Fuzzy logic presents many potential applications for modelling and simulation. In particular, this paper analyses one of the most popular fuzzy logic techniques: Mamdani systems. Mamdani systems can look particularly appealing because they are designed to incorporate expert knowledge in the form of IF-THEN rules expressed in natural language. While this is an attractive feature for modelling and simulating social and other complex systems, its actual application presents important caveats. This paper studies the potential use of Mamdani systems to explore the logical consequences of a model based on IF-THEN rules via simulation. We show that in the best-case scenario a Mamdani system provides a function that complies with its generating set of IF-THEN rules, which is a di erent exercise from that of finding the relation or consequences implied by those rules. In general, the logical consequences of a set of rules cannot be captured by a single function. Furthermore, the consequences of an IF-THEN rule in a Mamdani system can be very di erent from the consequences of that same rule in a system governed by the most basic principles of logical deductive inference. Thus, care must be taken when applying this tool to study "the consequences" of a set of hypothesis. Previous analyses have typically focused on particular steps of the Mamdani process, while here we present a holistic assessment of this technique for (deductive) simulation purposes.
Education is a systematic effort to create good learning conditions in increasing one's potential to have good knowledge, but in the teaching and learning process one often finds students who cannot achieve achievements in accordance with their intelligence and also the teacher's attitude in teaching and educating. The teaching and learning process is sometimes less effective, teachers tend to provide material using books and blackboards, thereby reducing students' interest in learning and affecting their learning achievement. Teachers have a huge influence on each student's development, but not all teachers are able to exercise their authority in the classroom. Teachers will be able to exercise their authority if they have good teaching skills. The use of fuzzy mamdani is able to calculate the extent of the teacher's authoritative relationship to student learning achievement based on the assessment data carried out. Based on the research results, the level of authority is divided into 3 membership functions (Bad, Fair, Good), from this data the highest value is 0.74 in the good membership function, 0.25 is sufficient and 0.00 is bad. So the category of the level of relationship between teacher authority and student learning achievement with a score of 84.95 is in the Good category. The value obtained from the calculation results can be a benchmark for the teacher's attitude and upbringing towards students.
World Health Organization (WHO) estimated that approximately 80 thousand children died every year in view of Childhood Tuberculosis. The disease needs an appropriate treatment considering the difficulties in establishing a diagnosis in pediatric patients. The incapability of children to produce sputum becomes one of the difficulties. Sputum is used to diagnose a person suffering from tuberculosis, based on Mycobacterium tuberculosis in sputum. In this paper, Mamdani, Tsukamoto and Sugeno-types Fuzzy Inference System are applied to assist the tuberculosis diagnosis. The different technique in these three methods is aimed to determine the most appropriate method for such diagnosis. The results show that, of the three types of Fuzzy Inference System, the best model is Sugeno model. Sugeno-type FIS has a better accuracy compared to both Mamdani and Tsukamoto ones at 93%, equivalent to a fault diagnosis in 13 of 180 patients. Here, Mamdani-type FIS is provided the diagnostic accuracy of 89%, equivalent to the fault diagnosis in 20 of 180 patients. On the other hand, Tsukamoto is provided the diagnostic accuracy of 92%, equivalent to fault diagnosis in 15 of 180 patients. Based on the three systems, the most precise output is found in Sugeno-type Fuzzy with a value by 95.1% while for Fuzzy Mamdani and Tsukamoto, it values are 93.4% and 94.5%, respectively. Also, the highest level for the system sensitivity is found in Sugeno with 97.2% in comparison to Tsukamoto FIS by 96.67% and Mamdani at 94.4%.
Both Takagi-Sugeno (TS) and Mamdani fuzzy systems are known to be universal approximators. We investigate whether one type of fuzzy approximators is more economical than the other. The TS fuzzy systems are the typical two-input single-output TS fuzzy systems. We first establish necessary conditions on minimal system configuration of the TS fuzzy systems as function approximators. We show that the number of the input fuzzy sets and fuzzy rules needed by the TS fuzzy systems depend on the number and locations of the extrema of the function to be approximated. The resulting conditions reveal the strength of the TS fuzzy approximators. The drawback, though, is that a large number of fuzzy rules must be employed to approximate periodic or highly oscillatory functions. We then compare these necessary conditions with the ones that we established for the general Mamdani fuzzy systems in our previous papers. Results of the comparison unveil that the minimal system configurations of the TS and Mamdani fuzzy systems are comparable. Finally, we prove that the minimal configuration of the TS fuzzy systems can be reduced and becomes smaller than that of the Mamdani fuzzy systems if nontrapezoidal or nontriangular input fuzzy sets are used. We believe that all the results in present paper hold for the TS fuzzy systems with more than two input variables but the proof seems to be mathematically difficult. Our new findings are valuable in designing more compact fuzzy systems, especially fuzzy controllers and models which are two most popular and successful applications of the fuzzy approximators.
This article proposes the Mamdani complex fuzzy inference system (Mamdani CFIS) to improve performance of the classical FIS and complex FIS. The applicability of the proposed CFIS is demonstrated by applying it to six commonly available datasets from UCI Machine Learning under the comparison with Mamdani FIS and the Adaptive Neuro Complex Fuzzy Inference System (ANCFIS). It is successfully proven that the proposed Mamdani CFIS is computationally less expensive and presents a more efficient method to handle time-series data and time-periodic phenomena, among all the fuzzy IS found thus far in the literature. Furthermore, the novelty of CFIS mainly lies in its implementation of the complex number throughout the entire procedures of computation. This gives much greater flexibility of implementing unexpected, nonlinear fluctuations.
The issue of fuzzy systems as universal approximators has drawn significant attention, but all results obtained are restricted to deterministic input-output (I/O) relationships. It should be noted that, in practice, many I/O systems, including fuzzy systems, operate in the environment which is essentially stochastic. In this paper, the Mamdani fuzzy systems are generalized as stochastic systems. By proving the Mamdani systems as universal approximators with L/sup 2/-norm, the approximation capability of the stochastic Mamdani systems to a class of random processes is systematically analyzed. In the mean square sense, such stochastic fuzzy systems are capable of approximating the prescribed random processes with arbitrary accuracy. Further, an efficient learning algorithm for the stochastic Mamdani systems is developed. Finally, a simulation example is employed to demonstrate our results.
The fundamental difference between an interval type-2 (IT2) fuzzy controller and a type-1 fuzzy controller is the footprint of uncertainty (FOU) of an IT2 fuzzy set. In this paper, we study how FOUs affect the analytical structure (i.e., the input-output mathematical relationship) of a broad class of IT2 Mamdani and takagi-sugeno (TS) controllers. The controllers employ arbitrary fuzzy rules, the Karnik-Mendel (KM) or Enhanced KM type-reducer, the minimum AND operator, and the centroid defuzzifier. The controllers utilize commonly used IT2 fuzzy sets for their input variables and any kind of type-2 fuzzy sets for their output variable. We prove that, with increase of FOUs of the input fuzzy sets, the Mamdani controllers approach constant controllers, and the TS controllers approach piecewise linear controllers. The resemblance to the constant or pricewise linear controllers increases as the FOUs increase. When all the FOUs are at their maximum (to reflect the highest level of uncertainties), the Mamdani and TS controllers become the constant controllers and piecewise linear controllers, respectively. We investigate how change in the resemblance takes place progressively as FOUs increase. We also show that an increase in the resemblance narrows control gain variations for part of the IT2 controllers, which can worsen control performance. These findings implicit controller design-too large FOUs are generally undesirable for the input fuzzy sets because they can make an IT2 controller behave like a constant or piecewise linear controller. Real-time control experiment results are provided to illustrate the theoretical analysis.
Penelitian ini adalah perancangan sistem perencanaan jumlah produksi roti menggunakan metode fuzzy mamdani di Judens Bakery Medan Sumatra utara. Judens Bakery merupakan salah satu toko baru yang bergerak dibidang makanan. Judens Bakery sering mengalami ketidakstabilan permintaa n pasar terhadap produksi roti yang terkadang tinggi dan rendah. Hal itu menjadi permasalahan bagi Judens Bakery dalam menentukan perencanaan jumlah produksi roti. Sehingga Judens Bakery sering memproduksi roti dan kue yang berlebih. Akibatnya dapat membuat kerugian bagi pihak Judens Bakery karena roti dan kue yang sudah tidak layak dipasarkan akan dibuang. Untuk mengelesaikan permasalahan tersebut perlu diselesaikan dengan merencanakan jumlah poduksi roti berdasarkan jumlah persediaan dan jumlah permintaan dengan menggunakan metode fuzzy Mamdani. Perancangan sistem ini dibuat berbasis dekstop dengan bahasa pemrograman Microsoft Visual Basic 6.0 dan database yang digunakan adalah microsoft acces. Berdasarkan rancangan sistem yang dihasilkan, maka dapat diket ahui rencana jumlah produksi dengan menerapkan metode fuzzy mamdani sehingga perusahaan dapat merencanakan jumlah produksi sesuai dengan jumlah permintaan. Dengan menggunakan aplikasi tersebut pihak Judens Bakery dapat merencanakan jumlah produksi roti lebih cepat, tepat dan efisien
In many decision support applications, it is important to guarantee the expressive power, easy formalization and interpretability of Mamdani-type fuzzy inference systems (FIS), while ensuring the computational efficiency and accuracy of Sugeno-type FIS. Hence, in this paper we present an approach to transform a Mamdani-type FIS into a Sugeno-type FIS. We consider the problem of mapping Mamdani FIS to Sugeno FIS as an optimization problem and by determining the first order Sugeno parameters, the transformation is achieved. To solve this optimization problem we compare three methods: least squares, genetic algorithms and an adaptive neuro-fuzzy inference system. An illustrative example is presented to discuss the approaches.
The database of a rule-based systemmay contain imprecisionswhich appear in the description of the rules given by the expert. Because such an inference can not be made by the methods which use classical two valued logic or many valued logic, Zadeh in (Zadeh, 1975) and Mamdani in (Mamdani, 1977) suggested an inference rule called compositional rule of inference. Using this inference rule, several methods for fuzzy reasoning were proposed. Zadeh (Zadeh, 1979) extends the traditional Modus Ponens rule in order to work with fuzzy sets, obtaining the Generalized Modus Ponens (GMP) rule.
Hybrid algorithm is the hot issue in Computational Intelligence (CI) study. From in-depth discussion on Simulation Mechanism Based (SMB) classification method and composite patterns, this paper presents the Mamdani model based Adaptive Neural Fuzzy Inference System (M-ANFIS) and weight updating formula in consideration with qualitative representation of inference consequent parts in fuzzy neural networks. M-ANFIS model adopts Mamdani fuzzy inference system which has advantages in consequent part. Experiment results of applying M-ANFIS to evaluate traffic Level of service show that M-ANFIS, as a new hybrid algorithm in computational intelligence, has great advantages in non-linear modeling, membership functions in consequent parts, scale of training data and amount of adjusted parameters.
Recent studies have shown that both Mamdani-type and Takagi-Sugeno-type fuzzy systems are universal approximators in that they can uniformly approximate continuous functions defined on compact domains with arbitrarily high approximation accuracy. In this paper, we investigate necessary conditions for general multiple-input single-output (MISO) Mamdani fuzzy systems as universal approximators with as minimal system configuration as possible. The general MISO fuzzy systems employ almost arbitrary continuous input fuzzy sets, arbitrary singleton output fuzzy sets, arbitrary fuzzy rules, product fuzzy logic AND, and the generalized defuzzifier containing the popular centroid defuzzifier as a special case. Our necessary conditions are developed under the practically sensible assumption that only a finite set of extrema of the multivariate continuous function to be approximated is available. We have first revealed a decomposition property of the general fuzzy systems: A r-input fuzzy system can always be decomposed to the sum of r simpler fuzzy systems where the first system has only one input variable, the second one two input variables, and the last one r input variables. Utilizing this property, we have derived some necessary conditions for the fuzzy systems to be universal approximators with minimal system configuration. The conditions expose the strength as well as limitation of the fuzzy approximation: (1) only a small number of fuzzy rules may be needed to uniformly approximate multivariate continuous functions that have a complicated formulation but a relatively small number of extrema; and (2) the number of fuzzy rules must be large in order to approximate highly oscillatory continuous functions. A numerical example is given to demonstrate our new results.
In this research, a new multilayered mamdani fuzzy inference system (Ml-MFIS) is proposed to diagnose hepatitis B. The proposed automated diagnosis of hepatitis B using multilayer mamdani fuzzy inference system (ADHB-ML-MFIS) expert system can classify the different stages of hepatitis B such as no hepatitis, acute HBV, or chronic HBV. The expert system has two input variables at layer I and seven input variables at layer II. At layer I, input variables are ALT and AST that detect the output condition of the liver to be normal or to have hepatitis or infection and/or other problems. The further input variables at layer II are HBsAg, anti-HBsAg, anti-HBcAg, anti-HBcAg-IgM, HBeAg, anti-HBeAg, and HBV-DNA that determine the output condition of hepatitis such as no hepatitis, acute hepatitis, or chronic hepatitis and other reasons that arise due to enzyme vaccination or due to previous hepatitis infection. This paper presents an analysis of the results accurately using the proposed ADHB-ML-MFIS expert system to model the complex hepatitis B processes with the medical expert opinion that is collected from the Pathology Department of Shalamar Hospital, Lahore, Pakistan. The overall accuracy of the proposed ADHB-ML-MFIS expert system is 92.2%.
Diabetes is a chronic disease in which there are high levels of sugar in the blood. Insulin is a hormone that regulates the blood glucose level in the body. Diabetes mellitus can be caused by too little insulin, a resistance to insulin, or both. Although research activities on controlling blood glucose have been attempted to lower the blood glucose level in the quickest possible time, there are some shortages in the amount of the insulin injection. In this paper, a complete model of the glucose--insulin regulation system, which is a nonlinear delay differential model, is used. The purpose of this paper is to follow the glucose profiles of a healthy person with minimum infused insulin. To achieve these purposes, an intelligent fuzzy controller based on a Mamdani-type structure, namely the swarm optimization tuned Mamdani fuzzy controller, is proposed for type 1 diabetic patients. The proposed fuzzy controller is optimized by a novel heuristic algorithm, namely linearly decreasing weight particle swarm optimization. To verify the robust performance of the proposed controller, a group of 4 tests is applied. Insensitivity to multiple meal disturbances, high accuracy, and superior robustness to model the parameter uncertainties are the key aspects of the proposed method. The simulation results illustrate the superiority of the proposed controller.
A wheeled human-conveyance vehicle (WHCV) with a low-level microprocessor is realized in this paper. WHCVs are environmentally friendly short-range transportation vehicles. This paper proposes a simple Mamdani-like fuzzy controller for self-balancing WHCV control. System stability is guaranteed by establishing sufficient conditions based on the Lyapunov stability analysis. Finally, experimental results show that the proposed Mamdani-like fuzzy control strategy can control the WHCV.
Fuzzy inference systems for diagnosis of diabetes are developed using Mamdani-type and Sugeno-type fuzzy models. The outcome obtained by two fuzzy inference systems is evaluated. This paper summarizes the essential variation among the Mamdani-type and Sugeno-type fuzzy inference systems. MATLAB fuzzy logic toolbox is used for the simulation of both the models. This also confirms which one is a superior choice of the two fuzzy inference systems for diagnosis of diabetes.
The main purpose of this study is to assess forest fire susceptibility maps (FFSMs) and their performances comparison using modified analytical hierarchy process (M-AHP) and Mamdani fuzzy logic (MFL) models in a geographic information system (GIS) environment. This study was carried out in the Minudasht Forests, Golestan Province, Iran, and was conducted in three main stages such as spatial data construction, forest fire modelling using M-AHP and MFL, and validation of constructed models using receiver operating characteristic (ROC) curve. At first, seven conditioning factors, such as altitude, slope aspect, slope angle, annual temperature, wind effect, land use, and normalized different vegetation index, were extracted from the spatial database. In the next step, FFSMs were prepared using M-AHP and MFL modules in a Netcad-GIS Architect environment. Finally, the ROC curves and area under the curves (AUCs) were estimated for validation purposes. The results showed that the AUCs for MFL and M-AHP are 88.20% and 77.72%, respectively. The results obtained in this study also showed that the MFL model performed better than the M-AHP model. These FFSMs can be applied for land use planning, management, and prevention of future fire hazards.
Maximum profit gained from maximum sales. Maximum sales means that they can meet the demands. If the products produced by the company is less than requests then the company will lose the opportunity to get maximum profit. Therefore, planning the Amount products in a company is very important in order to meet the market demand precisely and with the appropriate amount. Factors that need to be considered in determining the amount products, such as the demand and supply of old periods. The availability of production goods is still difficult to monitor by the company, because the system is still relying on manual calculations of the company employees, to assist the company in predicting the availability of production goods Effective then used the fuzzy logic calculations. During this time the availability of production goods in Salman Collection is seen from customer request. This makes the company not get the maximum profit because there is no planning the amount of production of goods. This study uses methods with a descriptive approach using the fuzzy logic Mamdani technique. The results of this research is an application of calculation of goods production based on the fuzzy manual calculations of the "logic Mamdani," Built applications can help the company determine the amount of production in accordance with consumer demand so that The demand at Salman Collection is fulfilled and the more optimal the amount that the company will produce.
Virtual reality applications which incorporate haptic devices to enrich userspsila sense of touch are increasing in number. Assessing the quality of experience (QoE) of these applications reflects the amount of overall satisfaction and benefit gained from the application plus it lays the foundation for ideal user-centric design in the future. In this paper we build on our QoE fuzzy logic model, previously simulated and tested, by comparing results from two different and well-established fuzzy systems: Mamdani and Sugeno. The results analytically demonstrate the essential differences between the two systems and the benefits of using either one in assessing the overall QoE.
At first sight, it seems that ordered linguistic values for all input variables and the output variable and a set of rules describing a monotone system are all that is needed for a monotone model. However, this is not the case. In this study, we show that the choice of the mathematical operators used when calculating the model output and the properties of the membership functions in the output domain are also of crucial importance to obtain a monotone input-output behavior. In the Mamdani-Assilian models considered in this study, the linguistic values of the input variables, as well as the output variable, are described by trapezoidal membership functions that form a fuzzy partition, the rule base is monotone, and the crisp output is obtained by the center-of-gravity (COG) defuzzification method. It is verified that for each of the three basic t-norms, i.e., the minimum T <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">M</sub> , the product T <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">P</sub> , and the Lukasiewicz t-norm T <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">L</sub> , a monotone input-output behavior is obtained for any monotone rule base, or at least for any monotone smooth rule base. The outcome of this study is a guideline for designers of monotone linguistic fuzzy models. For the t-norms T <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">M</sub> and T <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">L</sub> , models with a single input variable show a monotone input-output behavior for any monotone rule base when the linguistic output values in the consequents of the rules are defined by trapezoidal or triangular membership functions with intervals of changing membership degrees of equal length. The latter restriction can easily be bypassed by an auxiliary interpolation procedure. For the t-norm T <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">P</sub> , models with a single input variable show a monotone input-output behavior for any monotone rule base and any fuzzy output partition. When designing a monotone model with more than one input variable, one should opt for the t-norm T <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">P</sub> and use a monotone smooth rule base. It is shown that monotonicity of models with two input variables that apply T <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">P</sub> is guaranteed for any monotone smooth rule base and any fuzzy output partition. Finally, it is proved that a monotone input-output behavior is always obtained for models with three input variables that apply T <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">P</sub> and a monotone smooth rule base when the linguistic output values in the consequents of the rules are defined by trapezoidal or triangular membership functions of identical shape.