Search results for: Mamdani
Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 20

Search results for: Mamdani

20 Rule-Based Mamdani Type Fuzzy Modeling of Performances of Anode Side of Proton Exchange Membrane Fuel Cell Spin-Coated with Yttria-Stabilized Zirconia

Authors: Sadık Ata, Kevser Dincer

Abstract:

In this study, 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 parameters voltage density (V/cm2), and current density (A/cm2), temperature (°C), time (s); output parameter power density (W/cm2) 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 of PEM fuel cell.

Keywords: proton exchange membrane (PEM), fuel cell, rule-based Mamdani-type fuzzy (RMBTF) modeling, yttria-stabilized zirconia (YSZ)

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19 Improving the Performance of Proton Exchange Membrane Using Fuzzy Logic

Authors: Sadık Ata, Kevser Dincer

Abstract:

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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18 Fuzzy Logic Modeling of Evaluation the Urban Skylines by the Entropy Approach

Authors: Murat Oral, Seda Bostancı, Sadık Ata, Kevser Dincer

Abstract:

When evaluating the aesthetics of cities, an analysis of the urban form development depending on design properties with a variety of factors is performed together with a study of the effects of this appearance on human beings. Different methods are used while making an aesthetical evaluation related to a city. Entropy, in its preliminary meaning, is the mathematical representation of thermodynamic results. Measuring the entropy is related to the distribution of positional figures of a message or information from the probabilities standpoint. In this study, analysis of evaluation the urban skylines by the entropy approach was modelled with Rule-Based Mamdani-Type Fuzzy (RBMTF) modelling technique. 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 application data and RBMTF is done by using absolute fraction of variance (R2). The actual values and RBMTF results indicated that RBMTF can be successfully used for the analysis of evaluation the urban skylines by the entropy approach. As a result, RBMTF model has shown satisfying relation with experimental results, which suggests an alternative method to evaluation of the urban skylines by the entropy approach.

Keywords: urban skylines, entropy, rule-based Mamdani type, fuzzy logic

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17 Design of a Fuzzy Expert System for the Impact of Diabetes Mellitus on Cardiac and Renal Impediments

Authors: E. Rama Devi Jothilingam

Abstract:

Diabetes mellitus is now one of the most common non communicable diseases globally. India leads the world with largest number of diabetic subjects earning the title "diabetes capital of the world". In order to reduce the mortality rate, a fuzzy expert system is designed to predict the severity of cardiac and renal problems of diabetic patients using fuzzy logic. Since uncertainty is inherent in medicine, fuzzy logic is used in this research work to remove the inherent fuzziness of linguistic concepts and uncertain status in diabetes mellitus which is the prime cause for the cardiac arrest and renal failure. In this work, the controllable risk factors "blood sugar, insulin, ketones, lipids, obesity, blood pressure and protein/creatinine ratio" are considered as input parameters and the "the stages of cardiac" (SOC)" and the stages of renal" (SORD) are considered as the output parameters. The triangular membership functions are used to model the input and output parameters. The rule base is constructed for the proposed expert system based on the knowledge from the medical experts. Mamdani inference engine is used to infer the information based on the rule base to take major decision in diagnosis. Mean of maximum is used to get a non fuzzy control action that best represent possibility distribution of an inferred fuzzy control action. The proposed system also classifies the patients with high risk and low risk using fuzzy c means clustering techniques so that the patients with high risk are treated immediately. The system is validated with Matlab and is used as a tracking system with accuracy and robustness.

Keywords: Diabetes mellitus, fuzzy expert system, Mamdani, MATLAB

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16 Fuzzy Wavelet Model to Forecast the Exchange Rate of IDR/USD

Authors: Tri Wijayanti Septiarini, Agus Maman Abadi, Muhammad Rifki Taufik

Abstract:

The exchange rate of IDR/USD can be the indicator to analysis Indonesian economy. The exchange rate as a important factor because it has big effect in Indonesian economy overall. So, it needs the analysis data of exchange rate. There is decomposition data of exchange rate of IDR/USD to be frequency and time. It can help the government to monitor the Indonesian economy. This method is very effective to identify the case, have high accurate result and have simple structure. In this paper, data of exchange rate that used is weekly data from December 17, 2010 until November 11, 2014.

Keywords: the exchange rate, fuzzy mamdani, discrete wavelet transforms, fuzzy wavelet

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15 A Methodology of Using Fuzzy Logics and Data Analytics to Estimate the Life Cycle Indicators of Solar Photovoltaics

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

Abstract:

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

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14 Colonial Body: Historicizing the Becoming of the Kashmiri Body

Authors: Ain ul Khair

Abstract:

In this study, the author situates the formation of the Kashmiri body as colonized in the postcolonial society, on which India continues to execute and maintain colonial practices adopted and replicated from the Western colonial projects. This paper explores the formation of a Kashmiri body as a site of complete dehumanization, which has deliberately been politicized based on its religion, racialized because of its ethnic distinction, and consequently has been subjected to extreme forms of violence. This paper specifically looks at the creation of the Kashmiri colonized body through India’s colonial practices that are in continuity from the Western imperialist colonial projects through the historicization of the careful manufacturing of the Kashmiri colonial body through the lens of the political, legal, geographical, and demographic landscape of India’s colonial project. The paper looks at the framing of the colonial legal framework that informs the construction of the colonized Kashmiri body, drawing violence and religion at the center of it.

Keywords: historicization, colonial body, kashmir, india, pakistan, south asia, religion, political identity, politics, Mahmood Mamdani, Ann Stoler, Fanon

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13 The Formulation of Inference Fuzzy System as a Valuation Subsidiary Based Particle Swarm Optimization for Solves the Issue of Decision Making in Middle Size Soccer Robot League

Authors: Zahra Abdolkarimi, Naser Zouri

Abstract:

The actual purpose of RoboCup is creating independent team of robots in 2050 based of FiFa roles to bring the victory in compare of world star team. There is unbelievable growing of Robots created a collection of complex and motivate subject in robotic and intellectual ornate, also it made a mechatronics style base of theoretical and technical way in Robocop. Decision making of robots depends to environment reaction, self-player and rival player with using inductive Fuzzy system valuation subsidiary to solve issue of robots in land game. The measure of selection in compare with other methods depends to amount of victories percentage in the same team that plays accidentally.

Keywords: particle swarm optimization, chaos theory, inference fuzzy system, simulation environment rational fuzzy system, mamdani and assilian, deffuzify

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12 An Approaching Index to Evaluate a forward Collision Probability

Authors: Yuan-Lin Chen

Abstract:

This paper presents an approaching forward collision probability index (AFCPI) for alerting and assisting driver in keeping safety distance to avoid the forward collision accident in highway driving. The time to collision (TTC) and time headway (TH) are used to evaluate the TTC forward collision probability index (TFCPI) and the TH forward collision probability index (HFCPI), respectively. The Mamdani fuzzy inference algorithm is presented combining TFCPI and HFCPI to calculate the approaching collision probability index of the vehicle. The AFCPI is easier to understand for the driver who did not even have any professional knowledge in vehicle professional field. At the same time, the driver’s behavior is taken into account for suiting each driver. For the approaching index, the value 0 is indicating the 0% probability of forward collision, and the values 0.5 and 1 are indicating the 50% and 100% probabilities of forward collision, respectively. The AFCPI is useful and easy-to-understand for alerting driver to avoid the forward collision accidents when driving in highway.

Keywords: approaching index, forward collision probability, time to collision, time headway

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11 Artificial Intelligent Methodology for Liquid Propellant Engine Design Optimization

Authors: Hassan Naseh, Javad Roozgard

Abstract:

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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10 Fuzzy Inference System for Risk Assessment Evaluation of Wheat Flour Product Manufacturing Systems

Authors: Yas Barzegaar, Atrin Barzegar

Abstract:

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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9 Improvement of Direct Torque and Flux Control of Dual Stator Induction Motor Drive Using Intelligent Techniques

Authors: Kouzi Katia

Abstract:

This paper proposes a Direct Torque Control (DTC) algorithm of dual Stator Induction Motor (DSIM) drive using two approach intelligent techniques: Artificial Neural Network (ANN) approach replaces the switching table selector block of conventional DTC and Mamdani Fuzzy Logic controller (FLC) is used for stator resistance estimation. The fuzzy estimation method is based on an online stator resistance correction through the variations of stator current estimation error and its variation. The fuzzy logic controller gives the future stator resistance increment at the output. The main advantage of suggested algorithm control is to reduce the hardware complexity of conventional selectors, to avoid the drive instability that may occur in certain situation and ensure the tracking of the actual of the stator resistance. The effectiveness of the technique and the improvement of the whole system performance are proved by results.

Keywords: artificial neural network, direct torque control, dual stator induction motor, fuzzy logic estimator, switching table

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8 Fuzzy Inference System for Risk Assessment Evaluation of Wheat Flour Product Manufacturing Systems

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

Abstract:

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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7 Drinking Water Quality Assessment Using Fuzzy Inference System Method: A Case Study of Rome, Italy

Authors: Yas Barzegar, Atrin Barzegar

Abstract:

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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6 Fuzzy and Fuzzy-PI Controller for Rotor Speed of Gas Turbine

Authors: Mandar Ghodekar, Sharad Jadhav, Sangram Jadhav

Abstract:

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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5 The Fuzzy Logic Modeling of Performance Driver Seat’s Localised Cooling and Heating in Standard Car Air Conditioning System

Authors: Ali Ates, Sadık Ata, Kevser Dincer

Abstract:

In this study, performance of the driver seat‘s localized cooling and heating in a standard car air conditioning system was experimentally investigated and modeled with Rule-Based Mamdani-Type Fuzzy (RBMTF) modeling technique. Climate function at automobile is an important variable for thermal comfort. In the experimental study localized heating and cooling performances have been examined with the aid of a mechanism established to a vehicle. The equipment’s used in the experimental setup/mechanism have been provided and assembled. During the measurement, the status of the performance level has been determined. Input parameters revolutions per minute and time; output parameters car seat cooling temperature, car back cooling temperature, car seat heating temperature, car back heating temperature were described by RBMTF if-the 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), 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 could be successfully used in standard car air conditioning system.

Keywords: air conditioning system, cooling-heating, RMBTF modelling, car seat

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4 Stability Enhancement of a Large-Scale Power System Using Power System Stabilizer Based on Adaptive Neuro Fuzzy Inference System

Authors: Agung Budi Muljono, I Made Ginarsa, I Made Ari Nrartha

Abstract:

A large-scale power system (LSPS) consists of two or more sub-systems connected by inter-connecting transmission. Loading pattern on an LSPS always changes from time to time and varies depend on consumer need. The serious instability problem is appeared in an LSPS due to load fluctuation in all of the bus. Adaptive neuro-fuzzy inference system (ANFIS)-based power system stabilizer (PSS) is presented to cover the stability problem and to enhance the stability of an LSPS. The ANFIS control is presented because the ANFIS control is more effective than Mamdani fuzzy control in the computation aspect. Simulation results show that the presented PSS is able to maintain the stability by decreasing peak overshoot to the value of −2.56 × 10−5 pu for rotor speed deviation Δω2−3. The presented PSS also makes the settling time to achieve at 3.78 s on local mode oscillation. Furthermore, the presented PSS is able to improve the peak overshoot and settling time of Δω3−9 to the value of −0.868 × 10−5 pu and at the time of 3.50 s for inter-area oscillation.

Keywords: ANFIS, large-scale, power system, PSS, stability enhancement

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3 A Fuzzy Inference System for Predicting Air Traffic Demand Based on Socioeconomic Drivers

Authors: Nur Mohammad Ali, Md. Shafiqul Alam, Jayanta Bhusan Deb, Nowrin Sharmin

Abstract:

The past ten years have seen significant expansion in the aviation sector, which during the previous five years has steadily pushed emerging countries closer to economic independence. It is crucial to accurately forecast the potential demand for air travel to make long-term financial plans. To forecast market demand for low-cost passenger carriers, this study suggests working with low-cost airlines, airports, consultancies, and governmental institutions' strategic planning divisions. The study aims to develop an artificial intelligence-based methods, notably fuzzy inference systems (FIS), to determine the most accurate forecasting technique for domestic low-cost carrier demand in Bangladesh. To give end users real-world applications, the study includes nine variables, two sub-FIS, and one final Mamdani Fuzzy Inference System utilizing a graphical user interface (GUI) made with the app designer tool. The evaluation criteria used in this inquiry included mean square error (MSE), accuracy, precision, sensitivity, and specificity. The effectiveness of the developed air passenger demand prediction FIS is assessed using 240 data sets, and the accuracy, precision, sensitivity, specificity, and MSE values are 90.83%, 91.09%, 90.77%, and 2.09%, respectively.

Keywords: aviation industry, fuzzy inference system, membership function, graphical user interference

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2 A Combined Approach Based on Artificial Intelligence and Computer Vision for Qualitative Grading of Rice Grains

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

Abstract:

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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1 Transformation of Periodic Fuzzy Membership Function to Discrete Polygon on Circular Polar Coordinates

Authors: Takashi Mitsuishi

Abstract:

Fuzzy logic has gained acceptance in the recent years in the fields of social sciences and humanities such as psychology and linguistics because it can manage the fuzziness of words and human subjectivity in a logical manner. However, the major field of application of the fuzzy logic is control engineering as it is a part of the set theory and mathematical logic. Mamdani method, which is the most popular technique for approximate reasoning in the field of fuzzy control, is one of the ways to numerically represent the control afforded by human language and sensitivity and has been applied in various practical control plants. Fuzzy logic has been gradually developing as an artificial intelligence in different applications such as neural networks, expert systems, and operations research. The objects of inference vary for different application fields. Some of these include time, angle, color, symptom and medical condition whose fuzzy membership function is a periodic function. In the defuzzification stage, the domain of the membership function should be unique to obtain uniqueness its defuzzified value. However, if the domain of the periodic membership function is determined as unique, an unintuitive defuzzified value may be obtained as the inference result using the center of gravity method. Therefore, the authors propose a method of circular-polar-coordinates transformation and defuzzification of the periodic membership functions in this study. The transformation to circular polar coordinates simplifies the domain of the periodic membership function. Defuzzified value in circular polar coordinates is an argument. Furthermore, it is required that the argument is calculated from a closed plane figure which is a periodic membership function on the circular polar coordinates. If the closed plane figure is continuous with the continuity of the membership function, a significant amount of computation is required. Therefore, to simplify the practice example and significantly reduce the computational complexity, we have discretized the continuous interval and the membership function in this study. In this study, the following three methods are proposed to decide the argument from the discrete polygon which the continuous plane figure is transformed into. The first method provides an argument of a straight line passing through the origin and through the coordinate of the arithmetic mean of each coordinate of the polygon (physical center of gravity). The second one provides an argument of a straight line passing through the origin and the coordinate of the geometric center of gravity of the polygon. The third one provides an argument of a straight line passing through the origin bisecting the perimeter of the polygon (or the closed continuous plane figure).

Keywords: defuzzification, fuzzy membership function, periodic function, polar coordinates transformation

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