Kinds Of Membership Functions Research Articles

Application of adaptive network-based fuzzy inference system (ANFIS) in the numerical investigation of Cu/water nanofluid convective flow

The computational fluid dynamics (CFD) modeling is an applicable tool for the prediction of fluid flow characteristics (velocity, temperature, pressure, etc.). However, CFD requires a lot of time, computational efforts and as a result, much more expenses for complicated cases (e.g. turbulent flow, 3-dimensional calculations, etc.). The present work tries to conduct an investigation on the potential of the artificial intelligence algorithms in overcoming such barriers of CFD modeling. Turbulent forced convection of Cu/water nanofluid in a tube under constant heat flux is considered as a case study for the model development. The density and viscosity of the based fluid are enhanced by the suspension of the nanoparticles. This makes more pressure drop and as a result, imposes more pumping power. So, this paper is focused on a way to facilitate the prediction of the pressure of the nanofluid convective flow. The results of the CFD modeling are learned by the adaptive network-based fuzzy inference system (ANFIS), as the artificial intelligence method. The CFD modeling is done for several Cu nanoparticle volume fractions (i.e. 0.3, 0.5, 0.8, 1, and 2). Several types of variables as inputs (i.e. x, y, z, and nanoparticle volume fraction) and different kinds of membership functions (i.e. Generalized bell-shaped membership function (gbellmf), Gaussian membership function (gaussmf), Gaussian combination membership function (gauss2mf), Difference between two sigmoidal membership functions (dsigmf), Product of two sigmoidal membership functions (psigmf)) are examined until the intelligence requirements of the ANFIS are satisfied. Once the best intelligence of ANFIS has been achieved, there is no need for complicated CFD modeling. The ANFIS predictions show the highest compatibility with the CFD results. The maximum pressure drop was predicted around 1500 Pa. The results also revealed that for checking the intelligence condition the coefficient of determination (R2) is not solely sufficient and the error values must be considered as well. Considering the gauss2mf as the membership function and the nanoparticle volume fraction as the fourth input, the ANFIS could distinguish intelligently the pattern of data (changing the pressure with coordinates and particle fraction). For the best intelligence, the mean standard error was around zero, while the coefficient of determination was close to one. At this condition, the pressure of the nanofluid could be determined as a function of the nanoparticle volume fraction and anywhere inside the tube without using the CFD modeling.

A Novel Method to Evaluate the Effect of Slope Blasting under Impact Loading

In this paper, the quantitative evaluation of the explosion effect based on the fuzzy comprehensive evaluation method is proposed to describe the qualitative evaluation results. The selected state characteristic parameters are expressed by two kinds of membership functions, fuzzy normal and triangular distribution membership functions, and preliminary evaluation results are obtained. The validity index of the maximum membership principle is used to assess the accuracy of the evaluation results of two algorithms, and a relevant approaching degree is chosen to optimize the results. The entire evaluation process selects eleven indicators to form an evaluation set, including the boulder yield, root rate, flying distance of flyrock, explosive consumption, postcracking distance, detonator unit consumption, vibration velocity, loose coefficient, cast distance, throw rate, and blasted volume per meter of hole. Part of the indicator parameters are derived from field test monitoring, and another part of the indicator parameters are derived from numerical simulation. The simulation process uses the user-defined material interface function provided by LS-DYNA. And the numerical model of slope blasting is established by embedding the evolution relationship of tensile and compressive damage into the elastoplastic constitutive material. The evaluation method proposed in this paper is used to evaluate the postexplosion effect of Zijin Mountain gold-copper mine slope cast blasting. The results demonstrate that the fuzzy normal distribution membership function can correlate the state characteristic information and evaluation index effectively, and the working condition after explosion can be reflected accurately. Additionally, the influencing factors can be ranked by the importance degrees according to the calculated value of the evaluation index.

A Gray-Level Dynamic Range Modification Technique for Image Feature Extraction Using Fuzzy Membership Function

The features of an image must be unique so it is necessary to use certain techniques to ensure them. One of the common techniques is to modify the gray dynamic range of an image. In principle, the gray level dynamic range modification maps the gray level ranges from the input image to the new gray level range as an output image using a specific function. Fuzzy Membership Function (MF) is one kind of membership function that applies the Fuzzy Logic concept. This study uses Trapezoidal MF to map the gray dynamic range of each RGB component to produce a feature of an RGB image. The aim of this study is how to ensure the uniqueness of image features through the setting of Trapezoidal MF parameters to obtain the new dynamic range of gray levels that minimize the possibility of other features other than the selected feature. To test the performance of the proposed method, it also tries to be applied to the signature image. Mean Absolute Error (MAE) calculations between feature labels are performed to test authentication between signatures. The results obtained are for comparison of samples of signature images derived from the same source having a much smaller MAE than the comparison of samples of signature images originating from different sources.

ПОВЫШЕНИЕ ЭФФЕКТИВНОСТИ ВЕТРОЭНЕРГЕТИЧЕСКОЙ УСТАНОВКИ С ВЕРТИКАЛЬНОЙ ОСЬЮ ВРАЩЕНИЯ

The questions connected with increase of efficiency of functioning of a wind power plant with a vertical axis of rotation are considered.Such plants convert the energy of the wind flow into rotational energy of the generator shaft, pump or other actuators. An overview of the design options for wind turbines of this type is presented. For vertically-axial wind power plants, in comparison with horizontally-propeller ones, it is possible to increase their efficiency by providing insensitivity to wind direction change. This is possible provided that the angular position of the blades with respect to the wind flow is continuously and purposefully changed as the wind turbine rotates. The principle of increasing the efficiency of the wind power plant is proposed due to the synchronous control of the position of the blades, depending on the direction and speed of the wind flow. The implementation of this principle is considered in detail for a four-bladed wind turbine. Depending on the direction and magnitude of the wind flow, as well as the angular velocity of rotation of the turbine, the value of the angle of the initial installation of the blades was analytically obtained, which ensures the maximum efficiency of using the wind plant. The functional scheme of the control system of the orientation of the four blades is formed. This system uses information about the current power of the generator, the rotation speed of the wind turbine, the direction and speed of the wind flow, obtained from the respective sensors. A detailed functional diagram of one channel of the control system has been constructed taking into account the initial exposure of the blade, which additionally uses information about the current angular position of the blade and the speed of its turn. Each such channel contains a proportional-differential controller or fuzzy logic controller. The proposed fuzzy controller has two inputs of linguistic variables - the angle of rotation of the blade and the speed of its rotation. As a kind of membership functions, a triangular distribution is chosen. A system of rules for adjusting the fuzzy controller has been developed. The computer simulation of the channel functioning of the control system with two types of regulators for the mode of initial setting of the blades with a change in wind direction was performed. Comparison of the quality of the control system with a proportional-differential and fuzzy controller is performed

A prediction model of ammonia emission from a fattening pig room based on the indoor concentration using adaptive neuro fuzzy inference system

Ammonia (NH3) is considered one of the significant pollutions contributor to indoor air quality and odor gas emission from swine house because of the negative impact on the health of pigs, the workers and local environment. Prediction models could provide a reasonable way for pig industries and environment regulatory to determine environment control strategies and give an effective method to evaluate the air quality. The adaptive neuro fuzzy inference system (ANFIS) simulates human’s vague thinking manner to solve the ambiguity and nonlinear problems which are difficult to be processed by conventional mathematics. Five kinds of membership functions were used to build a well fitted ANFIS prediction model. It was shown that the prediction model with “Gbell” membership function had the best capabilities among those five kinds of membership functions, and it had the best performances compared with backpropagation (BP) neuro network model and multiple linear regression model (MLRM) both in wintertime and summertime, the smallest value of mean square error (MSE), mean absolute percentage error (MAPE) and standard deviation (SD) are 0.002 and 0.0047, 31.1599 and 23.6816, 0.0564 and 0.0802, respectively, and the largest coefficients of determination (R2) are 0.6351 and 0.6483, repectively. The ANFIS prediction model could be served as a beneficial strategy for the environment control system that has input parameters with highly fluctuating, complexity, and non-linear relationship.

A Modular Implementation Scheme for Nonsingleton Type-2 Fuzzy Logic Systems With Input Uncertainties

Using nonsingleton (NS) input fuzzifiers along with type-2 fuzzy systems to handle uncertainties in inputs has received some attention in recent years. However, the NS fuzzification schemes proposed so far have a limited impact because they are restricted to a particular kind of fuzzy sets only. This paper proposes a modular implementation scheme for NS type-2 fuzzy logic systems with input uncertainties. The proposed implementation scheme constitutes a generalized fuzzification which is independent of the forms/shapes of the fuzzy sets, i.e., both the NS fuzzifiers and the membership functions. To investigate the effectiveness of the proposed scheme, type-2 fuzzy logic controllers for three different applications, airplane altitude control, obstacle avoidance for a mobile robot, and a wall following robot, are developed. Additionally, for mapping NS fuzzifiers for real sensors, a sensory noise pattern recognition stage is also developed. Despite encountering various kinds of membership functions and input uncertainties along these three applications, the proposed scheme is able to successfully deal with all three applications. Moreover, the performance results in all three application setups show that NS fuzzification can improve the robustness of type-2 fuzzy logic systems against input uncertainties.

Interactive Decision Making for Fuzzy Random Multiobjective Linear Programming Problems with Variance Covariance Matrices Through Fractile Optimization

In this paper, we focus on fuzzy random multiobjective linear programming problems with variance covariance matrices through fractile optimization, and propose an interactive decision making method to obtain a satisfactory solution. In the proposed method, it is assumed that the decision maker has fuzzy goals for not only permissible probability levels but also the corresponding objective functions. Such fuzzy goals are quantified by eliciting the corresponding membership functions. Using the fuzzy decision, such two kinds of membership functions are integrated, andDf-Pareto optimal solution concept is defined in the integrated membership space. By using the bisection method and the convex programming technique, a satisfactory solution is obtained from among aDf-Pareto optimal solution set through the interaction with the decision maker.

Interactive fuzzy programming for multiobjective fuzzy random linear programming problems through possibility-based probability maximization

This paper presents interactive fuzzy programming for multiobjective fuzzy random linear programming problems through possibility-based probability maximization. In our proposed approach, it is assumed that the decision maker has fuzzy goals for not only original objective functions but also the corresponding distribution functions in a probability maximization model, and such fuzzy goals are quantified by eliciting the corresponding membership functions. Using the fuzzy decision, such two kinds of membership functions are integrated. The satisfactory solution is derived from among an extended Pareto optimal solution set through the interaction with the decision maker. An illustrative numerical example is provided to demonstrate the efficiency of the proposed method.

Reliability of fuzzy systems evaluation methodology using different types of vague sets

Purpose. Development of the reliability calculating methodology of fuzzy systems with components, reliability parameters of which are described by the membership functions of various kinds. Methodology. Systematic analysis of the known approaches to the assessment of the reliability of fuzzy systems with vague boundaries and different kinds of membership functions. Findings. A unified description and the new tabular algorithm of various arithmetic operations run between the various types of fuzzy sets are proposed and tabular methods of reliability analysis of the basic structures of fuzzy systems are developed. Originality. A generalized description of triangular and trapezoid-shaped accessory functions of fuzzy boundaries in a special tuples is introduced, analytical expressions for the formation of tabular schedules of their functions and the calculation of the reliability of fuzzy systems with complex structures are obtained: sequential, redundant - parallel, serial-parallel, parallel-serial. The practical value.The obtained models and tabular algorithms simplify the calculations of the reliability of complex electro-mechanical human-machine automation systems with fuzzy parameters and vague boundaries.

Reference Function Based Spatiotemporal Fuzzy Logic Control Design Using Support Vector Regression Learning

This paper presents a reference function based 3D FLC design methodology using support vector regression (SVR) learning. The concept of reference function is introduced to 3D FLC for the generation of 3D membership functions (MF), which enhance the capability of the 3D FLC to cope with more kinds of MFs. The nonlinear mathematical expression of the reference function based 3D FLC is derived, and spatial fuzzy basis functions are defined. Via relating spatial fuzzy basis functions of a 3D FLC to kernel functions of an SVR, an equivalence relationship between a 3D FLC and an SVR is established. Therefore, a 3D FLC can be constructed using the learned results of an SVR. Furthermore, the universal approximation capability of the proposed 3D fuzzy system is proven in terms of the finite covering theorem. Finally, the proposed method is applied to a catalytic packed-bed reactor and simulation results have verified its effectiveness.

Interactive Multiobjective Fuzzy Random Linear Programming through Fractile Criteria

We propose an interactive fuzzy decision making method for multiobjective fuzzy random linear programming problems through fractile criteria optimization. In the proposed method, it is assumed that the decision maker has fuzzy goals for not only objective functions but also permissible probability levels in a fractile optimization model, and such fuzzy goals are quantified by eliciting the corresponding membership functions. Using the fuzzy decision, such two kinds of membership functions are integrated. In the integrated membership space, the satisfactory solution is obtained from among an extended Pareto optimal solution set through the interaction with the decision maker. An illustrative numerical example is provided to demonstrate the feasibility and efficiency of the proposed method.

Fuzzy risk analysis based on ranking fuzzy numbers using [formula omitted]-cuts, belief features and signal/noise ratios

In this paper, we present a new approach for fuzzy risk analysis based on the ranking of fuzzy numbers. First, we propose a new method for ranking fuzzy numbers using the α-cuts, the belief feature and the signal/noise ratios, where α ∈ [0, 1]. The proposed method for ranking fuzzy numbers calculates the signal/noise ratio of each α-cut of a fuzzy number to evaluate the quantity and the quality of a fuzzy number, where the signal and the noise are defined as the middle-point and the spread of each α-cut of a fuzzy number, respectively. We use the value of α as the weight of the signal/noise ratio of each α-cut of a fuzzy number to calculate the ranking index of each fuzzy number. The proposed method can rank any kinds of fuzzy numbers with different kinds of membership functions. Then, we apply the proposed fuzzy ranking method to propose a fuzzy risk analysis algorithm to deal with fuzzy risk analysis problems. Because the proposed fuzzy risk analysis method considers the degrees of confidence of decision makers’ opinions, it is more flexible than the existing methods.

On the use of aggregation operations in information fusion processes

This position paper discusses the role of the existing body of fuzzy set aggregation operations in various kinds of problems where the process of fusion of items coming from several sources is central. Several kinds of membership functions can be useful according to the nature of the information to be merged: numerical vs. ordinal inputs, preferences vs. uncertain data, observations vs. constraints. In each case, some aggregation operations look more plausible or feasible than others. The aim of this discussion is to suggest directions for putting at work the results of recent mathematical investigations in the structure of aggregation operations.

IGCC technology for low grade Indian coals

In this paper, both coking and non-coking coals of India have been ranked for industrial use, using a powerful and sophisticated technique called fuzzy multi attribute decision making. Proximate analysis has been taken as the basis and the four important parameters of coal, viz. fixed carbon, volatile matter, moisture content and ash content have been considered for ranking purposes. These parameters have been treated as fuzzy sets over the ranges prescribed in literature. In order to give due weightages to the coal quality parameters depending on their importance, Saaty's analytic hierarchy process (AHP) (Saaty, 1983, 1992; Hanratty and Joseph, 1992) has been adopted. Later, Yager's (1978) fuzzy multi attribute decision making approach has been employed to arrive at the coal field having the best quality coal for industrial use. Also, Yager's model has been extended in that the three different aggregators have been used instead of the min operator. Three different kinds of membership functions, viz. linear, exponential and S-type for the parameters coupled with four kinds of aggregators: (i) min operator, (ii) fuzzy and, (iii) compensatory and (iv) a linear combination of min and max operators have been studied here. The S-type membership function, in combination with all the types of aggregators, turned out to be quite robust for the coking coals whereas for non-coking coals the S-type membership function with a linear combination of min and max operators proved to be superior to other combinations. The results, though, matched with an earlier study based on factor analysis in ranking the same field as the best quality field in both coking and non-coking coals, they differed significantly in the case of other coal fields. The advantage of the present approach is that the inherent fuzziness in the traditional treatment of the coal parameters has been modelled for the first time in a sophisticated and systematic mathematical framework. Also, the all important parameter, viz. fixed carbon has been given due weightage in this paper, which has not been done in earlier studies. These are the reasons behind the mismatch found between the present study and the one based on factor analysis.

Ranking of Indian coals via fuzzy multi attribute decision making

In this paper, both coking and non-coking coals of India have been ranked for industrial use, using a powerful and sophisticated technique called fuzzy multi attribute decision making. Proximate analysis has been taken as the basis and the four important parameters of coal, viz. fixed carbon, volatile matter, moisture content and ash content have been considered for ranking purposes. These parameters have been treated as fuzzy sets over the ranges prescribed in literature. In order to give due weightages to the coal quality parameters depending on their importance, Saaty's analytic hierarchy process (AHP) (Saaty, 1983, 1992; Hanratty and Joseph, 1992) has been adopted. Later, Yager's (1978) fuzzy multi attribute decision making approach has been employed to arrive at the coal field having the best quality coal for industrial use. Also, Yager's model has been extended in that the three different aggregators have been used instead of the min operator. Three different kinds of membership functions, viz. linear, exponential and S-type for the parameters coupled with four kinds of aggregators: (i) min operator, (ii) fuzzy and, (iii) compensatory and (iv) a linear combination of min and max operators have been studied here. The S-type membership function, in combination with all the types of aggregators, turned out to be quite robust for the coking coals whereas for non-coking coals the S-type membership function with a linear combination of min and max operators proved to be superior to other combinations. The results, though, matched with an earlier study based on factor analysis in ranking the same field as the best quality field in both coking and non-coking coals, they differed significantly in the case of other coal fields. The advantage of the present approach is that the inherent fuzziness in the traditional treatment of the coal parameters has been modelled for the first time in a sophisticated and systematic mathematical framework. Also, the all important parameter, viz. fixed carbon has been given due weightage in this paper, which has not been done in earlier studies. These are the reasons behind the mismatch found between the present study and the one based on factor analysis.

An integer fuzzy transportation problem

The well-known transportation problem [1] is often represented by a bipartite network that consists of two node-sets, i.e., sets of supply (or plant) and demand (or warehouse) nodes. The problem is to determine a flow such that the total transportation cost is minimized. However, in some situations, the values of supplies and demands may not be determined rigidly. Accordingly, we considered a fuzzy version of the transportation problem by introducing two kinds of membership functions which characterize fuzzy supplies and fuzzy demands [2]. The objective is to determine an optimal flow that maximizes the smallest value of all membership functions under the constraint that the total transportation cost must not exceed a certain upper limit. In this paper, we generalize the fuzzy transportation problem. That is, an integral constraint of flow is added to the problem. We call it IFTP: Integer Fuzzy Transportation Problem, in which it is assumed that every value of supply and demand is integer and that the values of commodities to be transported are all integers.

The max-min Delphi method and fuzzy Delphi method via fuzzy integration

Abstract The traditional Delphi method is one of the effective methods which enables forecasting by converging a possibility value through the feedback mechanism of the results of questionnaires, based on experts' judgments. Some points needing revision are: (1) By pinpointing the intuition of the first response on the part of experts, feasible inference values need to be extracted so that the quality-oriented and semantic structure of the responses may be analyzed. (2) By removing the effect caused by feedback in the Delphi method, natural and non-converged results need to be acquired; Moreover, two and more repetitive surveys are likely to cause a decline in the response rate, which may produce negative effects in the ensuing analyses. (3) In general, as it is repeated, the survey becomes more costly and time-consuming. In order to resolve these issues, we have identified two kinds of membership functions in regard to ‘the attainable period with a high degree’ and ‘the unattainable period with a high degree’. Next, through the implementation of the Max-Min Fuzzy Delphi Method and the New Delphi Method via Fuzzy Integration, we have developed algorithms which enable forecasting attainable periods. Third, we have applied such algorithms to two concrete questions, compared the result with one obtained from the Delphi method, and ascertained the feasible outcome. While more examination needs to be undertaken, the new methods look valid and applicable to further analyses of other questions and items on questionnaires. While both methods can forecast attainable periods, using these methods simultaneously as well as the traditional Delphi method, may prove a really effective result.

A Study of Fuzzy Programing for Optimizaiton of Beam Shapes.

Fuzzy programing is applied to determining optimum shapes of beams subjected to a moving load with constant velocity. The multi-objective optimization has two objective functions and a constraint. This problem is transformed to the unconstrained optimization problem by an augmented objective function. The membership functions of these objective functions are defined. Then, fuzzy mathematical programing is carried out. Fuzzy programing with three kinds of membership functions is solved interactively. The Lagrange multiplier method was used for unconstrained optimization, and dynamic programing was applied for the minimization of the augmented objective function.