Search results for: fuzzy arithmetic

Authors: B. Güney, Ç. Teke

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In recent years, rapid and correct decision making is crucial for both people and enterprises. However, uncertainty makes decision-making difficult. Fuzzy logic is used for coping with this situation. Thus, fuzzy linear programming models are developed in order to handle uncertainty in objective function and the constraints. In this study, a problem of a factory in food industry is investigated, required data is obtained and the problem is figured out as a fuzzy linear programming model. The model is solved using Zimmerman approach which is one of the approaches for fuzzy linear programming. As a result, the solution gives the amount of production for each product type in order to gain maximum profit.

Keywords: food industry, fuzzy linear programming, fuzzy logic, linear programming

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Authors: Yurii Bloshko, Oksana Olar

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This paper presents the analysis of 6 different classes of Petri nets: fuzzy Petri nets (FPN), generalized fuzzy Petri nets (GFPN), parameterized fuzzy Petri nets (PFPN), T2GFPN, flexible generalized fuzzy Petri nets (FGFPN), binary Petri nets (BPN). These classes were simulated in the special software PNeS® for the analysis of its pros and cons on the example of models which are dedicated to the decision-making process of passenger transport logistics. The paper includes the analysis of two approaches: when input values are filled with the experts’ knowledge; when fuzzy expectations represented by output values are added to the point. These approaches fulfill the possibilities of triples of functions which are replaced with different combinations of t-/s-norms.

Keywords: fuzzy petri net, intelligent computational techniques, knowledge representation, triangular norms

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Authors: Rashmi Tamhankar, Madhav Bapat

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In many projects, we have to use human judgment for determining the duration of the activities which may vary from person to person. Hence, there is vagueness about the time duration for activities in network planning. Fuzzy sets can handle such vague or imprecise concepts and has an application to such network. The vague activity times can be represented by triangular fuzzy numbers. In this paper, a general network with fuzzy activity times is considered and conditions for the critical path are obtained also we compute total float time of each activity. Several numerical examples are discussed.

Keywords: PERT, CPM, triangular fuzzy numbers, fuzzy activity times

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Authors: Lavinia B. Dulla

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The exploration study of the fuzzy regression approach attempts to present that fuzzy regression can be used as a possible alternative to classical regression. It likewise seeks to assess the differences and characteristics of simple linear regression and fuzzy regression using the width of prediction interval, mean absolute deviation, and variance of residuals. Based on the simple linear regression model, the fuzzy regression approach is worth considering as an alternative to simple linear regression when the sample size is between 10 and 20. As the sample size increases, the fuzzy regression approach is not applicable to use since the assumption regarding large sample size is already operating within the framework of simple linear regression. Nonetheless, it can be suggested for a practical alternative when decisions often have to be made on the basis of small data.

Keywords: fuzzy regression approach, minimum fuzziness criterion, interval regression, prediction interval

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Authors: Shih-Pin Chen, Shih-Syuan You

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Fuzzy regression models are useful for investigating the relationship between explanatory variables and responses in fuzzy environments. To overcome the deficiencies of previous models and increase the explanatory power of fuzzy data, the graded mean integration (GMI) representation is applied to determine representative crisp regression coefficients. A fuzzy regression model is constructed based on the modified dissemblance index (MDI), which can precisely measure the actual total error. Compared with previous studies based on the proposed MDI and distance criterion, the results from commonly used test examples show that the proposed fuzzy linear regression model has higher explanatory power and forecasting accuracy.

Keywords: dissemblance index, fuzzy linear regression, graded mean integration, mathematical programming

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Authors: Hafida Bouarfa, Mohamed Abed

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The main object of our work is the development and the validation of a system indicated Fuzzy Vulnerability. Fuzzy Vulnerability uses a fuzzy representation in order to tolerate the imprecision during the description of construction. At the the second phase, we evaluated the similarity between the vulnerability of a new construction and those of the whole of the historical cases. This similarity is evaluated on two levels: 1) individual similarity: bases on the fuzzy techniques of aggregation; 2) Global similarity: uses the increasing monotonous linguistic quantifiers (RIM) to combine the various individual similarities between two constructions. The third phase of the process of Fuzzy Vulnerability consists in using vulnerabilities of historical constructions narrowly similar to current construction to deduce its estimate vulnerability. We validated our system by using 50 cases. We evaluated the performances of Fuzzy Vulnerability on the basis of two basic criteria, the precision of the estimates and the tolerance of the imprecision along the process of estimation. The comparison was done with estimates made by tiresome and long models. The results are satisfactory.

Keywords: case based reasoning, fuzzy logic, fuzzy case based reasoning, seismic vulnerability

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Authors: Seyed Habib A. Rahmati, Mohsen Sadegh Amalnick

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Different terms of the statistical process control (SPC) has sketch in the fuzzy environment. However, measurement system analysis (MSA), as a main branch of the SPC, is rarely investigated in fuzzy area. This procedure assesses the suitability of the data to be used in later stages or decisions of the SPC. Therefore, this research focuses on some important measures of MSA and through a new method introduces the measures in fuzzy environment. In this method, which works based on Buckley approach, imprecision and vagueness nature of the real world measurement are considered simultaneously. To do so, fuzzy version of the gauge capability (Cg and Cgk) are introduced. The method is also explained through example clearly.

Keywords: measurement, SPC, MSA, gauge capability (Cg and Cgk)

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Authors: Liang-Hsuan Chen, Sheng-Shing Nien

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This study aims to develop approaches to formulate intuitionistic fuzzy regression (IFR) models for many decision-making applications in the fuzzy environments using intuitionistic fuzzy observations. Intuitionistic fuzzy numbers (IFNs) are used to characterize the fuzzy input and output variables in the IFR formulation processes. A mathematical programming problem (MPP) is built up to optimally determine the IFR parameters. Each parameter in the MPP is defined as a couple of alternative numerical variables with opposite signs, and an intuitionistic fuzzy error term is added to the MPP to characterize the uncertainty of the model. The IFR model is formulated based on the distance measure to minimize the total distance errors between estimated and observed intuitionistic fuzzy responses in the MPP resolution processes. The proposed approaches are simple/efficient in the formulation/resolution processes, in which the sign of parameters can be determined so that the problem to predetermine the sign of parameters is avoided. Furthermore, the proposed approach has the advantage that the spread of the predicted IFN response will not be over-increased, since the parameters in the established IFR model are crisp. The performance of the obtained models is evaluated and compared with the existing approaches.

Keywords: fuzzy sets, intuitionistic fuzzy number, intuitionistic fuzzy regression, mathematical programming method

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Authors: Dhruba Das

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In this paper, a method has been developed to construct the membership surfaces of row and column vectors and arithmetic operations of imprecise matrix. A matrix with imprecise elements would be called an imprecise matrix. The membership surface of imprecise vector has been already shown based on Randomness-Impreciseness Consistency Principle. The Randomness- Impreciseness Consistency Principle leads to defining a normal law of impreciseness using two different laws of randomness. In this paper, the author has shown row and column membership surfaces and arithmetic operations of imprecise matrix and demonstrated with the help of numerical example.

Keywords: imprecise number, imprecise vector, membership surface, imprecise matrix

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Authors: Bader Alkandari, Jamal Y. Madouh, Ahmad M. Alkandari, Anwar A. Alnaqi

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A new formulation of fuzzy linear estimation problem is presented. It is formulated as a linear programming problem. The objective is to minimize the spread of the data points, taking into consideration the type of the membership function of the fuzzy parameters to satisfy the constraints on each measurement point and to insure that the original membership is included in the estimated membership. Different models are developed for a fuzzy triangular membership. The proposed models are applied to different examples from the area of fuzzy linear regression and finally to different examples for estimating the electrical load on a busbar. It had been found that the proposed technique is more suited for electrical load estimation, since the nature of the load is characterized by the uncertainty and vagueness.

Keywords: fuzzy regression, load estimation, fuzzy linear parameters, electrical load estimation

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Authors: A. Mansouri, F. Krim

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This paper discusses the implementation and design of both linear PI and fuzzy controllers for DC-DC boost converters. Design of PI controllers is based on temporal response of closed-loop converters, while fuzzy controllers design is based on heuristic knowledge of boost converters. Linear controller implementation is quite straightforward relying on mathematical models, while fuzzy controller implementation employs one or more artificial intelligences techniques. Comparison between these boost controllers is made in design aspect. Experimental results show that the proposed fuzzy controller system is robust against input voltage and load resistance changing and in respect of start-up transient. Results indicate that fuzzy controller can achieve best control performance concerning faster transient response, steady-state response good stability and accuracy under different operating conditions. Fuzzy controller is more suitable to control boost converters.

Keywords: boost DC-DC converter, fuzzy, PI controllers, power electronics and control system

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Authors: Mustafa Bayram Gücen, Coşkun Yakar

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In this study, we have investigated the strict stability of fuzzy differential systems and we compare the classical notion of strict stability criteria of ordinary differential equations and the notion of strict stability of fuzzy differential systems. In addition that, we present definitions of stability and strict stability of fuzzy differential equations and also we have some theorems and comparison results. Strict Stability is a different stability definition and this stability type can give us an information about the rate of decay of the solutions. Lyapunov’s second method is a standard technique used in the study of the qualitative behavior of fuzzy differential systems along with a comparison result that allows the prediction of behavior of a fuzzy differential system when the behavior of the null solution of a fuzzy comparison system is known. This method is a usefull for investigating strict stability of fuzzy systems. First of all, we present definitions and necessary background material. Secondly, we discuss and compare the differences between the classical notion of stability and the recent notion of strict stability. And then, we have a comparison result in which the stability properties of the null solution of the comparison system imply the corresponding stability properties of the fuzzy differential system. Consequently, we give the strict stability results and a comparison theorem. We have used Lyapunov second method and we have proved a comparison result with scalar differential equations.

Keywords: fuzzy systems, fuzzy differential equations, fuzzy stability, strict stability

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Authors: Elda Maraj, Shkelqim Kuka

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Coronary heart disease causes many deaths in the world. Unfortunately, this problem will continue to increase in the future. In this paper, a fuzzy logic model to predict coronary heart disease is presented. This model has been developed with seven input variables and one output variable that was implemented for 30 patients in Albania. Here fuzzy logic toolbox of MATLAB is used. Fuzzy model inputs are considered as cholesterol, blood pressure, physical activity, age, BMI, smoking, and diabetes, whereas the output is the disease classification. The fuzzy sets and membership functions are chosen in an appropriate manner. Centroid method is used for defuzzification. The database is taken from University Hospital Center "Mother Teresa" in Tirana, Albania.

Keywords: coronary heart disease, fuzzy logic toolbox, membership function, prediction model

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Authors: S. Yaman, S. Rostami

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In this study, a black box modeling of the coupled-tank system is obtained by using fuzzy sets. The derived model is tested via adaptive neuro fuzzy inference system (ANFIS). In order to achieve a better control performance, the parameters of three different controller types, classical proportional integral controller (PID), fuzzy PID and function tuner method, are tuned by one of the evolutionary computation method, genetic algorithm. All tuned controllers are applied to the fuzzy model of the coupled-tank experimental setup and analyzed under the different reference input values. According to the results, it is seen that function tuner method demonstrates better robust control performance and guarantees the closed loop stability.

Keywords: function tuner method (FTM), fuzzy modeling, fuzzy PID controller, genetic algorithm (GA)

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Authors: N. Kaewpraek, W. Assawinchaichote

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This paper considers an H_∞ TS fuzzy state-derivative feedback controller for a class of nonlinear dynamical systems. A Takagi-Sugeno (TS) fuzzy model is used to approximate a class of nonlinear dynamical systems. Then, based on a linear matrix inequality (LMI) approach, we design an H_∞ TS fuzzy state-derivative feedback control law which guarantees L₂-gain of the mapping from the exogenous input noise to the regulated output to be less or equal to a prescribed value. We derive a sufficient condition such that the system with the fuzzy controller is asymptotically stable and H_∞ performance is satisfied. Finally, we provide and simulate a numerical example is provided to illustrate the stability and the effectiveness of the proposed controller.

Keywords: h-infinity fuzzy control, an LMI approach, Takagi-Sugano (TS) fuzzy system, the photovoltaic systems

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Authors: Shahabeddin Sotudian, M. H. Fazel Zarandi, I. B. Turksen

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Hepatitis is one of the most common and dangerous diseases that affects humankind, and exposes millions of people to serious health risks every year. Diagnosis of Hepatitis has always been a challenge for physicians. This paper presents an effective method for diagnosis of hepatitis based on interval Type-II fuzzy. This proposed system includes three steps: pre-processing (feature selection), Type-I and Type-II fuzzy classification, and system evaluation. KNN-FD feature selection is used as the preprocessing step in order to exclude irrelevant features and to improve classification performance and efficiency in generating the classification model. In the fuzzy classification step, an “indirect approach” is used for fuzzy system modeling by implementing the exponential compactness and separation index for determining the number of rules in the fuzzy clustering approach. Therefore, we first proposed a Type-I fuzzy system that had an accuracy of approximately 90.9%. In the proposed system, the process of diagnosis faces vagueness and uncertainty in the final decision. Thus, the imprecise knowledge was managed by using interval Type-II fuzzy logic. The results that were obtained show that interval Type-II fuzzy has the ability to diagnose hepatitis with an average accuracy of 93.94%. The classification accuracy obtained is the highest one reached thus far. The aforementioned rate of accuracy demonstrates that the Type-II fuzzy system has a better performance in comparison to Type-I and indicates a higher capability of Type-II fuzzy system for modeling uncertainty.

Keywords: hepatitis disease, medical diagnosis, type-I fuzzy logic, type-II fuzzy logic, feature selection

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Authors: Ismail Karaca, Ridvan Saracoglu, Omer Soner

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Fuzzy Logic, an advanced method to support decision-making, is used by various scientists in many disciplines. Fuzzy programming is a product of fuzzy logic, fuzzy rules, and implication. In marine science, fuzzy programming for ships is dramatically increasing together with autonomous ship studies. In this paper, a program to support the decision-making process for ship navigation has been designed. The program is produced in fuzzy logic and rules, by taking the marine accidents and expert opinions into account. After the program was designed, the program was tested by 46 ship accidents reported by the Transportation Safety Investigation Center of Turkey. Wind speed, sea condition, visibility, day/night ratio have been used as input data. They have been converted into a risk factor within the Fuzzy Logic Designer application and fuzzy rules set by marine experts. Finally, the expert's meteorological risk factor for each accident is compared with the program's risk factor, and the error rate was calculated. The main objective of this study is to improve the navigational safety of ships, by using the advance decision support model. According to the study result, fuzzy programming is a robust model that supports safe navigation.

Keywords: calculation of risk factor, fuzzy logic, fuzzy programming for ship, safety navigation of ships

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Authors: Jalel Khelil

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In order to improve reliability of Gas Turbine machine especially its generator equipment, a fault diagnosis system based on fuzzy approach is proposed. Three various methods namely K-NN (K-nearest neighbors), F-KNN (Fuzzy K-nearest neighbors) and FNM (Fuzzy nearest mean) are adopted to provide the measurement of relative strength of vibration defaults. Both applications consist of two major steps: Feature extraction and default classification. 09 statistical features are extracted from vibration signals. 03 different classes are used in this study which describes vibrations condition: Normal, unbalance defect, and misalignment defect. The use of the fuzzy approaches and the classification results are discussed. Results show that these approaches yield high successful rates of vibration default classification.

Keywords: fault diagnosis, fuzzy classification k-nearest neighbor, vibration

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Authors: Sujeet Kumar Singh, Shiv Prasad Yadav

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This paper develops an approach for solving intuitionistic fuzzy linear fractional programming (IFLFP) problem where the cost of the objective function, the resources, and the technological coefficients are triangular intuitionistic fuzzy numbers. Here, the IFLFP problem is transformed into an equivalent crisp multi-objective linear fractional programming (MOLFP) problem. By using fuzzy mathematical programming approach the transformed MOLFP problem is reduced into a single objective linear programming (LP) problem. The proposed procedure is illustrated through a numerical example.

Keywords: triangular intuitionistic fuzzy number, linear programming problem, multi objective linear programming problem, fuzzy mathematical programming, membership function

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Authors: Khaled Jaber

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The estimation of effort in software development is a complex task. The traditional Waterfall approach used to develop software systems requires a lot of time to estimate the effort needed to implement user requirements. Agile manifesto, however, is currently more used in the industry than the Waterfall to develop software systems. In Agile, the user requirement is referred to as a user story. Agile teams mostly use the Fibonacci sequence 1, 2, 3, 5, 8, 11, etc. in estimating the effort needed to implement the user story. This work shows through analysis that the Arithmetic sequence, e.g., 3, 6, 9, 12, etc., is more effective than the Fibonacci sequence in estimating the user stories. This paper mathematically and visually proves the effectiveness of the Arithmetic sequence over the FB sequence.

Keywords: agie, scrum, estimation, fibonacci sequence

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Authors: Yas Barzegar, Atrin Barzegar

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Drinking water quality assessment is a major issue today; technology and practices are continuously improving; Artificial Intelligence (AI) methods prove their efficiency in this domain. The current research seeks a hierarchical fuzzy model for predicting drinking water quality in Rome (Italy). The Mamdani fuzzy inference system (FIS) is applied with different defuzzification methods. The Proposed Model includes three fuzzy intermediate models and one fuzzy final model. Each fuzzy model consists of three input parameters and 27 fuzzy rules. The model is developed for water quality assessment with a dataset considering nine parameters (Alkalinity, Hardness, pH, Ca, Mg, Fluoride, Sulphate, Nitrates, and Iron). Fuzzy-logic-based methods have been demonstrated to be appropriate to address uncertainty and subjectivity in drinking water quality assessment; it is an effective method for managing complicated, uncertain water systems and predicting drinking water quality. The FIS method can provide an effective solution to complex systems; this method can be modified easily to improve performance.

Keywords: water quality, fuzzy logic, smart cities, water attribute, fuzzy inference system, membership function

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Authors: Leticia Cervantes, Edith Garcia, Oscar Castillo

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At today, there are several control problems where the main objective is to obtain the best control in the study to decrease the error in the application. Many techniques can use to control these problems such as Neural Networks, PID control, Fuzzy Logic, Optimization techniques and many more. In this case, fuzzy logic with fuzzy system and an optimization technique are used to control the case of study. In this case, Ant Lion Optimization is used to optimize a fuzzy system to control the velocity of a simple treadmill. The main objective is to achieve the control of the velocity in the control problem using the ALO optimization. First, a simple fuzzy system was used to control the velocity of the treadmill it has two inputs (error and error change) and one output (desired speed), then results were obtained but to decrease the error the ALO optimization was developed to optimize the fuzzy system of the treadmill. Having the optimization, the simulation was performed, and results can prove that using the ALO optimization the control of the velocity was better than a conventional fuzzy system. This paper describes some basic concepts to help to understand the idea in this work, the methodology of the investigation (control problem, fuzzy system design, optimization), the results are presented and the optimization is used for the fuzzy system. A comparison between the simple fuzzy system and the optimized fuzzy systems are presented where it can be proving the optimization improved the control with good results the major findings of the study is that ALO optimization is a good alternative to improve the control because it helped to decrease the error in control applications even using any control technique to optimized, As a final statement is important to mentioned that the selected methodology was good because the control of the treadmill was improve using the optimization technique.

Keywords: ant lion optimization, control problem, fuzzy control, fuzzy system

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Authors: Yas Barzegaar, Atrin Barzegar

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The aim of this research is to develop an intelligent system to analyze the risk level of wheat flour product manufacturing system. The model consists of five Fuzzy Inference Systems in two different layers to analyse the risk of a wheat flour product manufacturing system. The first layer of the model consists of four Fuzzy Inference Systems with three criteria. The output of each one of the Physical, Chemical, Biological and Environmental Failures will be the input of the final manufacturing systems. The proposed model based on Mamdani Fuzzy Inference Systems gives a performance ranking of wheat flour products manufacturing systems. The first step is obtaining data to identify the failure modes from expert’s opinions. The second step is the fuzzification process to convert crisp input to a fuzzy set., then the IF-then fuzzy rule applied through inference engine, and in the final step, the defuzzification process is applied to convert the fuzzy output into real numbers.

Keywords: failure modes, fuzzy rules, fuzzy inference system, risk assessment

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Authors: P. W. Tsai, J. W. Chen, C. W. Chen, C. Y. Chen

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In recent years, many researchers are involved in the field of fuzzy theory. However, there are still a lot of issues to be resolved. Especially on topics related to controller design such as the field of robot, artificial intelligence, and nonlinear systems etc. Besides fuzzy theory, algorithms in swarm intelligence are also a popular field for the researchers. In this paper, a concept of utilizing one of the swarm intelligence method, which is called Bacterial-GA Foraging, to find the stabilized common P matrix for the fuzzy controller system is proposed. An example is given in in the paper, as well.

Keywords: half-circle fuzzy numbers, predictions, swarm intelligence, Lyapunov method

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Authors: Michael Lousis

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The systematic identification of the most conspicuous and significant errors made by learners during three-years of testing of their progress in learning Arithmetic throughout the development of the Kassel Project in England and Greece was accomplished. How much retentive these errors were over three-years in the officially provided school instruction of Arithmetic in these countries has also been shown. The learners’ errors in Arithmetic stemmed from a sample, which was comprised of two hundred (200) English students and one hundred and fifty (150) Greek students. The sample was purposefully selected according to the students’ participation in each testing session in the development of the three-year project, in both domains simultaneously in Arithmetic and Algebra. Specific teaching practices have been invented and are presented in this study for subverting these learners’ errors, which were found out to be retentive to the level of the nationally provided mathematical education of each country. The invention and the development of these proposed teaching practices were founded on the rationality of the theoretical accounts concerning the explanation, prediction and control of the errors, on the conceptual metaphor and on an analysis, which tried to identify the required cognitive components and skills of the specific tasks, in terms of Psychology and Cognitive Science as applied to information-processing. The aim of the implementation of these instructional practices is not only the subversion of these errors but the achievement of the mathematical competence, as this was defined to be constituted of three elements: appropriate representations - appropriate meaning - appropriately developed schemata. However, praxis is of paramount importance, because there is no independent of science ‘real-truth’ and because praxis serves as quality control when it takes the form of a cognitive method.

Keywords: arithmetic, cognitive science, cognitive psychology, information-processing paradigm, Kassel project, level of the nationally provided mathematical education, praxis, remedial mathematical teaching practices, retentiveness of errors

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Authors: Mandar Ghodekar, Sharad Jadhav, Sangram Jadhav

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Speed control of rotor during startup and under varying load conditions is one of the most difficult tasks of gas turbine operation. In this paper, power plant gas turbine (GE9001E) is considered for this purpose and fuzzy and fuzzy-PI rotor speed controllers are designed. The goal of the presented controllers is to keep the turbine rotor speed within predefined limits during startup condition as well as during operating condition. The fuzzy controller and fuzzy-PI controller are designed using Takagi-Sugeno method and Mamdani method, respectively. In applying the fuzzy-PI control to a gas-turbine plant, the tuning parameters (Kp and Ki) are modified online by fuzzy logic approach. Error and rate of change of error are inputs and change in fuel flow is output for both the controllers. Hence, rotor speed of gas turbine is controlled by modifying the fuel ƒflow. The identified linear ARX model of gas turbine is considered while designing the controllers. For simulations, demand power is taken as disturbance input. It is assumed that inlet guide vane (IGV) position is fixed. In addition, the constraint on the fuel flow is taken into account. The performance of the presented controllers is compared with each other as well as with H∞ robust and MPC controllers for the same operating conditions in simulations.

Keywords: gas turbine, fuzzy controller, fuzzy PI controller, power plant

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Authors: Atrin Barzegar, Yas Barzegar, Stefano Marrone, Francesco Bellini, Laura Verde

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The aim of this research is to develop an intelligent system to analyze the risk level of wheat flour product manufacturing system. The model consists of five Fuzzy Inference Systems in two different layers to analyse the risk of a wheat flour product manufacturing system. The first layer of the model consists of four Fuzzy Inference Systems with three criteria. The output of each one of the Physical, Chemical, Biological and Environmental Failures will be the input of the final manufacturing systems. The proposed model based on Mamdani Fuzzy Inference Systems gives a performance ranking of wheat flour products manufacturing systems. The first step is obtaining data to identify the failure modes from expert’s opinions. The second step is the fuzzification process to convert crisp input to a fuzzy set., then the IF-then fuzzy rule applied through inference engine, and in the final step, the defuzzification process is applied to convert the fuzzy output into real numbers.

Keywords: failure modes, fuzzy rules, fuzzy inference system, risk assessment

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Authors: Michael Gidey Gebru

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Most DEA models operate in a static environment with input and output parameters that are chosen by deterministic data. However, due to ambiguity brought on shifting market conditions, input and output data are not always precisely gathered in real-world scenarios. Fuzzy numbers can be used to address this kind of ambiguity in input and output data. Therefore, this work aims to expand crisp DEA into DEA with fuzzy environment. In this study, the input and output data are regarded as fuzzy triangular numbers. Then, the DEA model with fuzzy environment is solved using a multi-objective method to gauge the Decision Making Units’ efficiency. Finally, the developed DEA model is illustrated with an application on real data 50 educational institutions.

Keywords: efficiency, DEA, fuzzy, decision making units, higher education institutions

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Authors: Joseph Siani

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Over the last decades, dissatisfaction with global indicators of economic performance, such as GDP (Gross Domestic Product) per capita, has shifted the attention to what is now referred to as multidimensional poverty. In this framework, poverty goes beyond income to incorporate aspects of well-being not captured by income measures alone. This paper applies the totally fuzzy approach to estimate the fuzzy index of poverty (FIP) in fourteen Sub-Saharan African (SSA) countries using Demographic and Health Survey (DHS) data and explores whether pictures created by the standard headcount ratio at $1.90 a day and the fuzzy index of poverty tell a similar story. The results suggest that there is indeed considerable mismatch between poverty headcount and the fuzzy index of multidimensional poverty, meaning that the majority of the most deprived people (as identified by the fuzzy index of multidimensional poverty) would not be identified by the poverty headcount ratio. Moreover, we find that poverty is distributed differently by colonial heritage (language). In particular, the most deprived countries in SSA are French-speaking.

Keywords: fuzzy set approach, multidimensional poverty, poverty headcount, overlap, Sub-Saharan Africa

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Authors: Michal Wolk, Bat-Sheva Hadad, Orly Rubinsten

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Objective: The visuospatial perception system process that allows us to decompose and recompose small quantities into a whole is often called “groupitizing.” Previous studies have been found that adults use groupitizing processes in quantity estimation tasks and link this ability of subgroups recognition to arithmetic proficiency. This pilot study examined if adults with math difficulties benefit from visuospatial grouping cues when asked to estimate the quantity of a given set. It also compared the tipping point in which a significant improvement occurs in adults with typical development compared to adults with math difficulties. Method: In this pilot research, we recruited adults with low arithmetic abilities and matched controls. Participants were asked to estimate the quantity of a given set. Different grouping cues were displayed (space, color, or none) with different visual configurations (different quantities-different shapes, same quantities- different shapes, same quantities- same shapes). Results: Both groups showed significant performance improvement when grouping cues appeared. However, adults with low arithmetic abilities benefited from the grouping cues already in very small quantities as four. Conclusion: impaired perceptual groupitizing abilities may be a characteristic of low arithmetic abilities.

Keywords: groupitizing, math learning disability, quantity estimation, visual perception system

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