Exponential Membership Function Research Articles

A fuzzy approach to multicriteria assignment problem using exponential membership functions

In this paper, we extend the classical assignment problem to the multicriteria assignment problem by considering three criteria: cost, time and quality subject to many realistic constraints including multi-job assignment and a knapsack-type resource constraint. The paper addresses the uncertainty of the real-life assignment problem by formulating a fuzzy cost–time–quality assignment problem using exponential membership functions. We define fuzzy goal for each criterion as per the preferences of the decision-maker and aggregate the fuzzy goals using product operator. In order to obtain optimal assignment plans, the resultant nonlinear 0-1 optimization problem is solved using genetic algorithm for different choices of the shape parameters in the exponential membership functions. As an illustrative example, we consider a fuzzy manpower planning problem.

Exponential Membership Function Evaluation based on Frequency

Exponential Membership Function Evaluation based on Frequency

Duality in Fuzzy Quadratic Programming with Exponential Membership Functions

In this paper, we have presented fuzzy primal-dual quadratic programming problems and proved appropriate duality results taking exponential membership function.

Gain-scheduled directional guidance controller design using a genetic algorithm for automatic precision landing

This paper discusses the guidance controller design problem of an aircraft in automatic landing and touchdown flight, subject to dangerous and unpredictable gusts known as wind-shear and to directional crosswind. The associated airplane in the landing flight was statically unstable in this paper. The wind-shear, based on the Dryden gust model, was included in the nonlinear airplane model. A directional guidance control system with gain-scheduling fuzzy logic was proposed in this paper. In fuzzy logic, an even number of exponential membership functions in the output are considered and their shape, decay rate, and scaling factors are optimized using a genetic algorithm. In this control system, the glide slope capture logic and the flare logic were also included for longitudinal and lateral control, respectively. The nonlinear aircraft model simulation illustrated that the proposed guidance control system shows satisfactory performances in accurate touchdowns and is adequately robust to the strong crosswind and wind-shear turbulences.

Using fuzzy theory and information entropy for water quality assessment in Three Gorges region, China

Considering that the water quality assessment is a fuzzy concept with multiple indicators and classes, and there are still some limits of fuzzy comprehensive evaluation method, the fuzzy mathematics method and the information entropy theory are combined to establish an improved fuzzy comprehensive evaluation method for water quality assessment. In this method, the exponential membership function has been adopted to solve the zero-weight problem, and the information entropy has been used to modify the coefficients of weight in order to exploit the useful information of data to a maximum extent. In addition, the weighted average principle has been taken to replace the maximum membership principle for reserving the information in the assessment coefficients as much as possible. The water quality of Three Gorges region is taken as an example and the results show that the improved fuzzy comprehensive evaluation method is superior to the traditional model and worth to be recommended.

Bector–Chandra type duality in fuzzy linear programming with exponential membership functions

In this paper, we study a pair of fuzzy primal–dual linear programming problems and calculate duality results using an aspiration level approach. We use an exponential membership function, which is in contrast to the earlier works that relied on a linear membership function. As the fuzzy environment causes a duality gap, we investigate how choosing the exponential membership function impacts this gap. This issue is particularly important for fuzzy linear programming where, in general, the primal and dual objective values may not be bounded.

Fuzzy modelling based estimation of short circuit severity in pulse gas metal arc welding

Avoiding short circuit is an essential condition for achieving good quality welds in pulse gas metal arc welding (GMAW-P). Estimating short circuit in any welding process is dependent on proper selection and optimisation of welding process parameters. Such optimisation is critical in the GMAW-P, wherein wire melting is closely dictated by numerous pulsing parameters in comparison to the conventional GMAW process. Fuzzy logic-based models are an excellent alternative in such situations, where a complex relationship between the large number of predictor variables (independents, inputs) and predicted variables (dependents, outputs) exist and are not easy to articulate in the usual terms of correlations or differences between groups. In this paper, we have proposed an input-output fuzzy model for estimating the short circuit severity in terms of number of shorts per pulse for the GMAW-P process. Eighteen factors representing the characteristics of the pulse waveforms are employed as predictor variables and the short circuit severity (or number of shorts per pulse) is predicted on the basis of a modified exponential membership function fitted to the fuzzy sets derived from predictor variables. The exponential membership function is modified by two structural parameters that are estimated by optimising the criterion function associated with the fuzzy modelling. The experimental data consists of GMAW-P welding of 6XXX group of aluminium alloys. The results demonstrate that the proposed fuzzy model could estimate the short circuit severity with high accuracy.

Fuzzy model based recognition of handwritten numerals

This paper presents the recognition of handwritten Hindi and English numerals by representing them in the form of exponential membership functions which serve as a fuzzy model. The recognition is carried out by modifying the exponential membership functions fitted to the fuzzy sets. These fuzzy sets are derived from features consisting of normalized distances obtained using the Box approach. The membership function is modified by two structural parameters that are estimated by optimizing the entropy subject to the attainment of membership function to unity. The overall recognition rate is found to be 95% for Hindi numerals and 98.4% for English numerals.

ARITHMETICAL OPERATIONS OF EXPONENTIAL FUZZY NUMBERS USING THE FUNCTION PRINCIPLE

Fuzzy numbers with exponential membership function are quite common in real world cases. In this paper, we applied Graded Mean Integration Representation Method to compute the representation of exponential fuzzy numbers. Then the Function Principle is applied to generate the arithmetical operations of exponential fuzzy numbers. By the way, some properties of operation under the Function Principle are proved. Finally, an application of the lifetime of the lamps of projectors is proposed.

Exponential membership function in stochastic fuzzy goal programming

Considering the stochastic fuzzy goal programming, this paper provides a study of four known fuzzy goal programming models. This study is considered in the case of stochastic fuzzy goal programming. The chance-constrained approach and the exponential membership function are utilized to transform Iskander's structure of stochastic fuzzy goal program [M.G. Iskander, A fuzzy weighted additive approach for stochastic fuzzy goal programming, Applied Mathematics and Computation 154 (2004) 543-553] to its equivalent deterministic-crisp, according to each one of the four models. The exponential membership function is considered with increasing rate of change and with decreasing rate of change. The decision-maker should precisely set his goals relative weights in two models, and his preemptive priority structure in the other two. A numerical example is given for illustration.

Off-line signature verification and forgery detection using fuzzy modeling

Automatic signature verification is a well-established and an active area of research with numerous applications such as bank check verification, ATM access, etc. This paper proposes a novel approach to the problem of automatic off-line signature verification and forgery detection. The proposed approach is based on fuzzy modeling that employs the Takagi–Sugeno (TS) model. Signature verification and forgery detection are carried out using angle features extracted from box approach. Each feature corresponds to a fuzzy set. The features are fuzzified by an exponential membership function involved in the TS model, which is modified to include structural parameters. The structural parameters are devised to take account of possible variations due to handwriting styles and to reflect moods. The membership functions constitute weights in the TS model. The optimization of the output of the TS model with respect to the structural parameters yields the solution for the parameters. We have also derived two TS models by considering a rule for each input feature in the first formulation (Multiple rules) and by considering a single rule for all input features in the second formulation. In this work, we have found that TS model with multiple rules is better than TS model with single rule for detecting three types of forgeries; random, skilled and unskilled from a large database of sample signatures in addition to verifying genuine signatures. We have also devised three approaches, viz., an innovative approach and two intuitive approaches using the TS model with multiple rules for improved performance.

Function approximation via particular input space partition and region-based exponential membership functions

This paper presents an algorithm to build a compact fuzzy model for approximating unknown nonlinear functions. According to the coordinates of input–output pairs in the Cartesian product-space, the proposed algorithm partitions the input space into several characteristic regions, whose boundaries are determined by the local-minimum, local-maximum, and turning points of the training data. The region-based exponential functions are chosen as membership functions of antecedents, with consequents of rules as singletons, to construct the fuzzy model. Finally, five examples demonstrate that the proposed fuzzy model indeed improves performance in the approximating of nonlinear functions.

An exponential membership function for fuzzy multiple objective linear programming

The operator “min” is one of the most frequently used aggregation operators in fuzzy decision. However, this operator is the softest operator and no allowance is made for any compensation. The “product” and other operators, some of them may be compensatory, are seldom used because of the nonlinearity of the resulting problem. In this paper, an exponential, instead of linear membership function is proposed. The advantages of using exponential membership are two fold. First, the resulting problems can be transformed to linear ones when the “product” and several other nonlinear aggregate operators are used. Secondly, exponential representation is more realistic than the linear ones usually used for some practical applications.

A fuzzy approximation scheme for sequential learning in pattern recognition

An adaptive learning scheme, based on a fuzzy approximation to the gradient descent method for training a pattern classifier using unlabeled samples, is described. The objective function defined for the fuzzy ISODATA clustering procedure is used as the loss function for computing the gradient. Learning is based on simultaneous fuzzy decisionmaking and estimation. It uses conditional fuzzy measures on unlabeled samples. An exponential membership function is assumed for each class, and the parameters constituting these membership functions are estimated, using the gradient, in a recursive fashion. The induced possibility of occurrence of each class is useful for estimation and is computed using 1) the membership of the new sample in that class and 2) the previously computed average possibility of occurrence of the same class. An inductive entropy measure is defined in terms of induced possibility distribution to measure the extent of learning. The method is illustrated with relevant examples.

On fuzzy goals and maximizing decisions in stochastic optimal control

Fuzzy set theory has developed significantly in a mathematical direction during the past several years but few applications have emerged. This paper investigates the role of fuzzy set theory in certain optimal control formulations. In particular, it is shown that the well-known quadratic performance criterion in deterministic optimal control is equivalent to the exponential membership function of a certain fuzzy decision (set). In a stochastic setting, similar equivalences establish new definitions for “confluence of goals” and “maximizing decision” in fuzzy set theory. These and other definitions could lead to the development of a more applicable theory of fuzzy sets.

Fuzzy Tuning In Motion Control

This paper presents a methodology which uses fuzzy logic and some engineering heuristics to tune the controller parameters in motion control systems for improving robustness. Simple tuning schemes are applied for continuously changing the gain and time-constant of widely used proportionalintegral controllers, dependent on the control error and its rate of change. Fuzzy tuning can also be applied to robust modal control using the state space approach. Predictive coefficients of an unknown input observer are tuned taking into account the change of estimated disturbances. More complicated schemes are given for tuning the dynamic feedforward coefficient in relation to the signs of the error and the change of the estimated disturbance. Conditional schemes are also proposed to tune the robust feedback gain according to the signs of the error and the change of error. Using singletons and exponential membership functions, and the centroid technique for defuzzification, all the fuzzy schemes result in explicit expressions, thus the tuning process is easy and the computational cost is low. Simulation results are provided to verify the system robustness to parameter variations and changing environments. Servo drives are chosen here as controlled objects, however, the proposed method can be applied to other linearised dynamic systems suffering from severe uncertainties.