			Home About us Contact

Membership Functions (membership + function)

Distribution by Scientific Domains

Engineering	42%
Business, Economics, Finance and Accounting	11%

Kinds of Membership Functions

fuzzy membership function

Selected Abstracts

Delay-dependent fault estimation for uncertain time-delay nonlinear systems: an LMI approach

INTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL, Issue 18 2006
Sing Kiong Nguang
Abstract This paper deals with the problem of robust fault estimation for uncertain time-delay Takagi,Sugeno (TS) fuzzy models. The aim of this study is to design a delay-dependent fault estimator ensuring a prescribed ,, performance level for the fault estimation error, irrespective of the uncertainties and the time delays. Sufficient conditions for the existence of a robust fault estimator are given in terms of linear matrix inequalities (LMIs). Membership functions' (MFs) characteristics are incorporated into the fault estimator design to reduce the conservativeness of neglecting these characteristics. Finally, a numerical example is given to illustrate the effectiveness of the proposed design techniques. Copyright © 2006 John Wiley & Sons, Ltd. [source]

A combined S-transform and fuzzy expert system for phase selection in digital relaying

EUROPEAN TRANSACTIONS ON ELECTRICAL POWER, Issue 5 2008
S. R. Samantaray
Abstract This paper presents a new approach for faulty phase selection in transmission line based on combined S-transform and Fuzzy Expert System (FES). The S-transform with complex window is used to generate S-contours (time,frequency contours), which ,time-localizes' the fault. Features such as standard deviation (sd) and change in energy (ce) of the S-contours for half cycle post fault current samples are calculated and fuzzified with simple triangular membership function. The fuzzified inputs are fed to the FES and the corresponding fuzzy rule is fired to provide the output as "1" for faulty phase and ground involved and "0" for no-fault. The proposed integrated approach is tested for all 11 types of shunt faults with a wide range of operating conditions of the power system network. For testing the robustness of the proposed technique, the same is applied for the faults created on experimental set up with different operating conditions and provides accurate results. The output from the FES shows the fastness of the proposed technique and thus suitable for online application. Copyright © 2007 John Wiley & Sons, Ltd. [source]

Automatic generation control of multi-area power system using fuzzy logic controller

EUROPEAN TRANSACTIONS ON ELECTRICAL POWER, Issue 3 2008
P. Subbaraj
Abstract This paper presents an application of Fuzzy Logic Controller (FLC) with triangular and gauss membership functions to study Automatic Generation Control (AGC) of a four-area interconnected power system. Out of the four areas three have steam turbines and one has hydro turbine. All steam turbines in the system contain the reheat effect of non-linearity and hydro turbine contains upper and lower constraints for generation rate. The result proves that the performance of FLC with Gaussian membership function is better than that of conventional controller. Copyright © 2007 John Wiley & Sons, Ltd. [source]

Probabilistic safety analysis of structures under hybrid uncertainty

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 4 2007
Subrata Chakraborty
Abstract The probabilistic and the possibilistic methods of safety evaluation of structure under uncertain parameters have been developed independently. When the structural system is defined with some of the input parameters as possibilistic and others are sufficient enough to model as probabilistic, available literatures normally start with either probabilistic or possibilistic description of all the variables. This may pose restriction on necessary flexibility to the designer at early stage of modelling of the structural system. The primary objective of the present work is to critically examine various emerging methods of transformation of the possibilistic variables to equivalent probabilistic variables so that probabilistic safety evaluation approach becomes compatible with the nature and quality of the input data. Relying on the fundamental concept of equivalent transformations, i.e. the entropy based transformation and the scaling of fuzzy membership function, the reliability analysis is proposed in the framework of second moment format. In doing so, the bounds on the reliability indices based on the evidence theory are also obtained encompassing the first-order reliability analysis for consistent comparison among alternative transformations. Finally, the reliability computation under hybrid uncertainty is elucidated numerically with examples for comparative study on the suitability of the transformation alternatives. Copyright © 2006 John Wiley & Sons, Ltd. [source]

Solution of fuzzy matrix games: An application of the extension principle

INTERNATIONAL JOURNAL OF INTELLIGENT SYSTEMS, Issue 8 2007
Shiang-Tai Liu
Conventional game theory is concerned with how rational individuals make decisions when they are faced with known payoffs. This article develops a solution method for the two-person zero-sum game where the payoffs are only approximately known and can be represented by fuzzy numbers. Because the payoffs are fuzzy, the value of the game is fuzzy as well. Based on the extension principle, a pair of two-level mathematical programs is formulated to obtain the upper bound and lower bound of the value of the game at possibility level ,. By applying a dual formulation and a variable substitution technique, the pair of two-level mathematical programs is transformed to a pair of ordinary one-level linear programs so they can be manipulated. From different values of ,, the membership function of the fuzzy value of the game is constructed. It is shown that the two players have the same fuzzy value of the game. An example illustrates the whole idea of a fuzzy matrix game. © 2007 Wiley Periodicals, Inc. Int J Int Syst 22: 891,903, 2007. [source]

Memory effects description by neural networks with delayed feedback connections

INTERNATIONAL JOURNAL OF INTELLIGENT SYSTEMS, Issue 4 2004
Petia D. Koprinkova
For the purpose of dynamic systems modeling, it was proposed to include feedback connections or delay elements in the classical feed-forward neural network structure so that the present output of the neural network depends on its previous values. These delay elements can be connected to the hidden and/or output neurons of the main neural network. Each delay element gets a value of a state variable at a past time instant and keeps this value during a single sampling period. The groups of delay elements record the values of the state variables for a given time period in the past. Changing the number of the delay elements, which belongs to one group, a shorter or a longer time period in the past can be accounted for. Thus, the connection weights determine the influence of the past process states on the present state in a similar way as it is in the time delay kernel or cause-effect relation membership function (CER-MF) models. Specific feed-forward neural networks with time delay connections are used to solve the problem of neural network chemostat modeling as well as specific kinetic rates modeling. The weights of the feedback connections obtained during model training are discussed as the points of a time delay kernel or as the strength levels in a CER model (the points in the CER-MF). The corresponding changes in these weights with the changing time period in the past are shown. © 2004 Wiley Periodicals, Inc. [source]

Hybrid identification of fuzzy rule-based models

INTERNATIONAL JOURNAL OF INTELLIGENT SYSTEMS, Issue 1 2002
Sung-Kwun Oh
In this study, we propose a hybrid identification algorithm for a class of fuzzy rule-based systems. The rule-based fuzzy modeling concerns structure optimization and parameter identification using the fuzzy inference methods and hybrid structure combined with two methods of optimization theories for nonlinear systems. Two types of inference methods of a fuzzy model concern a simplified and linear type of inference. The proposed hybrid optimal identification algorithm is carried out using a combination of genetic algorithms and an improved complex method. The genetic algorithms determine initial parameters of the membership function of the premise part of the fuzzy rules. In the sequel, the improved complex method (being in essence a powerful auto-tuning algorithm) leads to fine-tuning of the parameters of the respective membership functions. An aggregate performance index with a weighting factor is proposed in order to achieve a balance between performance of the fuzzy model obtained for the training and testing data. Numerical examples are included to evaluate the performance of the proposed model. They are also contrasted with the performance of the fuzzy models existing in the literature. © 2002 John Wiley & Sons, Inc. [source]

Fuzzy approach to dependability performance evaluation

QUALITY AND RELIABILITY ENGINEERING INTERNATIONAL, Issue 7 2008
Dejan Ivezi
Abstract This paper presents a model for dependability performance evaluation by fuzzy sets utilization. Basic dependability indicators (reliability, maintainability and maintenance support) are used for the analysis of technical systems' conditions from the aspects of design, construction, maintenance and logistics. These indicators as well as associated dependability expressions itself are described by linguistic variables, which are characterized by a membership function to the defined classes. The proposed model is primarily appropriate for introduction, analysis and synthesis of information related to quality of systems in operation. Such data are often available only as experts' judgment and estimations. A practical engineering example (mechanical system at bucket wheel excavator) has been presented to demonstrate the proposed dependability analysis and synthesis model. Copyright © 2008 John Wiley & Sons, Ltd. [source]

Fuzzy Targeting Indices and Orderings

BULLETIN OF ECONOMIC RESEARCH, Issue 1 2004
Paul Makdissi
D31; D63; I32 Abstract The targeting efficiency and the coverage of social programs for the poor are typically analyzed by partitioning the total population in four mutually exclusive groups: the poor who benefit from a program or policy, the poor who do not benefit, the non-poor who benefit, and the non-poor who do not benefit. While useful, this partition into crisp sets may not capture the difficulty of identifying the poor. This paper presents a method that consists of using a membership function to identify to what extent households can be considered as poor or non-poor. The method builds on fuzzy sets theory whereby the definition of the boundaries of a set, say the poor or the non-poor, is fuzzy. We characterize the properties that membership functions should have, and we test for the robustness of targeting performance comparisons to the choice of the membership function. [source]

Automatic generation control of multi-area power system using fuzzy logic controller

Neurofuzzy Modeling of Context,Contingent Proximity Relations

GEOGRAPHICAL ANALYSIS, Issue 2 2007
Xiaobai Yao
The notion of proximity is one of the foundational elements in humans' understanding and reasoning of the geographical environments. The perception and cognition of distances plays a significant role in many daily human activities. Yet, few studies have thus far provided context,contingent translation mechanisms between linguistic proximity descriptors (e.g., "near,""far") and metric distance measures. One problem with previous fuzzy logic proximity modeling studies is that they presume the form of the fuzzy membership functions of proximity relations. Another problem is that previous studies have fundamental weaknesses in considering context factors in proximity models. We argue that statistical approaches are ill suited to proximity modeling because of the inherently fuzzy nature of the relations between linguistic and metric distance measures. In this study, we propose a neurofuzzy system approach to solve this problem. The approach allows for the dynamic construction of context,contingent proximity models based on sample data. An empirical case study with human subject survey data is carried out to test the validity of the approach and to compare it with the previous statistical approach. Interpretation and prediction accuracy of the empirical study are discussed. [source]

Adaptive TS-FNN control for a class of uncertain multi-time-delay systems: The exponentially stable sliding mode-based approach

INTERNATIONAL JOURNAL OF ADAPTIVE CONTROL AND SIGNAL PROCESSING, Issue 4 2009
Tung-Sheng Chiang
Abstract This paper presents an adaptive Takagi,Sugeno fuzzy neural network (TS-FNN) control for a class of multiple time-delay uncertain nonlinear systems. First, we develop a sliding surface guaranteed to achieve exponential stability while considering mismatched uncertainty and unknown delays. This exponential stability result based on a novel Lyapunov,Krasovskii method is an improvement when compared with traditional schemes where only asymptotic stability is achieved. The stability analysis is transformed into a linear matrix inequalities problem independent of time delays. Then, a sliding mode control-based TS-FNN control scheme is proposed to achieve asymptotic stability for the controlled system. Since the TS-FNN combines TS fuzzy rules and a neural network structure, fewer numbers of fuzzy rules and tuning parameters are used compared with the traditional pure TS fuzzy approach. Moreover, all the fuzzy membership functions are tuned on-line even in the presence of input uncertainty. Finally, simulation results show the control performance of the proposed scheme. Copyright © 2008 John Wiley & Sons, Ltd. [source]

A genetic-based neuro-fuzzy controller for blind equalization of time-varying channels

INTERNATIONAL JOURNAL OF ADAPTIVE CONTROL AND SIGNAL PROCESSING, Issue 7 2008
Siba Prasada Panigrahi
Abstract This paper presents a neuro-fuzzy network (NFN) where all its parameters can be tuned simultaneously using genetic algorithms (GAs). The approach combines the merits of fuzzy logic theory, neural networks and GAs. The proposed NFN does not require a priori knowledge about the system and eliminates the need for complicated design steps such as manual tuning of input,output membership functions, and selection of fuzzy rule base. Although, only conventional GAs have been used, convergence results are very encouraging. A well-known numerical example derived from literature is used to evaluate and compare the performance of the network with other equalizing approaches. Simulation results show that the proposed neuro-fuzzy controller, all parameters of which have been tuned simultaneously using GAs, offers advantages over existing equalizers and has improved performance. From the perspective of application and implementation, this paper is very interesting as it provides a new method for performing blind equalization. The main contribution of this paper is the use of learning algorithms to train a feed-forward neural network for M-ary QAM and PSK signals. This paper also provides a platform for researchers of the area for further development. Copyright © 2008 John Wiley & Sons, Ltd. [source]

From fuzzy sets to shadowed sets: Interpretation and computing

INTERNATIONAL JOURNAL OF INTELLIGENT SYSTEMS, Issue 1 2009
Witold Pedrycz
In this study, we discuss a concept of shadowed sets and present their applications. To establish some sound compromise between the qualitative Boolean (two-valued) description of data and quantitative membership grades, we introduce an interpretation framework of shadowed sets. Shadowed sets are discussed as three-valued constructs induced by fuzzy sets assuming three values (that could be interpreted as full membership, full exclusion, and uncertain membership). The algorithm of converting membership functions into this quantification is a result of a certain optimization problem guided by the principle of uncertainty localization. We revisit fundamental ideas of relational calculus in the setting of shadowed sets. We demonstrate how shadowed sets help in problems in data interpretation in fuzzy clustering by leading to the three-valued quantification of data structure that consists of core, shadowed, and uncertain structure. © 2008 Wiley Periodicals, Inc. [source]

Dempster,Shafer models for object recognition and classification

INTERNATIONAL JOURNAL OF INTELLIGENT SYSTEMS, Issue 3 2006
A.P. Dempster
We consider situations in which each individual member of a defined object set is characterized uniquely by a set of variables, and we propose models and associated methods that recognize or classify a newly observed individual. Inputs consist of uncertain observations on the new individual and on a memory bank of previously identified individuals. Outputs consist of uncertain inferences concerning degrees of agreement between the new object and previously identified objects or object classes, with inferences represented by Dempster,Shafer belief functions. We illustrate the approach using models constructed from independent simple support belief functions defined on binary variables. In the case of object recognition, our models lead to marginal belief functions concerning how well the new object matches objects in memory. In the classification model, we compute beliefs and plausibilities that the new object lies in defined subsets of an object set. When regarded as similarity measures, our belief and plausibility functions can be interpreted as candidate membership functions in the terminology of fuzzy logic. © 2006 Wiley Periodicals, Inc. Int J Int Syst 21: 283,297, 2006. [source]

Hybrid learning architecture for fuzzy control of quadruped walking robots

INTERNATIONAL JOURNAL OF INTELLIGENT SYSTEMS, Issue 2 2005
Huosheng Hu
This article presents a hybrid learning architecture for fuzzy control of quadruped walking robots in the RoboCup domain. It combines reactive behaviors with deliberative reasoning to achieve complex goals in uncertain and dynamic environments. To achieve real-time and robust control performance, fuzzy logic controllers (FLCs) are used to encode the behaviors and a two-stage learning scheme is adopted to make these FLCs be adaptive to complex situations. The first stage is called structure learning, in which the rule base of an FLC is generated by a Q-learning scheme. The second stage is called parameter learning, in which the parameters of membership functions in input fuzzy sets are learned by using a real value genetic algorithm. The experimental results are provided to show the suitability of the architecture and effectiveness of the proposed learning scheme. © 2005 Wiley Periodicals, Inc. Int J Int Syst 20: 131,152, 2005. [source]

Parameterized fuzzy operators in fuzzy decision making

INTERNATIONAL JOURNAL OF INTELLIGENT SYSTEMS, Issue 9 2003
Qian Song
The basic operations of fuzzy sets, such as negation, intersection, and union, usually are computed by applying the one-complement, minimum, and maximum operators to the membership functions of fuzzy sets. However, different decision agents may have different perceptions for these fuzzy operations. In this article, the concept of parameterized fuzzy operators will be introduced. A parameter , will be used to represent the degree of softness. The variance of , captures the differences of decision agents' subjective attitudes and characteristics, which result in their differing perceptions. The defined parameterized fuzzy operators also should satisfy the axiomatic requirements for the traditional fuzzy operators. A learning algorithm will be proposed to obtain the parameter , given a set of training data for each agent. In this article, the proposed parameterized fuzzy operators will be used in individual decision-making problems. An example is given to show the concept and application of the parameterized fuzzy operators. © 2003 Wiley Periodicals, Inc. [source]

A fuzzy goal programming procedure for solving quadratic bilevel programming problems

INTERNATIONAL JOURNAL OF INTELLIGENT SYSTEMS, Issue 5 2003
Bijay Baran Pal
This article presents a fuzzy goal programming (FGP) procedure for solving quadratic bilevel programming problems (QBLPP). In the proposed approach, the membership functions for the defined fuzzy objective goals of the decision makers (DM) at both the levels are developed first. Then, a quadratic programming model is formulated by using the notion of distance function minimizing the degree of regret to satisfaction of both DMs. At the first phase of the solution process, the quadratic programming model is transformed into an equivalent nonlinear goal programming (NLGP) model to maximize the membership value of each of the fuzzy objective goals on the extent possible on the basis of their priorities in the decision context. Then, at the second phase, the concept of linear approximation technique in goal programming is introduced for measuring the degree of satisfaction of the DMs at both the levels by arriving at a compromised decision regarding the optimality of two different sets of decision variables controlled separately by each of them. A numerical example is provided to illustrate the proposed approach. © 2003 Wiley Periodicals, Inc. [source]

A structure identification method of submodels for hierarchical fuzzy modeling using the multiple objective genetic algorithm

INTERNATIONAL JOURNAL OF INTELLIGENT SYSTEMS, Issue 5 2002
Kanta Tachibana
Fuzzy models describe nonlinear input-output relationships with linguistic fuzzy rules. A hierarchical fuzzy modeling is promising for identification of fuzzy models of target systems that have many input variables. In the identification, (1) determination of a hierarchical structure of submodels, (2) selection of input variables of each submodel, (3) division of input and output space, (4) tuning of membership functions, and (5) determination of fuzzy inference method are carried out. This article presents a hierarchical fuzzy modeling method with an uneven division method of input space of each submodel. For selecting input variables of submodels, the multiple objective genetic algorithm (MOGA) is utilized. MOGA finds multiple models with different input variables and different numbers of fuzzy rules as compromising solutions. A human designer can choose desirable ones from these candidates. The proposed method is applied to acquisition of fuzzy rules from cyclists' pedaling data. In spite of a small number of data, the obtained model was able to give detailed suggestions to each cyclist. © 2002 Wiley Periodicals, Inc. [source]

Hybrid identification of fuzzy rule-based models

Designs and analyses of various fuzzy controllers with region-wise linear PID subcontrollers

INTERNATIONAL JOURNAL OF INTELLIGENT SYSTEMS, Issue 12 2001
C. W. Tao
To reduce the complexity of PID-like fuzzy controllers with three inputs, designs and analyses of various fuzzy controllers with region-wise linear PID subcontrollers are presented in this paper. The proposed region-wise linear PID subcontrollers are composed of one dimensional fuzzy mechanism. And the triangular-type membership functions are adopted for the input variables of the fuzzy controllers. All the possible structures of fuzzy controllers with region-wise linear PID subcontrollers are discussed. According to the number of one-dimensional fuzzy mechanisms included in the structure of the fuzzy controllers, the fuzzy controllers are classified into three main categories. An algorithm is provided to construct effective fuzzy controllers with lowest complexity among all the possible structures. Also, the properties of various designs of fuzzy controllers with region-wise linear PID subcontrollers are compared. The simulation results are included to demonstrate the performances of three basic types of proposed fuzzy controllers with the linear, nonlinear, and delayed plants. © 2001 John Wiley & Sons, Inc. [source]

Evaluation of driver satisfaction of travel information on variable message signs using fuzzy aggregation

JOURNAL OF ADVANCED TRANSPORTATION, Issue 1 2008
Dongmin Lee
Driver satisfaction regarding travel information provided by variable message signs (VMS), which are part of the Nam-Mountain Tunnel ATIS, was evaluated using fuzzy aggregation. Application of fuzzy aggregation to analyze driver satisfaction allows one to represent the variability and complexity of human perception with great fidelity. A fuzzy weighted average using two sets of fuzzy membership functions was applied to evaluate individual satisfactions of delay and travel time information provided. Then, those individual satisfactions were aggregated to estimate the driver group's overall satisfaction. The evaluated overall satisfaction was 0.65 for delay information and 0.63 for travel time information. Through these results, it was found that users of the travel information provided by the VMS in the Nam-Mountain Tunnel ATIS were somewhat satisfied with the service quality. Those overall satisfactions were compared with a conventional weighted average and traffic operational effects to demonstrate the usefulness of the developed fuzzy method. [source]

Fuzzy goal programming model: an overview of the current state-of-the art

JOURNAL OF MULTI CRITERIA DECISION ANALYSIS, Issue 5-6 2009
Belaïd Aouni
Abstract The standard Goal Programming (GP) model considers the aspiration levels (goals) as precise and deterministic. However, in practice, there are many decision-making situations where the decision-maker is not able to establish the goal values precisely. The goals fuzziness is more related to the nature of the objectives involved in the decision-making situation. The Fuzzy Goal Programming (FGP) Model has been developed in the earliest of the 80s to deal with such situations. The concept of membership functions, based on fuzzy sets theory, has been used for modelling the goals fuzziness in the GP. The aim of this paper is to give an overview of the current state-of-the art regarding the FGP model. Copyright © 2010 John Wiley & Sons, Ltd. [source]

Solving multi-objective dynamic optimization problems with fuzzy satisfying method

OPTIMAL CONTROL APPLICATIONS AND METHODS, Issue 5 2003
Cheng-Liang Chen
Abstract This article proposes a novel algorithm integrating iterative dynamic programming and fuzzy aggregation to solve multi-objective optimal control problems. First, the optimal control policies involving these objectives are sequentially determined. A payoff table is then established by applying each optimal policy in series to evaluate these multiple objectives. Considering the imprecise nature of decision-maker's judgment, these multiple objectives are viewed as fuzzy variables. Simple monotonic increasing or decreasing membership functions are then defined for degrees of satisfaction for these linguistic objective functions. The optimal control policy is finally searched by maximizing the aggregated fuzzy decision values. The proposed method is rather easy to implement. Two chemical processes, Nylon 6 batch polymerization and Penicillin G fed-batch fermentation, are used to demonstrate that the method has a significant potential to solve real industrial problems. Copyright © 2003 John Wiley & Sons, Ltd. [source]

Fault Diagnosis Based on the Fuzzy-Recurrent Neural Network

ASIAN JOURNAL OF CONTROL, Issue 2 2001
Zhao Xiang
ABSTRACT A fuzzy-recurrent neural network (FRNN) has been constructed by adding some feedback connections to a feedforward fuzzy neural network (FNN). The FRNN expands the modeling ability of a FNN in order to deal with temporal problems. A basic concept of the FRNN is first to use process or expert knowledge, including appropriate fuzzy logic rules and membership functions, to construct an initial structure and to then use parameter-learning algorithms to fine-tune the membership functions and other parameters. Its recurrent property makes it suitable for dealing with temporal problems, such as on-line fault diagnosis. In addition, it also provides human-understandable meaning to the normal feedforward multilayer neural network, in which the internal units are always opaque to users. In a word, the trained FRNN has good interpreting ability and one-step-ahead predicting ability. To demonstrate the performance of the FRNN in diagnosis, a comparison is made with a conventional feedforward network. The efficiency of the FRNN is verified by the results. [source]