Learning fuzzy inference systems using an adaptive membership function scheme

An adaptive membership function scheme for general additive fuzzy systems is proposed in this paper. The proposed scheme can adapt a proper membership function for any nonlinear input-output mapping, based upon a minimum number of rules and an initial approximate membership function. This parameter adjustment procedure is performed by computing the error between the actual and the desired decision surface. Using the proposed adaptive scheme for fuzzy system, the number of rules can be minimized. Nonlinear function approximation and truck backer-upper control system are employed to demonstrate the viability of the proposed method

Fuzzy set based multiobjective allocation of resources and its applications

AbstractThis paper presents results of research into the use of the Bellman-Zadeh approach to decision making in a fuzzy environment for solving multiobjective optimization problems. Its application conforms to the principle of guaranteed result and provides constructive lines in obtaining harmonious solutions on the basis of analyzing associated maxmin problems. The use of the Bellman-Zadeh approach has served as a basis for solving a problem of multiobjective allocation of resources (or their shortages) and developing a corresponding adaptive interactive decision-making system (AIDMS1). Its calculating kernel permits one to solve maxmin problems using an algorithm based on a nonlocal search (modification of the Gelfand's and Tsetlin's “long valley” method). The AIDMS1 includes procedures for considering linguistic variables to reflect conditions that are difficult to formalize as well as procedures for constructing and correcting vectors of importance factors for goals. The use of these procedures permits one to realize an adaptive approach to processing information of a decision maker to provide successive improving of the solution quality. C++ windows of the AIDMS1 are presented for input, output, and special possibilities related to considering linguistic variables and constructing and correcting vectors of importance factors. The results of the paper are universally applicable and are already being used to solve power engineering problems

Fuzzy sets and models of decision making

AbstractResults of research into the use of fuzzy sets for handling various forms of uncertainty in optimization problems related to the design and control of complex systems are presented. Much attention is given to considering the uncertainty of goals that is associated with a multicriteria character of many optimization problems. The application of a multicriteria approach is needed to solve 1.(1)|problems in which solution consequences cannot be estimated on the basis of a single criterion, that involves the necessity of analyzing a vector of criteria, and2.(2)|problems that may be considered on the basis of a single criterion but their unique solutions are not achieved because the uncertainty of information produces so-called decision uncertainty regions, and the application of additional criteria can serve as a convincing means to contract these regions.According to this, two classes of models (〈X, M〉 and 〈X, R〉 models) are considered with applying the Bellman-Zadeh approach and techniques of fuzzy preference relations to their analysis. The consideration of 〈X, R〉 models is associated with a general approach to solving a wide class of optimization problems with fuzzy coefficients. This approach consists in formulating and analyzing one and the same problem within the framework of interrelated models with constructing equivalent analogs with fuzzy coefficients in objective functions alone. It allows one to maximally cut off dominated alternatives. The subsequent contraction of the decision uncertainty region is associated with reduction of the problem to multicriteria decision making in a fuzzy environment with its analysis applying one of two techniques based on fuzzy preference relations. The results of the paper are of a universal character and are already being used to solve problems of power engineering

Modelling and optimizing multiple attribute decisions by using fuzzy sets

The purpose of this paper is to present a coherent perspective of modeling and optimizing multiple attribute decisions by using fuzzy sets. In management practice we face most of the time the situation in which a problem have several possible solutions and each solution can be analyzed using multiple criteria models. In the same time, in real life decision making process there is a given level of uncertainty which makes difficult a clear cut analytical analysis. The object of this article is to build a model approach for making multiple criteria decision using fuzzy sets of objects. Elaborating multiple attribute decisions involves performing an assessment and selecting from a given and finite set of possible alternative courses of action in the presence of a given and finite, and usually conflicting set of attributes and criteria.decision making, fuzzy sets, modeling, multiple criteria optimization.

Multiscale localized differential quadrature in 2D partial differential equation for mechanics of shape memory alloys

In this research, the applicability of the Multiscale Localized Differential Quadrature (MLDQ) method in two-dimensional shape memory alloy (SMA) model was explored. The MLDQ method was governed in solving several partial differential equations. Besides, the finite difference (FD) method was used to solve some examples of partial differential equations and the solutions obtained were compared with those obtained by MLDQ method in order to show the accuracy of the numerical method. The MLDQ method was developed by increasing the number of grid points in critical region, and approximating the derivatives at the certain selected grid points. This present method together with the fourth-order Runge-Kutta (RK) method has been applied in differential equations such as wave equation and high gradient problems,. The MLDQ method can achieves accurate numerical solutions compared with FD method which is a low order numerical method by using a few number of grid points. The multiscale method was employed at the critical region which can break down the region of interest from coarser into finer grid points. Furthermore, FORTRAN programs were developed based on MLDQ method in solving some problems as above. The shared memory architecture of parallel computing was done by using OpenMP in order to reduce the time taken in simulating the numerical results. Consequently, the results show that the MLDQ method was a good numerical technique in two-dimensional SMA