Search results for: Fuzzy multi-objective optimization problem

Authors: W. Wongthatsanekorn, N. Matheekrieangkrai

Abstract:

This research proposes Bee Algorithm (BA) to optimize Ready Mixed Concrete (RMC) truck scheduling problem from single batch plant to multiple construction sites. This problem is considered as an NP-hard constrained combinatorial optimization problem. This paper provides the details of the RMC dispatching process and its related constraints. BA was then developed to minimize total waiting time of RMC trucks while satisfying all constraints. The performance of BA is then evaluated on two benchmark problems (3 and 5construction sites) according to previous researchers. The simulation results of BA are compared in term of efficiency and accuracy with Genetic Algorithm (GA) and all problems show that BA approach outperforms GA in term of efficiency and accuracy to obtain optimal solution. Hence, BA approach could be practically implemented to obtain the best schedule.

Keywords: Bee Colony Optimization, Ready Mixed Concrete Problem.

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Authors: Sumanpreet Kaur, Harjit Pal Singh, Vikas Khullar

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In Wireless Sensor Network (WSN), the sensor containing motes (nodes) incorporate batteries that can lament at some extent. To upgrade the energy utilization, clustering is one of the prototypical approaches for split sensor motes into a number of clusters where one mote (also called as node) proceeds as a Cluster Head (CH). CH selection is one of the optimization techniques for enlarging stability and network lifespan. Deterministic Stable Election Protocol (DSEP) is an effectual clustering protocol that makes use of three kinds of nodes with dissimilar residual energy for CH election. Fuzzy Logic technology is used to expand energy level of DSEP protocol by using fuzzy inference system. This paper presents protocol DSEP using Fuzzy Logic (DSEP-FL) CH by taking into account four linguistic variables such as energy, concentration, centrality and distance to base station. Simulation results show that our proposed method gives more effective results in term of a lifespan of network and stability as compared to the performance of other clustering protocols.

Keywords: Deterministic stable election protocol, energy model, fuzzy logic, wireless sensor network.

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Authors: Omid Jadidi, Fatemeh Firouzi, Enzo Bagliery

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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

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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: 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: 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: Ghada Elshafei, Abdelazim Negm

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Recently, the green architecture becomes a significant way to a sustainable future. Green building designs involve finding the balance between comfortable homebuilding and sustainable environment. Moreover, the utilization of the new technologies such as artificial intelligence techniques are used to complement current practices in creating greener structures to keep the built environment more sustainable. The most common objectives in green buildings should be designed to minimize the overall impact of the built environment that effect on ecosystems in general and in particularly human health and natural environment. This will lead to protecting occupant health, improving employee productivity, reducing pollution and sustaining the environmental. In green building design, multiple parameters which may be interrelated, contradicting, vague and of qualitative/quantitative nature are broaden to use. This paper presents a comprehensive critical state- ofart- review of current practices based on fuzzy and its combination techniques. Also, presented how green architecture/building can be improved using the technologies that been used for analysis to seek optimal green solutions strategies and models to assist in making the best possible decision out of different alternatives.

Keywords: Green architecture/building, technologies, optimization, strategies, fuzzy techniques and models.

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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: P. Saravanan, T. Arunkumar

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Vehicular Adhoc Network (VANET) is a new technology which aims to ensure intelligent inter-vehicle communications, seamless internet connectivity leading to improved road safety, essential alerts, and access to comfort and entertainment. VANET operations are hindered by mobile node’s (vehicles) uncertain mobility. Routing algorithms use metrics to evaluate which path is best for packets to travel. Metrics like path length (hop count), delay, reliability, bandwidth, and load determine optimal route. The proposed scheme exploits link quality, traffic density, and intersections as routing metrics to determine next hop. This study enhances Geographical Routing Protocol (GRP) using fuzzy controllers while rules are optimized with Bee Swarm Optimization (BSO). Simulations results are compared to conventional GRP.

Keywords: Bee Swarm Optimization (BSO), Geographical Routing Protocol (GRP), Vehicular Adhoc Network (VANET).

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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: Ioannis N. Koukoulis, Clio G. Vossou, Christopher G. Provatidis

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The aim of the current work is to present a comparison among three popular optimization methods in the inverse elastostatics problem (IESP) of flaw detection within a solid. In more details, the performance of a simulated annealing, a Hooke & Jeeves and a sequential quadratic programming algorithm was studied in the test case of one circular flaw in a plate solved by both the boundary element (BEM) and the finite element method (FEM). The proposed optimization methods use a cost function that utilizes the displacements of the static response. The methods were ranked according to the required number of iterations to converge and to their ability to locate the global optimum. Hence, a clear impression regarding the performance of the aforementioned algorithms in flaw identification problems was obtained. Furthermore, the coupling of BEM or FEM with these optimization methods was investigated in order to track differences in their performance.

Keywords: Elastostatic, inverse problem, optimization.

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Authors: Tarek M. Mahmoud

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Selecting the routes and the assignment of link flow in a computer communication networks are extremely complex combinatorial optimization problems. Metaheuristics, such as genetic or simulated annealing algorithms, are widely applicable heuristic optimization strategies that have shown encouraging results for a large number of difficult combinatorial optimization problems. This paper considers the route selection and hence the flow assignment problem. A genetic algorithm and simulated annealing algorithm are used to solve this problem. A new hybrid algorithm combining the genetic with the simulated annealing algorithm is introduced. A modification of the genetic algorithm is also introduced. Computational experiments with sample networks are reported. The results show that the proposed modified genetic algorithm is efficient in finding good solutions of the flow assignment problem compared with other techniques.

Keywords: Genetic Algorithms, Flow Assignment, Routing, Computer network, Simulated Annealing.

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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: Teerapun Saeheaw, Nivit Charoenchai, Wichai Chattinnawat

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This paper proposes a meta-heuristic called Ant Colony Optimization to solve multi-objective production problems. The multi-objective function is to minimize lead time and work in process. The problem is related to the decision variables, i.e.; distance and process time. According to decision criteria, the mathematical model is formulated. In order to solve the model an ant colony optimization approach has been developed. The proposed algorithm is parameterized by the number of ant colonies and the number of pheromone trails. One example is given to illustrate the effectiveness of the proposed model. The proposed formulations; Max-Min Ant system are then used to solve the problem and the results evaluate the performance and efficiency of the proposed algorithm using simulation.

Keywords: Ant colony optimization, multi-objective problems.

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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: Ahmed A.D. Sarhan, Lim Siew Fen, Mum Wai Yip, M. Sayuti

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Ti6Al4V alloy is highly used in the automotive and aerospace industry due to its good machining characteristics. Micro EDM drilling is commonly used to drill micro hole on extremely hard material with very high depth to diameter ratio. In this study, the parameters of micro-electrical discharge machining (EDM) in drilling of Ti6Al4V alloy is optimized for higher machining accuracy with less hole-dilation and hole taper ratio. The micro-EDM machining parameters includes, peak current and pulse on time. Fuzzy analysis was developed to evaluate the machining accuracy. The analysis shows that hole-dilation and hole-taper ratio are increased with the increasing of peak current and pulse on time. However, the surface quality deteriorates as the peak current and pulse on time increase. The combination that gives the optimum result for hole dilation is medium peak current and short pulse on time. Meanwhile, the optimum result for hole taper ratio is low peak current and short pulse on time.

Keywords: Micro EDM, Ti-6Al-4V alloy, fuzzy logic based analysis, optimization, machining accuracy.

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Authors: Vahid Hajipour, Samira V. Noshafagh, Reza Tavakkoli-Moghaddam

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This article proposes a novel Pareto-based multiobjective meta-heuristic algorithm named non-dominated ranking genetic algorithm (NRGA) to solve multi-facility location-allocation problem. In NRGA, a fitness value representing rank is assigned to each individual of the population. Moreover, two features ranked based roulette wheel selection including select the fronts and choose solutions from the fronts, are utilized. The proposed solving methodology is validated using several examples taken from the specialized literature. The performance of our approach shows that NRGA algorithm is able to generate true and well distributed Pareto optimal solutions.

Keywords: Non-dominated ranking genetic algorithm, Pareto solutions, Multi-facility location-allocation problem.

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

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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

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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: Shuangquan Liu, Jinwen Wang, Dada Wang

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A case study of the generation scheduling optimization of the multi-hydroplants on the Yuan River Basin in China is reported in this paper. Concerning the uncertainty of the inflows, the long/mid-term generation scheduling (LMTGS) problem is solved by a stochastic model in which the inflows are considered as stochastic variables. For the short-term generation scheduling (STGS) problem, a constraint violation priority is defined in case not all constraints are satisfied. Provided the stage-wise separable condition and low dimensions, the hydroplant-based operational region schedules (HBORS) problem is solved by dynamic programming (DP). The coordination of LMTGS and STGS is presented as well. The feasibility and the effectiveness of the models and solution methods are verified by the numerical results.

Keywords: generation scheduling, multi-hydroplants, optimization.

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

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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: Hao Wu, Jonathan L. Shapiro

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The Bayesian Optimization Algorithm (BOA) is an algorithm based on the estimation of distributions. It uses techniques from modeling data by Bayesian networks to estimating the joint distribution of promising solutions. To obtain the structure of Bayesian network, different search algorithms can be used. The key point that BOA addresses is whether the constructed Bayesian network could generate new and useful solutions (strings), which could lead the algorithm in the right direction to solve the problem. Undoubtedly, this ability is a crucial factor of the efficiency of BOA. Varied search algorithms can be used in BOA, but their performances are different. For choosing better ones, certain suitable method to present their ability difference is needed. In this paper, a greedy search algorithm and a stochastic search algorithm are used in BOA to solve certain optimization problem. A method using Kullback-Leibler (KL) Divergence to reflect their difference is described.

Keywords: Bayesian optimization algorithm, greedy search, KL divergence, stochastic search.

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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: Ali Dorostkar

Abstract:

In this paper, a basic schematic of fractional dimensional optimization problem is presented. As will be shown, a method is performed based on a relation between roots and tangent lines of function in fractional dimensions for an arbitrary initial point. It is shown that for each polynomial function with order N at least N tangent lines must be existed in fractional dimensions of 0 < α < N+1 which pass exactly through the all roots of the proposed function. Geometrical analysis of tangent lines in fractional dimensions is also presented to clarify more intuitively the proposed method. Results show that with an appropriate selection of fractional dimensions, we can directly find the roots. Method is presented for giving a different direction of optimization problems by the use of fractional dimensions.

Keywords: Tangent line, fractional dimension, root, optimization problem.

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

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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: 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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