Quadratic Membership Functions Research Articles

Multi-Objective Reliability Optimization using Fuzzy Nonlinear Programming with Interval Membership Functions and Bias Functions: A Comparison of Particle Swarm Optimization and Genetic Algorithm

Multi-objective reliability optimization is a complex problem that involves simultaneously optimizing multiple objectives while ensuring that the system meets certain reliability requirements. In this paper, we present a methodology for solving multi-objective reliability optimization problems using fuzzy nonlinear programming. The methodology involves representing the reliability of each component as a triangular interval number and each objective function as an interval membership function. Conflicts between objectives are resolved using linear and nonlinear membership functions, and exponential and quadratic membership functions are used to obtain definite biases towards the objective. The proposed methodology employs Particle Swarm Optimization (PSO) or Genetic Algorithm (GA) to solve the problem, and the approach is compared with GA for linear and nonlinear membership functions. The results indicate the effectiveness of the methodology in addressing multi-objective reliability optimization problems

On Stability and Stabilization of T–S Fuzzy Systems With Time-Varying Delays via Quadratic Fuzzy Lyapunov Matrix

This article proposes improved stability and stabilization criteria for Takagi–Sugeno (T–S) fuzzy systems with time-varying delays. First, a novel augmented fuzzy Lyapunov–Krasovskii functional (LKF) including the quadratic fuzzy Lyapunov matrix is constructed, which can provide much information of T–S fuzzy systems and help to achieve the lager allowable delay upper bounds. Then, improved delay-dependent stability and stabilization criteria are derived for the studied systems. Compared with the traditional methods, since the third-order Bessel–Legendre inequality and the extended reciprocally convex matrix inequality are well employed in the derivative of the constructed LKF to give tighter bounds of the single integral terms, the conservatism of derived criteria is further reduced. In addition, the quadratic fuzzy Lyapunov matrix introduced in LKF, which contains the quadratic membership functions, is also an important reason for obtaining less conservative results. Finally, numerical examples demonstrate that the proposed method is less conservative than some existing ones and the studied system can be well controlled by the designed controller.

Fuzzy Programming With Quadratic Membership Functions For Multi-objective Transportation Problem

In the present paper, a fuzzy programming model with quadratic membership functions has been developed for the solution of a Multi-Objective Transportation problem. In literature, several fuzzy programming approaches exist with various types of membership functions such as linear, exponential, hyperbolic etc. These membership functions are defined, by taking the lower and upper values of the objective functions into account. In some cases, these methods fail to obtain an integer compromise optimal solution. In the present method, two coefficients of the quadratic membership functions are determined by the lower and upper values of the objective functions. The other coefficient is taken as a variable in the fuzzy programming approach. This means that the membership curve is fixed at the two end points and set free in between. Application of the method on numerical examples proved that the approach could generate integer compromise optimal solutions.

Quadratic Bi-level Programming Problem Based On Fuzzy Goal Programming Approach

This paper presents fuzzy goal programming approach to quadratic bi-level programming problem. In the model formulation of the problem, we construct the quadratic membership functions by determining individual best solutions of the quadratic objective functions subject to the system constraints. The quadratic membership functions are then transformed into equivalent linear membership functions by first order Taylor series approximation at the individual best solution point. Since the objectives of upper and lower level decision makers are potentially conflicting in nature, a possible relaxation of each level decisions are considered by providing preference bounds on the decision variables for avoiding decision deadlock. Then fuzzy goal programming approach is used for achieving highest degree of each of the membership goals by minimizing deviational variables. Numerical examples are provided in order to demonstrate the efficiency of the proposed approach.

Fuzzy Goal Programming Approach to Quadratic BiLevel MultiObjective Programming Problem

paper deals with fuzzy goal programming approach to quadratic bilevel multiobjective programming prob lem involving a single decision maker with multiple objectives at the upper level and a single decision maker with multiple objectives at the lower level. The objective functions of each level decision maker are quadratic in nature and the system constraints are linear functions. In the model formulation of the problem, we first determine the individual best solution of the quadratic objective functions subject to the system constraints and construct the quadratic membership functions of the objective functions of both levels. The quadratic membership functions are then transformed into equivalent linear membership functions by first order Taylor series at the individual best solution point. A possible relaxation of each level decision is considered by providing preference bounds on the decision variables for avoiding decision deadlock. Fuzzy goal programming approach is then used to achieve maximum degree of each of the membership goals by minimizing negative deviational variables. To demonstrate the efficiency of the proposed approach, an illustrative numerical example is provided.

MultiObjective Quadratic Programming Problem: A Priority based Fuzzy Goal Programming

This paper presents priority based fuzzy goal programming approach to multi-objective quadratic programming problem. In the proposed approach, we construct the quadratic membership functions by determining the individual best solution of the objective functions subject to the system constraints. The quadratic membership functions are then transformed into equivalent linear membership functions at the individual best solution point by first order Taylor series approximation. Then fuzzy goal programming approach is used for achieving highest degree of each of the membership goals by minimizing negative deviational variables. Then, sensitivity analysis with the variations of the priority structure is performed to identify the most appropriate priority structure in the decision-making context by using distance function. A numerical example is solved in order to show the efficiency of the proposed approach. General Terms Multi-objective quadratic programming.

Improvement of Generalization Ability of a Fuzzy Classifier with Hyperbox Regions by Quadratic Membership Functions

In this paper we discuss a fuzzy classifier with hyperbox regions which has quadratic membership functions. First we define the classifier with quadratic membership functions and then discuss the training method that maximizes the recognition rate by counting the net increase in the recognition rate when the slope and the center of a membership function are separately changed. Finally, we demonstrate the recognition improvement by quadratic membership functions for four data sets.

Function approximation with polynomial membership functions and alternating cluster estimation

Nonlinear functions are often approximated using local linear models. Sets of local linear models can be represented as a first-order Takagi Sugeno (TS) system. triangular and trapezoidal left-hand side membership functions are not compatible with TS systems because they lead to non-differentiable input-output characteristics. We develop a method to determine parameters of piecewise quadratic membership functions to obtain characteristics which exactly match the rule centers and the corresponding slopes. The right-hand side parameters are obtained using (i) fuzzy c-elliptotypes alternating optimization and (ii) alternating cluster estimation. In our experiments the smoothest and most accurate approximations are obtained with piecewise quadratic membership functions and alternating cluster estimation.

Fuzzy logic models with improved accuracy and continuous differentiability

One method of obtaining a fuzzy logic model (FLM) for use in process optimization and control involves the fuzzy weighting of many simple, often linear, functions. The method of identifying the fuzzy weighting scheme typically makes use of triangular membership functions and the minimum operator, both of which result in a model with discontinuous derivatives. Alternate methods of model identification that make use of continuously differentiable membership functions and the product operator will be discussed here. These methods result in models that have improved predictive capabilities for smooth, complex processes typical of those found in the semiconductor manufacturing industry. In addition, with continuously differentiable membership functions and the product operator, the FLM will have continuous derivatives. As a result, the operation of algorithms that rely on derivatives obtained from the model will be enhanced. Three types of FLM's and an artificial neural network (ANN) model were obtained for eight different sets of data representing three processes, and the resulting models were compared. The predictive capability of each model was estimated by computing the multiple correlation coefficient, R/sub predict//sup 2/, over a large number of points distributed throughout the input space. For one of the most complex examples studied, a simulated six-input chemical vapor deposition process, the traditional FLM using the minimum operator and triangular membership functions had R/sub predict//sup 2/=-0.43, indicating very poor predictive capability. The fuzzy logic model using the product operator and triangular membership functions had R/sub predict//sup 2/=0.87. The fuzzy logic model using the product operator and piece wise defined quadratic membership functions with continuous first derivatives had R/sub predict//sup 2/=0.92. The ANN model for the same data had R/sub predict//sup 2/=0.73. Similar results were observed for each example presented, indicating appropriately defined FLM's can meet or exceed the modeling capabilities of artificial neural networks for nonlinear, multi-dimensional problems.

Identification of possibilistic linear systems by quadratic membership functions of fuzzy parameters

Abstract We have already discussed several models of the possibilities linear regression analysis under the assumption that probabilitioes parameters in the models are non-interactive, i.e., the possibilistic distribution of parameters is defined by minimum operators. In this paper, quadratic membership functions as defined by A. Celmiņs are considered to propose an identification method of interactive fuzzy parameters in possibilistic linear systems. Our method can be reduced to linear programming, so that it is very easy to obtain the posssibilistic distribution of parameters.