Discrete Membership Functions Research Articles

Model Predictive Thrust Control for Linear Induction Machine: A Fuzzy Optimization Approach

Model predictive thrust control (MPTC) is one of the most effective approaches for linear induction machine (LIM) drive system. It can achieve the optimization of multiple objectives with suitable weighting factors, such as low ripples and fast dynamic performance. Due to the longitudinal end effect, the selection of weighting factor becomes particularly important in LIM. However, the process of tuning the weighting factors in the objective function is very long and tedious. In this article, a dynamic fuzzy MPTC approach is proposed to solve the multi-objective problem for minimizing the flux and thrust ripples. Based on the fuzzy optimization technique, the tuning process of weighting factors can be transformed into a discrete membership function. A “max-min” objective function of voltage vectors is employed to select a more balanced switch combination on the Pareto optimal-frontier for LIM. Furthermore, this approach can adapt to different operating conditions by adjusting objective priority of membership function. At last, comprehensive simulation and experimental results are conducted to demonstrate the effectiveness and feasibility of the proposed method.

РАЗРАБОТКА АЛГОРИТМА ИНТЕРПРЕТАЦИИ ВХОДНЫХ ПЕРЕМЕННЫХ НЕЧЕТКОГО ЛОГИЧЕСКОГО КОНТРОЛЛЕРА ДЛЯ СИСТЕМ РЕАЛЬНОГО ВРЕМЕНИ

The purpose of the research work is to develop an algorithm for interpreting input variables by a discrete membership function of a fuzzy set for embedded and real-time systems. To achieve the goal set in the scientific work, the following tasks were solved: the study of fuzzy logical inference in automatic control systems: analysis of the fuzzy set building, representation of a discrete input values; development of an algorithm and software implementation for real-time systems. Methods for setting input variables for fuzzy logic systems were considered, an algorithmic implementation of the representation of the input value as an element of a fuzzy set and automatic calculation of the membership function was proposed.

General 3-D Type-II Fuzzy Logic Systems in the Polar Frame: Concept and Practice

This paper deals with the concept and application of general three-dimensional (3-D) type-2 fuzzy logic systems in the polar frame (G3DT2FLS). 1 1 Because many acronyms are used in this paper, they are summarized in Table I for the convenience of the reader. We focused on the automatic membership function (MF) Generator, general type-2 polar fuzzy membership, new geometric operators in polar frame, inference consisting of fuzzy 3-D polar rules and antecedents/consequents $\theta$ -slice and $\alpha$ -planes. The cubic smoothing spline is introduced to generate the upper and lower MFs according to the information theory. Three indices of compactness, smoothness, and entropy are employed for tuning of MFs. A measure of ultrafuzziness, min, max, equal, and reduced ultrafuzziness are suggested for the polar method. Additionally, the set theoretic operations of 3-D type-2 fuzzy sets in the polar frame are discussed. We also prove the join, meet, centroid, and type-reduction operations in the polar frame. Several rule sets are given to show the usefulness and complexity of the proposed method. The performance of the partial general 3D polar type-2 fuzzy logic system showed linear growth as the number of rules was increased. Computation time tests showed that the algorithm reduces the computation time by a maximum of 67% compared with discrete MF and is shown by an extreme 98% for the geometric procedure. These results indicate significant improvements in computation time for the spline interpolation over the existing methods.

A fuzzy set based solution method for multiobjective optimal design problem of mechanical and structural systems using functional-link net

The principle of solving multiobjective optimization problems with fuzzy sets theory is studied. Membership function is the key to introduce the fuzzy sets theory to multiobjective optimization. However, it is difficult to determine membership functions in engineering applications. On the basis of rapid quadratic optimization in the learning of weights, simplification in hardware as well as in computational procedures of functional-link net, discrete membership functions are used as sample training data. When the network converges, the continuous membership functions implemented with the network. Membership functions based on functional-link net have been used in multiobjective optimization. An example is given to illustrate the method.

Elasto‐plastic finite element analysis with fuzzy parameters

AbstractIn this paper, an elastoplastic analysis based on fuzzy mathematics and using finite element method will be described. The Drucker–Prager yield criterion and the elasto‐plastic matrix are fuzzified for the non‐linear analyses which adopt the initial stress method for the solution. A numerical example is given to illustrate the possible variations in the displacements and the extent of plastic zones at the discrete membership functions. A reliability index of a membership grade based on the concept of non‐probabilistic entropy is also proposed.

Fuzzy logic control of aggregate production planning

Rinks used linguistic variables of the sort proposed by Zadeh for cost, inventory, production, and work force. He operated on these with fuzzy if-ten rules in a manner like that used by Mamdani and Assilan to control a steam engine. The Rinks membership functions and rules were subjective creations. Nevertheless, he obtained results that compared favorably to both prior and subsequent heuristic treatments of the HMMS data. We have developed a C language fuzzy logic controller (FLC) that uses the Rinks discrete membership functions and closely reproduces his results. We have used this FLC to investigate the effect of granularity of the discretization on the quality of solution. We have also used Wang-Mendel learning to improve the rule base. This paper discusses these results and suggests areas for further investigation.

Fuzzy decision making with multiple objectives and discrete membership functions

A multiple objective decision making problem in which fuzzy sets are used to represent the decision maker's valuations of the objectives is addressed. A method presented by Yager is demonstrated to be inconsistent with a more general approach suggested by Baldwin & Guild. An alternative model which is consistent with the Baldwin & Guild model is presented. This model is shown to be consistent with the Standard non-fuzzy approach when the associated preferences are no longer vague.