell load instead of only power level in traditional algorithms. Simulation results show that network performance in terms of number of handovers and handover occurrence distance is improved.

Keywords: vertical handover, fuzzy control theory, power level, speed, target cell load

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Authors: Shiuh-Jer Huang, Yun-Han Yeh

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A four-wheel drive electric vehicle was built with hub DC motors and FPGA embedded control structure. A 40 steps manual adjusting motorcycle shock absorber was refitted with DC motor driving mechanism to construct as a semi-active suspension system. Accelerometer and potentiometer sensors are installed to measure the sprung mass acceleration and suspension system compression or rebound states for control purpose. An intelligent fuzzy logic controller was proposed to real-time search appropriate damping ratio based on vehicle running condition. Then, a robust fuzzy sliding mode controller (FSMC) is employed to regulate the target damping ratio of each wheel axis semi-active suspension system. Finally, different road surface conditions are chosen to evaluate the control performance of this semi-active suspension and compare with that of passive system based on wheel axis acceleration signal.

Keywords: acceleration, FPGA, Fuzzy sliding mode control, semi-active suspension

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Authors: Irina Khutsishvili

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In the present research, a decision support methodology for the multi-attribute group decision-making (MAGDM) problem is developed, namely for the selection of investment projects. The objective of the investment project selection problem is to choose the best project among the set of projects, seeking investment, or to rank all projects in descending order. The project selection is made considering a set of weighted attributes. To evaluate the attributes in our approach, expert assessments are used. In the proposed methodology, lingual expressions (linguistic terms) given by all experts are used as initial attribute evaluations, since they are the most natural and convenient representation of experts' evaluations. Then lingual evaluations are converted into trapezoidal fuzzy numbers, and the aggregate trapezoidal hesitant fuzzy decision matrix will be built. The case is considered when information on the attribute weights is completely unknown. The attribute weights are identified based on the De Luca and Termini information entropy concept, determined in the context of hesitant fuzzy sets. The decisions are made using the extended Technique for Order Performance by Similarity to Ideal Solution (TOPSIS) method under a hesitant fuzzy environment. Hence, a methodology is based on a trapezoidal valued hesitant fuzzy TOPSIS decision-making model with entropy weights. The ranking of alternatives is performed by the proximity of their distances to both the fuzzy positive-ideal solution (FPIS) and the fuzzy negative-ideal solution (FNIS). For this purpose, the weighted hesitant Hamming distance is used. An example of investment decision-making is shown that clearly explains the procedure of the proposed methodology.

Keywords: In the present research, a decision support methodology for the multi-attribute group decision-making (MAGDM) problem is developed, namely for the selection of investment projects. The objective of the investment project selection problem is to choose the best project among the set of projects, seeking investment, or to rank all projects in descending order. The project selection is made considering a set of weighted attributes. To evaluate the attributes in our approach, expert assessments are used. In the proposed methodology, lingual expressions (linguistic terms) given by all experts are used as initial attribute evaluations since they are the most natural and convenient representation of experts' evaluations. Then lingual evaluations are converted into trapezoidal fuzzy numbers, and the aggregate trapezoidal hesitant fuzzy decision matrix will be built. The case is considered when information on the attribute weights is completely unknown. The attribute weights are identified based on the De Luca and Termini information entropy concept, determined in the context of hesitant fuzzy sets. The decisions are made using the extended Technique for Order Performance by Similarity to Ideal Solution (TOPSIS) method under a hesitant fuzzy environment. Hence, a methodology is based on a trapezoidal valued hesitant fuzzy TOPSIS decision-making model with entropy weights. The ranking of alternatives is performed by the proximity of their distances to both the fuzzy positive-ideal solution (FPIS) and the fuzzy negative-ideal solution (FNIS). For this purpose, the weighted hesitant Hamming distance is used. An example of investment decision-making is shown that clearly explains the procedure of the proposed methodology.

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Authors: O. Badagadze, G. Sirbiladze, I. Khutsishvili

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The work proposes a decision support methodology for the credit risk minimization in selection of investment projects. The methodology provides two stages of projects’ evaluation. Preliminary selection of projects with minor credit risks is made using the Expertons Method. The second stage makes ranking of chosen projects using the Possibilistic Discrimination Analysis Method. The latter is a new modification of a well-known Method of Fuzzy Discrimination Analysis.

Keywords: expert valuations, expertons, investment project risks, positive and negative discriminations, possibility distribution

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Authors: J. Shamash

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The high-school curriculum in algebra deals mainly with the solution of different types of equations. However, modern algebra has a completely different viewpoint and is concerned with algebraic structures and operations. A question then arises: What might be the relevance and contribution of an abstract algebra course for developing expertise and mathematical perspective in secondary school mathematics instruction? This is the focus of this paper. The course Algebra: From Equations to Structures is a carefully designed abstract algebra course for Israeli secondary school mathematics teachers. The course provides an introduction to algebraic structures and modern abstract algebra, and links abstract algebra to the high-school curriculum in algebra. It follows the historical attempts of mathematicians to solve polynomial equations of higher degrees, attempts which resulted in the development of group theory and field theory by Galois and Abel. In other words, algebraic structures grew out of a need to solve certain problems, and proved to be a much more fruitful way of viewing them. This theorems in both group theory and field theory. Along the historical ‘journey’, many other major results in algebra in the past 150 years are introduced, and recent directions that current research in algebra is taking are highlighted. This course is part of a unique master’s program – the Rothschild-Weizmann Program – offered by the Weizmann Institute of Science, especially designed for practicing Israeli secondary school teachers. A major component of the program comprises mathematical studies tailored for the students at the program. The rationale and structure of the course Algebra: From Equations to Structures are described, and its relevance to teaching school algebra is examined by analyzing three kinds of data sources. The first are position papers written by the participating teachers regarding the relevance of advanced mathematics studies to expertise in classroom instruction. The second data source are didactic materials designed by the participating teachers in which they connected the mathematics learned in the mathematics courses to the school curriculum and teaching. The third date source are final projects carried out by the teachers based on material learned in the course.

Keywords: abstract algebra , linking abstract algebra and school mathematics, school algebra, secondary school mathematics, teacher professional development

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Authors: Yousfi Abdelkader, Chaker Abdelkader, Bot Youcef

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This article proposes a five-level shunt active power filter for power quality improvement using a interval type-2 fuzzy logic controller (IT2 FLC). The reference compensating current is extracted using the P-Q theory. The majority of works previously reported are based on two-level inverters with a conventional Proportional integral (PI) controller, which requires rigorous mathematical modeling of the system. In this paper, a IT2 FLC controlled five-level active power filter is proposed to overcome the problem associated with PI controller. The IT2 FLC algorithm is applied for controlling the DC-side capacitor voltage as well as the harmonic currents of the five-level active power filter. The active power filter with a IT2 FLC is simulated in MATLAB Simulink environment. The simulated response shows that the proposed shunt active power filter controller has produced a sinusoidal supply current with low harmonic distortion and in phase with the source voltage.

Keywords: power quality, shunt active power filter, interval type-2 fuzzy logic controller (T2FL), multilevel inverter

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Authors: Itumeleng Phage

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Students’ comprehension of graphs may be affected by the characteristics of the discipline in which the graph is used, the type of the task as well as the background of the students who are the readers or interpreters of the graph. This research study investigated these aspects of the graph comprehension of 152 first-year undergraduate physics students by comparing their responses to corresponding tasks in the mathematics and physics disciplines. The discipline characteristics were analysed for four task-related constructs namely coordinates, representations, area and slope. Students’ responses to corresponding visual decoding and judgement tasks set in mathematics and kinematics contexts were statistically compared. The effects of the participants’ gender, year of school completion and study course were determined as reader characteristics. The results of the empirical study indicated that participants generally transferred their mathematics knowledge on coordinates and representation of straight line graphs to the physics contexts, but not in the cases of parabolic and hyperbolic functions or area under graphs. Insufficient understanding of the slope concept contributed to weak performances on this construct in both mathematics and physics contexts. Discipline characteristics seem to play a vital role in students’ understanding, while reader characteristics had insignificant to medium effects on their responses.

Keywords: kinematics graph, discipline characteristics, constructs, coordinates, representations, area and slope

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Authors: Meziane Belkacem

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We aim at converting the original 3D Lorenz-Haken equations, which describe laser dynamics –in terms of self-pulsing and chaos- into 2-second-order differential equations, out of which we extract the so far missing mathematics and corroborations with respect to nonlinear interactions. Leaning on basic trigonometry, we pull out important outcomes; a fundamental result attributes chaos to forbidden periodic solutions inside some precisely delimited region of the control parameter space that governs the bewildering dynamics.

Keywords: Physics, optics, nonlinear dynamics, chaos

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Authors: Murat Gunduz, Mustafa Ozdemir

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In this research, a framework is to be proposed to model the safety performance in construction sites. Determinants of safety performance are to be defined through extensive literature review and a multidimensional safety performance model is to be developed. In this context, a questionnaire is to be administered to construction companies with sites. The collected data through questionnaires including linguistic terms are then to be defuzzified to get concrete numbers by using fuzzy set theory which provides strong and significant instruments for the measurement of ambiguities and provides the opportunity to meaningfully represent concepts expressed in the natural language. The validity of the proposed safety performance model, relationships between determinants of safety performance are to be analyzed using the structural equation modeling (SEM) which is a highly strong multi variable analysis technique that makes possible the evaluation of latent structures. After validation of the model, a safety performance index assessment tool is to be proposed by the help of software. The proposed safety performance assessment tool will be based on the empirically validated theoretical model.

Keywords: Fuzzy set theory, safety performance assessment, safety index, structural equation modeling (SEM), construction sites

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Authors: Jonqlan Lin, C. Y. Tasi, K. H. Lin

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This paper addresses the issue of the autonomous mobile robot (AMR) navigation task based on the hybrid control modes. The novel hybrid control mode, based on multi-sensors information by using the fuzzy approach, has been presented in this research. The system operates in real time, is robust, enables the robot to operate with imprecise knowledge, and takes into account the physical limitations of the environment in which the robot moves, obtaining satisfactory responses for a large number of different situations. An experiment is simulated and carried out with a pioneer mobile robot. From the experimental results, the effectiveness and usefulness of the proposed AMR obstacle avoidance and navigation scheme are confirmed. The experimental results show the feasibility, and the control system has improved the navigation accuracy. The implementation of the controller is robust, has a low execution time, and allows an easy design and tuning of the fuzzy knowledge base.

Keywords: autonomous mobile robot, obstacle avoidance, MEMS, hybrid control mode, navigation control

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Authors: Zhanna Dedovets

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Fostering a mathematical style of thinking is crucial for cultivating intellectual personalities capable of thriving in modern society. Intuitive thinking stands as a cornerstone among the components of mathematical cognition, playing a pivotal role in grasping mathematical truths across various disciplines. This article delves into the exploration of leveraging search activities rooted in students' intuitive thinking, particularly when tackling geometric problems. Emphasizing both student engagement with the task and their active involvement in the search process, the study underscores the importance of heuristic procedures and the freedom for students to chart their own problem-solving paths. Spanning several years (2019-2023) at the Physics and Mathematics Lyceum of Dushanbe, the research engaged 17 teachers and 78 high school students. After assessing the initial levels of intuitive thinking in both control and experimental groups, the experimental group underwent training following the authors' methodology. Subsequent analysis revealed a significant advancement in thinking levels among the experimental group students. The methodological approaches and teaching materials developed through this process offer valuable resources for mathematics educators seeking to enhance their students' learning experiences effectively.

Keywords: teaching of mathematics, intuitive thinking, heuristic procedures, geometric problem, students.

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Authors: R. M. Kashim

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The study investigates the conceptual and procedural knowledge of rational number in primary school teachers, specifically, the primary school teachers level of conceptual knowledge about rational number and the primary school teachers level of procedural knowledge about rational numbers. The study was carried out in Bauchi metropolis in Bauchi state of Nigeria. A Conceptual and Procedural Knowledge Test was used as the instrument for data collection, 54 mathematics teachers in Bauchi primary schools were involved in the study. The collections were analyzed using mean and standard deviation. The findings revealed that the primary school mathematics teachers in Bauchi metropolis posses a low level of conceptual knowledge of rational number and also possess a high level of Procedural knowledge of rational number. It is therefore recommended that to be effective, teachers teaching mathematics most posses a deep understanding of both conceptual and procedural knowledge. That way the most knowledgeable teachers in mathematics deliver highly effective rational number instructions. Teachers should not ignore the mathematical concept aspect of rational number teaching. This is because only the procedural aspect of Rational number is highlighted during instructions; this often leads to rote - learning of procedures without understanding the meanings. It is necessary for teachers to learn rational numbers teaching method that focus on both conceptual knowledge and procedural knowledge teaching.

Keywords: conceptual knowledge, primary school teachers, procedural knowledge, rational numbers

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Authors: Nazir Amir

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Teaching approaches to present science and mathematics content amongst academically-low-achieving students may need to be different than approaches that are adopted for the more academically-inclined students, primarily due to the different learning needs and learning styles of these students. In crafting out lessons to motivate and engage these students, teachers need to consider the backgrounds of these students and have a good understanding of their interests so that lessons can be presented in ways that appeal to them, and made relevant not just to the world around them, but also to their personal experiences. This presentation highlights how the author worked with a Professional Learning Community (PLC) of teachers in crafting out fun and feasible classroom teaching approaches to present science and mathematics content in ways that are made Relevant, Appealing, and Personal (RAP) to groups of academically-low-achieving students in Singapore. Feedback from the students and observations from their work suggest that they were engaged through the RAP-modes of instruction, and were able to appreciate the role of science and mathematics through a variety of low-cost design-based STEM (Science, Technology, Engineering, and Mathematics) activities. Such results imply that teachers teaching academically-low-achieving students, and those in under-resourced communities, could consider infusing RAP-infused instructions into their lessons in getting students develop positive attitudes towards STEM subjects.

Keywords: STEM Education, STEAM Education, Curriculum Instruction, Academically At-Risk Students, Singapore

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Authors: Wann-Ming Wey

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In recent years, the problems of global climate change and natural disasters have induced the concerns and attentions of environmental sustainability issues for the public. Aside from the environmental planning efforts done for human environment, Transit-Oriented Development (TOD) has been widely used as one of the future solutions for the sustainable city development. In order to be more consistent with the urban sustainable development, the development of the built environment planning based on the concept of Green TOD which combines both TOD and Green Urbanism is adapted here. The connotation of the urban development under the green TOD including the design toward environment protect, the maximum enhancement resources and the efficiency of energy use, use technology to construct green buildings and protected areas, natural ecosystems and communities linked, etc. Green TOD is not only to provide the solution to urban traffic problems, but to direct more sustainable and greener consideration for future urban development planning and design. In this study, we use both the TOD and Green Urbanism concepts to proceed to the study of the built environment planning and design. Fuzzy Delphi Technique (FDT) is utilized to screen suitable criteria of the green TOD. Furthermore, Fuzzy Analytic Network Process (FANP) and Quality Function Deployment (QFD) were then developed to evaluate the criteria and prioritize the alternatives. The study results can be regarded as the future guidelines of the built environment planning and designing under green TOD development in Taiwan.

Keywords: green TOD, built environment, fuzzy delphi technique, quality function deployment, fuzzy analytic network process

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Authors: Katarina Rogulj, Ivana Racetin, Jelena Kilic

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In this study, the fuzzy logic approach (FLA) was developed for construction project management (CPM) under uncertainty and duality. The focus was on decision making in selecting the type of the glass facade for a residential-commercial building in the main design. The adoption of fuzzy sets was capable of reflecting construction managers’ reliability level over subjective judgments, and thus the robustness of the system can be achieved. An α-cuts method was utilized for discretizing the fuzzy sets in FLA. This method can communicate all uncertain information in the optimization process, taking into account the values of this information. Furthermore, FLA provides in-depth analyses of diverse policy scenarios that are related to various levels of economic aspects when it comes to the construction projects' valid decision making. The developed approach is applied to CPM to demonstrate its applicability. Analyzing the materials of glass facades, variants were defined. The development of the FLA for the CPM included relevant construction projec'ts stakeholders that were involved in the criteria definition to evaluate each variant. Using fuzzy Decision-Making Trial and Evaluation Laboratory Method (DEMATEL) comparison of the glass facade was conducted. This way, a rank, according to the priorities for inclusion into the main design, of variants is obtained. The concept was tested on a residential-commercial building in the city of Rijeka, Croatia. The newly developed methodology was then compared with the existing one. The aim of the research was to define an approach that will improve current judgments and decisions when it comes to the material selection of buildings facade as one of the most important architectural and engineering tasks in the main design. The advantage of the new methodology compared to the old one is that it includes the subjective side of the managers’ decisions, as an inevitable factor in each decision making. The proposed approach can help construction projects managers to identify the desired type of glass facade according to their preference and practical conditions, as well as facilitate in-depth analyses of tradeoffs between economic efficiency and architectural design.

Keywords: construction projects management, DEMATEL, fuzzy logic approach, glass façade selection

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Authors: Guorong Sui, Xingwei Jia, Chenhui Yin, Xiumin Gao

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In the processing of camera-based high precision and non-contact measurement, the geometric-optical aberration is always inevitably disturbing the measuring system. Moreover, the aberration is different with the different focal length, which will increase the difficulties of the system’s calibration. Therefore, to understand the relationship between the focal length as a function of aberration properties is a very important issue to the calibration of the measuring systems. In this study, we propose a new mathematics model, which is based on the plane calibration method by Zhang Zhengyou, and establish a relationship between the focal length and aberration coefficient. By using the mathematics model and carefully modified compensation templates, the calibration precision of the system can be dramatically improved. The experiment results show that the relative error is less than 1%. It is important for optoelectronic imaging systems that apply to measure, track and position by changing the camera’s focal length.

Keywords: camera calibration, aberration coefficient, vision measurement, focal length, mathematics model

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Authors: Chayanika Rout, Debjani Chakraborty, Adrijit Goswami

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Our work presents an inventory model which illustrates imperfect production and imperfect inspection processes for deteriorating items. A cost-minimizing model is studied considering two types of inspection errors, namely, Type I error of falsely screening out a proportion of non-defects, thereby passing them on for rework and Type II error of falsely not screening out a proportion of defects, thus selling those to customers which incurs a penalty cost. The screened items are reworked; however, no returns are entertained due to deteriorating nature of the items. In more practical situations, certain parameters such as the demand rate and the deterioration rate of inventory cannot be accurately determined, and therefore, they are assumed to be triangular fuzzy numbers in our model. We calculate the optimal lot size that must be produced in order to minimize the total inventory cost for both the crisp and the fuzzy models. A numerical example is also considered to exemplify the procedure which is followed by the analysis of sensitivity of various parameters on the decision variable and the objective function.

Keywords: deteriorating items, EPQ, imperfect quality, rework, type I and type II inspection errors

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Authors: Abder-Rahman Ali, Antoine Vacavant, Manuel Grand-Brochier, Adélaïde Albouy-Kissi, Jean-Yves Boire

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In this paper, we present a new segmentation approach for liver lesions in regions of interest within MRI (Magnetic Resonance Imaging). This approach, based on a two-cluster Fuzzy C-Means methodology, considers the parameter variable compactness to handle uncertainty. Fine boundaries are detected by a local recursive merging of ambiguous pixels with a sequential forward floating selection with Zernike moments. The method has been tested on both synthetic and real images. When applied on synthetic images, the proposed approach provides good performance, segmentations obtained are accurate, their shape is consistent with the ground truth, and the extracted information is reliable. The results obtained on MR images confirm such observations. Our approach allows, even for difficult cases of MR images, to extract a segmentation with good performance in terms of accuracy and shape, which implies that the geometry of the tumor is preserved for further clinical activities (such as automatic extraction of pharmaco-kinetics properties, lesion characterization, etc).

Keywords: defuzzification, floating search, fuzzy clustering, Zernike moments

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Authors: Eugenia Vomvoridi-Ivanovic

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It is broadly assumed that participation in field experiences will help pre-service teachers (PSTs) bridge theory to practice. However, this is often not the case since PSTs who are placed in classrooms with large numbers of students from diverse linguistic, cultural, racial, and ethnic backgrounds (culturally diverse students (CDS)) usually observe ineffective mathematics teaching practices that are in contrast to those discussed in their teacher preparation program. Over the past decades, the educational research community has paid increasing attention to investigating out-of-school learning contexts and how participation in such contexts can contribute to the achievement of underrepresented groups in Science, Technology, Engineering, and mathematics (STEM) education and their expanded participation in STEM fields. In addition, several research studies have shown that students display different kinds of mathematical behaviors and discourse practices in out-of-school contexts than they do in the typical mathematics classroom since they draw from a variety of linguistic and cultural resources to negotiate meanings and participate in joint problem solving. However, almost no attention has been given to exploring these contexts as field experiences for pre-service mathematics teachers. The purpose of this study was to explore how participation in a community based after-school field experience promotes understanding of the content pedagogy concepts introduced in elementary mathematics methods courses, particularly as they apply to teaching mathematics to CDS. This study draws upon a situated, socio-cultural theory of teacher learning that centers on the concept of learning as situated social practice, which includes discourse, social interaction, and participation structures. Consistent with exploratory case study methodology, qualitative methods were employed to investigate how a cohort of twelve participating pre-service teacher's approach to pedagogy and their conversations around teaching and learning mathematics to CDS evolved through their participation in the after-school field experience, and how they connected the content discussed in their mathematics methods course with their interactions with the CDS in the after-school. Data were collected over a period of one academic year from the following sources: (a) audio recordings of the PSTs' interactions with the students during the after-school sessions, (b) PSTs' after-school field-notes, (c) audio-recordings of weekly methods course meetings, and (d) other document data (e.g., PST and student generated artifacts, PSTs' written course assignments). The findings of this study reveal that the PSTs benefitted greatly through their participation in the after-school field experience. Specifically, after-school participation promoted a deeper understanding of the content pedagogy concepts introduced in the mathematics methods course and gained a greater appreciation for how students learn mathematics with understanding. Further, even though many of PSTs' assumptions about the mathematical abilities of CDS were challenged and PSTs began to view CDSs' cultural and linguistic backgrounds as resources (rather than obstacles) for learning, some PSTs still held negative stereotypes about CDS and teaching and learning mathematics to CDS in particular. Insights gained through this study contribute to a better understanding of how informal mathematics learning contexts may provide a valuable context for pre-service teacher's learning to teach mathematics to CDS.

Keywords: after-school mathematics program, pre-service mathematical education of teachers, qualitative methods, situated socio-cultural theory, teaching culturally diverse students

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Authors: Onesimus Bulus Shiaki

Abstract:

The study investigated the effect of cooperative learning strategy on mathematics achievement and retention among senior secondary school students of different abilities in Taraba State Nigeria. Cooperative learning strategy could hopefully contribute to students’ achievement which will spur the teachers to develop strategies for better learning. The quasi-experimental of pretest, posttest and control group design was adopted in this study. A sample of one hundred and sixty-four (164) Senior Secondary Two (SS2) students were selected from a population of twelve thousand, eight hundred and seventy-three (12,873) SS2 Students in Taraba State. Two schools with equivalent mean scores in the pre-test were randomly assigned to experimental and control groups. The experimental group students were stratified according to ability levels of low, medium and high. The experimental group was guided by the research assistants using the cooperative learning instructional package. After six weeks post-test was administered to the two groups while the retention test was administered two weeks after the post-test. The researcher developed a 50-item Mathematics Achievement Test (MAT) which was validated by experts obtaining the reliability coefficient of 0.87. Mean scores and standard deviations were used to answer the research questions while the Analysis of Co-variance (ANCOVA) was used to test the hypotheses. Major findings from the statistical analysis showed that cooperative learning strategy has a significant effect on the mean achievement of students as well as retention among students of high, medium and low ability in mathematics. However, cooperative learning strategy has no effect on the interaction of ability level and retention. Based on the results obtained, it was therefore recommended that the adoption of the use of cooperative learning strategy in the teaching and learning of mathematics in senior secondary schools be initiated, maintained and sustained for the benefit of senior secondary school students in Taraba State. Periodic Government sponsored in-service training in form of long vacation training programme, workshops, conferences and seminars on the nature, scope, and use of cooperative learning strategy should be organized for senior secondary school mathematics teachers in Taraba state.

Keywords: ability level, cooperative learning, mathematics achievement, retention

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Authors: Cristina-Maria Păcurar

Abstract:

The paper presents an original Python-based application that outlines the advantages of combining some elementary notions of mathematics with the study of a programming language. The application support refers to some of the first lessons of analytic geometry, meaning conics and quadrics and their reduction to a standard form, as well as some related notions. The chosen programming language is Python, not only for its closer to an everyday language syntax – and therefore, enhanced readability – but also for its highly reusable code, which is of utmost importance for a mathematician that is accustomed to exploit already known and used problems to solve new ones. The purpose of this paper is, on one hand, to support the idea that one of the most appropriate means to initiate one into programming is throughout mathematics, and reciprocal, one of the most facile and handy ways to assimilate some basic knowledge in the study of mathematics is to apply them in a personal project. On the other hand, besides being a mean of learning both programming and analytic geometry, the application subject to this paper is itself a useful tool for it can be seen as an independent original Python package for analytic geometry.

Keywords: analytic geometry, conics, python, quadrics

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Authors: Aman Berhe, Camille Guinaudeau, Claude Barras

Abstract:

In order to facilitate information seeking in large collections of multimedia documents with long and progressive content (such as broadcast news or TV series), one can extract the semantic links that exist between semantically coherent parts of documents, i.e., scenes. The links can then create a coherent collection of scenes from which it is easier to perform content analysis, topic extraction, or information retrieval. In this paper, we focus on TV series structuring and propose two approaches for scene linking at different levels of granularity (episode and season): a fuzzy online clustering technique and a graph-based community detection algorithm. When evaluated on the two first seasons of the TV series Game of Thrones, we found that the fuzzy online clustering approach performed better compared to graph-based community detection at the episode level, while graph-based approaches show better performance at the season level.

Keywords: multimedia collection structuring, progressive content, scene linking, fuzzy clustering, community detection

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Authors: Riyadh Jamegh, Alla Eldin Kassam, Sawsan Sabih

Abstract:

In order to overcome uncertainty conditions and inability to meet customers' requests due to these conditions, organizations tend to reserve a certain safety stock level (SSL). This level must be chosen carefully in order to avoid the increase in holding cost due to excess in SSL or shortage cost due to too low SSL. This paper used soft computing fuzzy logic to identify optimal SSL; this fuzzy model uses the dynamic concept to cope with high complexity environment status. The proposed model can deal with three input variables, i.e., demand stability level, raw material availability level, and on hand inventory level by using dynamic fuzzy logic to obtain the best SSL as an output. In this model, demand stability, raw material, and on hand inventory levels are described linguistically and then treated by inference rules of the fuzzy model to extract the best level of safety stock. The aim of this research is to provide dynamic approach which is used to identify safety stock level, and it can be implanted in different industries. Numerical case study in the dairy industry with Yogurt 200 gm cup product is explained to approve the validity of the proposed model. The obtained results are compared with the current level of safety stock which is calculated by using the traditional approach. The importance of the proposed model has been demonstrated by the significant reduction in safety stock level.

Keywords: inventory optimization, soft computing, safety stock optimization, dairy industries inventory optimization

Procedia PDF Downloads 126