Search results for: fuzzy transportation problem.

Authors: K. M. Oba

Abstract:

The transportation modelling technique was adopted in the solution of the problem of transportation of Plaster of Paris (POP) cement from three supply locations (construction materials markets) to three demand locations (construction sites) in Port Harcourt. The study was carried out for 40 kg bags of POP cement fully loaded on 600 bags per truck from the three selected construction materials markets in Port Harcourt. The costs of transporting the POP cement were determined and subjected to the North-West Corner, Least Cost, and Vogel’s approximation methods to determine the initial feasible solution. Of the three results, the Least Cost Method turned out to have the lowest cost. Using the Stepping Stone Method, the optimum shipping cost was finally attained after two successive iterations. The optimum shipping cost was calculated to be $1,690 or ₦1,774,500 as of October 2023. As a result of this study, the application of transportation modelling can boost the effective management of the transportation of POP cement in construction projects.

Keywords: Cost of POP cement, management of transportation, optimization of shipping cost, Plaster of Paris, transportation model.

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Authors: Seyed Habib A. Rahmati, Mohsen Sadegh Amalnick

Abstract:

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: SPC, MSA, gauge capability, Cg, Cgk.

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Authors: A. M. Pashayev, D. D. Askerov, C. Ardil, R. A. Sadiqov, P. S. Abdullayev

Abstract:

Researches show that probability-statistical methods application, especially at the early stage of the aviation Gas Turbine Engine (GTE) technical condition diagnosing, when the flight information has property of the fuzzy, limitation and uncertainty is unfounded. Hence the efficiency of application of new technology Soft Computing at these diagnosing stages with the using of the Fuzzy Logic and Neural Networks methods is considered. According to the purpose of this problem training with high accuracy of fuzzy multiple linear and non-linear models (fuzzy regression equations) which received on the statistical fuzzy data basis is made. For GTE technical condition more adequate model making dynamics of skewness and kurtosis coefficients- changes are analysed. Researches of skewness and kurtosis coefficients values- changes show that, distributions of GTE workand output parameters of the multiple linear and non-linear generalised models at presence of noise measured (the new recursive Least Squares Method (LSM)). The developed GTE condition monitoring system provides stage-by-stage estimation of engine technical conditions. As application of the given technique the estimation of the new operating aviation engine technical condition was made.

Keywords: aviation gas turbine engine, technical condition, fuzzy logic, neural networks, fuzzy statistics

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Authors: S. J. Hosseini Ghoncheh, M. Paripour

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In this paper the Huang-s method for solving a m×n fuzzy linear system when, m≤ n, is considered. The method in detail is discussed and illustrated by solving some numerical examples.

Keywords: Fuzzy number, fuzzy linear systems, Huang's method.

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Authors: Shih-Pin Chen, Shih-Syuan You

Abstract:

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: Xinhua Zhang, Kelin Li

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In this paper, the problem of stability analysis for a class of impulsive stochastic fuzzy neural networks with timevarying delays and reaction-diffusion is considered. By utilizing suitable Lyapunov-Krasovskii funcational, the inequality technique and stochastic analysis technique, some sufficient conditions ensuring global exponential stability of equilibrium point for impulsive stochastic fuzzy cellular neural networks with time-varying delays and diffusion are obtained. In particular, the estimate of the exponential convergence rate is also provided, which depends on system parameters, diffusion effect and impulsive disturbed intention. It is believed that these results are significant and useful for the design and applications of fuzzy neural networks. An example is given to show the effectiveness of the obtained results.

Keywords: Exponential stability, stochastic fuzzy cellular neural networks, time-varying delays, impulses, reaction-diffusion terms.

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Authors: Omid Jadidi, Fatemeh Firouzi, Enzo Bagliery

Abstract:

Supplier selection, in real situation, is affected by several qualitative and quantitative factors and is one of the most important activities of purchasing department. Since at the time of evaluating suppliers against the criteria or factors, decision makers (DMS) do not have precise, exact and complete information, supplier selection becomes more difficult. In this case, Grey theory helps us to deal with this problem of uncertainty. Here, we apply Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) method to evaluate and select the best supplier by using interval fuzzy numbers. Through this article, we compare TOPSIS with some other approaches and afterward demonstrate that the concept of TOPSIS is very important for ranking and selecting right supplier.

Keywords: TOPSIS, fuzzy number, MADM, Supplier selection

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Authors: Samit Kumar Majumder

Abstract:

In this paper the concept of Q-fuzzification of ideals of Γ-semigroups has been introduced and some important properties have been investigated. A characterization of regular Γ-semigroup in terms of Q-fuzzy ideals has been obtained. Operator semigroups of a Γ-semigroup has been made to work by obtaining various relationships between Q-fuzzy ideals of a Γ-semigroup and that of its operator semigroups.

Keywords: Q-Fuzzy set, Γ-semigroup, Regular Γ-semigroup, Q-Fuzzy left(right) ideal, Operator semigroups.

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Authors: Imran C.T., Syibrah M.N., Mohd Lazim A.

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Fuzzy sets theory affirmed that the linguistic value for every contraries relation is complementary. It was stressed in the intuitionistic fuzzy sets (IFS) that the conditions for contraries relations, which are the fuzzy values, cannot be greater than one. However, complementary in two contradict phenomena are not always true. This paper proposes a new idea condition for conflicting bifuzzy sets by relaxing the condition of intuitionistic fuzzy sets. Here, we will critically forward examples using triangular fuzzy number in formulating a new condition for conflicting bifuzzy sets (CBFS). Evaluation of positive and negative in conflicting phenomena were calculated concurrently by relaxing the condition in IFS. The hypothetical illustration showed the applicability of the new condition in CBFS for solving non-complement contraries intuitionistic evaluation. This approach can be applied to any decision making where conflicting is very much exist.

Keywords: Conflicting bifuzzy set, conflicting degree, fuzzy sets, fuzzy numbers.

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Authors: Chen-Yu Wang, Tsung-Chien Chen, Ming-Hui Lee, Jen-Feng Huang

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In this paper, the innovative intelligent fuzzy weighted input estimation method (FWIEM) can be applied to the inverse heat transfer conduction problem (IHCP) to estimate the unknown time-varying heat flux efficiently as presented. The feasibility of this method can be verified by adopting the temperature measurement experiment. We would like to focus attention on the heat flux estimation to three kinds of samples (Copper, Iron and Steel/AISI 304) with the same 3mm thickness. The temperature measurements are then regarded as the inputs into the FWIEM to estimate the heat flux. The experiment results show that the proposed algorithm can estimate the unknown time-varying heat flux on-line.

Keywords: Fuzzy Weighted Input Estimation Method, IHCP andHeat Flux.

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Authors: K. A. Sumithradevi, Vijayalakshmi. M. N., Annamma Abraham., Dr. Vasanta

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The various applications of VLSI circuits in highperformance computing, telecommunications, and consumer electronics has been expanding progressively, and at a very hasty pace. This paper describes a new model for partitioning a circuit using DBSCAN and fuzzy ARTMAP neural network. The first step is concerned with feature extraction, where we had make use DBSCAN algorithm. The second step is the classification and is composed of a fuzzy ARTMAP neural network. The performance of both approaches is compared using benchmark data provided by MCNC standard cell placement benchmark netlists. Analysis of the investigational results proved that the fuzzy ARTMAP with DBSCAN model achieves greater performance then only fuzzy ARTMAP in recognizing sub-circuits with lowest amount of interconnections between them The recognition rate using fuzzy ARTMAP with DBSCAN is 97.7% compared to only fuzzy ARTMAP.

Keywords: VLSI, Circuit partitioning, DBSCAN, fuzzyARTMAP.

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Authors: C. Ardil

Abstract:

This study uses two-dimensional standard fuzzy sets to enhance multiple criteria decision-making analysis for passenger aircraft selection, allowing decision-makers to express judgments with uncertain and vague information. Using two-dimensional fuzzy numbers, three decision makers evaluated three aircraft alternatives according to seven decision criteria. A validity analysis based on two-dimensional standard fuzzy weighted geometric (SFWG) and two-dimensional standard fuzzy weighted average (SFGA) operators is conducted to test the proposed approach's robustness and effectiveness in the fuzzy multiple criteria decision making (MCDM) evaluation process. 

Keywords: Standard fuzzy sets (SFSs), aircraft selection, multiple criteria decision making, intuitionistic fuzzy sets (IFSs), SFWG, SFGA, MCDM

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Authors: Aarthi Chandramohan, M. V. C. Rao

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This paper presents three new methodologies for the basic operations, which aim at finding new ways of computing union (maximum) and intersection (minimum) membership values by taking into effect the entire membership values in a fuzzy set. The new methodologies are conceptually simple and easy from the application point of view and are illustrated with a variety of problems such as Cartesian product of two fuzzy sets, max –min composition of two fuzzy sets in different product spaces and an application of an inverted pendulum to determine the impact of the new methodologies. The results clearly indicate a difference based on the nature of the fuzzy sets under consideration and hence will be highly useful in quite a few applications where different values have significant impact on the behavior of the system.

Keywords: Centroid, fuzzy set operations, intersection, triangular norms , triangular S-norms, union.

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Authors: Wudhichai Assawinchaichote

Abstract:

This paper examines the problem of designing robust H controllers for for HIV/AIDS infection system with dual drug dosages described by a Takagi-Sugeno (S) fuzzy model. Based on a linear matrix inequality (LMI) approach, we develop an H controller which guarantees the L2-gain of the mapping from the exogenous input noise to the regulated output to be less than some prescribed value for the system. A sufficient condition of the controller for this system is given in term of Linear Matrix Inequalities (LMIs). The effectiveness of the proposed controller design methodology is finally demonstrated through simulation results. It has been shown that the anti-HIV vaccines are critically important in reducing the infected cells.

Keywords: H∞ Fuzzy control; Takagi-Sugeno (TS) fuzzy model; Linear Matrix Inequalities (LMIs); HIV/AIDS infection system

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Authors: Sara Mohtashami, Habib Rajabi Mashhadi

Abstract:

With the growth of electricity generation from gas energy gas pipeline reliability can substantially impact the electric generation. A physical disruption to pipeline or to a compressor station can interrupt the flow of gas or reduce the pressure and lead to loss of multiple gas-fired electric generators, which could dramatically reduce the supplied power and threaten the power system security. Gas pressure drops during peak loading time on pipeline system, is a common problem in network with no enough transportation capacity which limits gas transportation and causes many problem for thermal domain power systems in supplying their demand. For a feasible generation scheduling planning in networks with no sufficient gas transportation capacity, it is required to consider gas pipeline constraints in solving the optimization problem and evaluate the impacts of gas consumption in power plants on gas pipelines operating condition. This paper studies about operating of gas fired power plants in critical conditions when the demand of gas and electricity peak together. An integrated model of gas and electric model is used to consider the gas pipeline constraints in the economic dispatch problem of gas-fueled thermal generator units.

Keywords:

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Authors: Mustafa Bayram Gücen, Coşkun Yakar

Abstract:

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: S. Sadi-Nezhad, K. Khalili Damghani, N. Pilevari

Abstract:

In this article, a mathematical programming model for choosing an optimum portfolio of investments is developed. The investments are considered as investment projects. The uncertainties of the real world are associated through fuzzy concepts for coefficients of the proposed model (i. e. initial investment costs, profits, resource requirement, and total available budget). Model has been coded by using LINGO 11.0 solver. The results of a full analysis of optimistic and pessimistic derivative models are promising for selecting an optimum portfolio of projects in presence of uncertainty.

Keywords: Fuzzy Programming, Fuzzy Knapsack, FuzzyCapital Budgeting, Fuzzy Project Selection

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Authors: H. Nemmour, Y. Chibani

Abstract:

Decision fusion is one of hot research topics in classification area, which aims to achieve the best possible performance for the task at hand. In this paper, we investigate the usefulness of this concept to improve change detection accuracy in remote sensing. Thereby, outputs of two fuzzy change detectors based respectively on simultaneous and comparative analysis of multitemporal data are fused by using fuzzy integral operators. This method fuses the objective evidences produced by the change detectors with respect to fuzzy measures that express the difference of performance between them. The proposed fusion framework is evaluated in comparison with some ordinary fuzzy aggregation operators. Experiments carried out on two SPOT images showed that the fuzzy integral was the best performing. It improves the change detection accuracy while attempting to equalize the accuracy rate in both change and no change classes.

Keywords: change detection, decision fusion, fuzzy logic, remote sensing.

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Authors: S.R. Khuntia, K.B. Mohanty, S. Panda, C. Ardil

Abstract:

This paper presents a comparative study of various controllers for the speed control of DC motor. The most commonly used controller for the speed control of dc motor is Proportional- Integral (P-I) controller. However, the P-I controller has some disadvantages such as: the high starting overshoot, sensitivity to controller gains and sluggish response due to sudden disturbance. So, the relatively new Integral-Proportional (I-P) controller is proposed to overcome the disadvantages of the P-I controller. Further, two Fuzzy logic based controllers namely; Fuzzy control and Neuro-fuzzy control are proposed and the performance these controllers are compared with both P-I and I-P controllers. Simulation results are presented and analyzed for all the controllers. It is observed that fuzzy logic based controllers give better responses than the traditional P-I as well as I-P controller for the speed control of dc motor drives.

Keywords: Proportional-Integral (P-I) controller, Integral- Proportional (I-P) controller, Fuzzy logic control, Neuro-fuzzy control, Speed control, DC Motor drive.

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Authors: Hamed Vahdat Nejad, Hameed Reza Pourreza, Hasan Ebrahimi

Abstract:

A new fuzzy filter is presented for noise reduction of images corrupted with additive noise. The filter consists of two stages. In the first stage, all the pixels of image are processed for determining noisy pixels. For this, a fuzzy rule based system associates a degree to each pixel. The degree of a pixel is a real number in the range [0,1], which denotes a probability that the pixel is not considered as a noisy pixel. In the second stage, another fuzzy rule based system is employed. It uses the output of the previous fuzzy system to perform fuzzy smoothing by weighting the contributions of neighboring pixel values. Experimental results are obtained to show the feasibility of the proposed filter. These results are also compared to other filters by numerical measure and visual inspection.

Keywords: Additive noise, Fuzzy logic, Image processing, Noise reduction.

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Authors: S. Yaman, S. Rostami

Abstract:

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, fuzzy modeling, fuzzy PID controller, genetic algorithm.

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Authors: G. M. Mir, N. A. Shah, Moinuddin

Abstract:

Efficient handoff algorithms are a cost-effective way of enhancing the capacity and QoS of cellular system. The higher value of hysteresis effectively prevents unnecessary handoffs but causes undesired cell dragging. This undesired cell dragging causes interference or could lead to dropped calls in microcellular environment. The problems are further exacerbated by the corner effect phenomenon which causes the signal level to drop by 20-30 dB in 10-20 meters. Thus, in order to maintain reliable communication in a microcellular system new and better handoff algorithms must be developed. A fuzzy based handoff algorithm is proposed in this paper as a solution to this problem. Handoff on the basis of ratio of slopes of normal signal loss to the actual signal loss is presented. The fuzzy based solution is supported by comparing its results with the results obtained in analytical solution.

Keywords: Slope ratio, handoff, corner effect, fuzzy logic.

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Authors: Wen-Lung Huang, Shih-Pin Chen

Abstract:

This paper investigates the optimization problem of multi-product aggregate production planning (APP) with fuzzy data. From a comprehensive viewpoint of conserving the fuzziness of input information, this paper proposes a method that can completely describe the membership function of the performance measure. The idea is based on the well-known Zadeh-s extension principle which plays an important role in fuzzy theory. In the proposed solution procedure, a pair of mathematical programs parameterized by possibility level a is formulated to calculate the bounds of the optimal performance measure at a . Then the membership function of the optimal performance measure is constructed by enumerating different values of a . Solutions obtained from the proposed method contain more information, and can offer more chance to achieve the feasible disaggregate plan. This is helpful to the decision-maker in practical applications.

Keywords: fuzzy data, aggregate production planning, membership function, parametric programming

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Authors: Fadl M. Ba-Alwi, Kamal K. Bharadwaj

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In this paper a novel algorithm is proposed that integrates the process of fuzzy hierarchy generation and rule discovery for automated discovery of Production Rules with Fuzzy Hierarchy (PRFH) in large databases.A concept of frequency matrix (Freq) introduced to summarize large database that helps in minimizing the number of database accesses, identification and removal of irrelevant attribute values and weak classes during the fuzzy hierarchy generation.Experimental results have established the effectiveness of the proposed algorithm.

Keywords: Data Mining, Degree of subsumption, Freq matrix, Fuzzy hierarchy.

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Authors: Hassan Naraghi

Abstract:

In this paper, we define permutable and mutually permutable fuzzy subgroups of a group. Then we study their relation with permutable and mutually permutable subgroups of a group. Also we study some properties of fuzzy quasinormal subgroup. We define superfuzzy subset of a fuzzy subset and we study some properties of superfuzzy subset of a fuzzy subset.

Keywords: Permutable fuzzy subgroup, mutually permutable fuzzy subgroup, fuzzy quasinormal subgroup, superfuzzy subset.

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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: A. R. Tavakolpour-Saleh, H. Jokar

Abstract:

Liquid level control of conical tank system is known to be a great challenge in many industries such as food processing, hydrometallurgical industries and wastewater treatment plant due to its highly nonlinear characteristics. In this research, an adaptive fuzzy PID control scheme is applied to the problem of liquid level control in a nonlinear tank process. A conical tank process is first modeled and primarily simulated. A PID controller is then applied to the plant model as a suitable benchmark for comparison and the dynamic responses of the control system to different step inputs were investigated. It is found that the conventional PID controller is not able to fulfill the controller design criteria such as desired time constant due to highly nonlinear characteristics of the plant model. Consequently, a nonlinear control strategy based on gain-scheduling adaptive control incorporating a fuzzy logic observer is proposed to accurately control the nonlinear tank system. The simulation results clearly demonstrated the superiority of the proposed adaptive fuzzy control method over the conventional PID controller.

Keywords: Adaptive control, fuzzy logic, conical tank, PID controller.

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Authors: Nasser Shamskia, Seyyed Habib Rahmati, Hassan Haleh , Seyyedeh Hoda Rahmati

Abstract:

The main criteria of designing in the most hydraulic constructions essentially are based on runoff or discharge of water. Two of those important criteria are runoff and return period. Mostly, these measures are calculated or estimated by stochastic data. Another feature in hydrological data is their impreciseness. Therefore, in order to deal with uncertainty and impreciseness, based on Buckley-s estimation method, a new fuzzy method of evaluating hydrological measures are developed. The method introduces triangular shape fuzzy numbers for different measures in which both of the uncertainty and impreciseness concepts are considered. Besides, since another important consideration in most of the hydrological studies is comparison of a measure during different months or years, a new fuzzy method which is consistent with special form of proposed fuzzy numbers, is also developed. Finally, to illustrate the methods more explicitly, the two algorithms are tested on one simple example and a real case study.

Keywords: Fuzzy Discharge, Fuzzy estimation, Fuzzy ranking method, Hydrological data

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Authors: George E. Tsekouras, Dimitris Papageorgiou, Sotiris Kotsiantis, Christos Kalloniatis, Panagiotis Pintelas

Abstract:

We develop a three-step fuzzy logic-based algorithm for clustering categorical attributes, and we apply it to analyze cultural data. In the first step the algorithm employs an entropy-based clustering scheme, which initializes the cluster centers. In the second step we apply the fuzzy c-modes algorithm to obtain a fuzzy partition of the data set, and the third step introduces a novel cluster validity index, which decides the final number of clusters.

Keywords: Categorical data, cultural data, fuzzy logic clustering, fuzzy c-modes, cluster validity index.

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Authors: Thair Sh. Mahmoud, Tang Sai Hong, Mohammed H. Marhaban

Abstract:

In this paper, Neuro-Fuzzy based Fuzzy Subtractive Clustering Method (FSCM) and Self Tuning Fuzzy PD-like Controller (STFPDC) were used to solve non-linearity and trajectory problems of pitch AND yaw angles of Twin Rotor MIMO system (TRMS). The control objective is to make the beams of TRMS reach a desired position quickly and accurately. The proposed method could achieve control objectives with simpler controller. To simplify the complexity of STFPDC, ANFIS based FSCM was used to simplify the controller and improve the response. The proposed controllers could achieve satisfactory objectives under different input signals. Simulation results under MATLAB/Simulink® proved the improvement of response and superiority of simplified STFPDC on Fuzzy Logic Controller (FLC).

Keywords: Fuzzy Subtractive Clustering Method, Neuro Fuzzy, Self Tuning Fuzzy Controller, and Twin Rotor MIMO System.

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