Fuzzy set operations

About: Fuzzy set operations is a research topic. Over the lifetime, 29480 publications have been published within this topic receiving 955884 citations.

Correlation Coefficient Between Fuzzy Numbers Based On Central Interval

Abstract: When we deal with crisp data, it is very common to find the correlation between variables. Here, we propose a method to calculate the correlation coefficient for fuzzy data, but rather than defining the correlation on the intuitionistic fuzzy sets like most of the previous works, we adopt the method from central interval. This interval can be used as a crisp set approximation with respect to a fuzzy quantity. This indices can be applied for comparison of fuzzy numbers namely fuzzy correlations in fuzzy environments and expert's systems. Finally some of their applications are mentioned.

Tsukamoto-type neural fuzzy inference network

Abstract: A Tsukamoto-type neural fuzzy inference network (TNFIN) is proposed. The TNFIN consists of a special five-layer feedforward neural fuzzy network. The fuzzy implication used in the paper is actually an inverse function transformation rather than the standard linguistic "if/then" rule. A hybrid learning algorithm combining the least square estimation method and the gradient descent method has been used to tune the parameters and speed up the learning process. To demonstrate the capability of the proposed TNFIN, two simulation examples (one in nonlinear function mapping and one in chaos time series prediction) are applied for validating the model. Simulation results show that the TNFIN model with less parameters and smaller iteration numbers produces the remarkable results.

Chattering-free fuzzy variable structure control for multivariable nonlinear systems

Abstract: Graphical abstractFLC-VSC for multivariable nonlinear systems is presented. The main contribution of this work is the development of new functions for chattering elimination without sacrificing invariant properties (Figs. 1 and 2 represent the temporal evolution of s1 and s2 before applying the proposed algorithm and Figs. 3 and 4 after applying the proposed algorithm respectively). Fig. 5 shows fuzzy sets of the switching surface. Fig. 6 shows the transient response of a two-link robot model. Display Omitted HighlightsA fuzzy based variable structure control for multivariable nonlinear systems is presented.A generic matrix formulation of the FLC-VSC algorithm for nonlinear multivariable systems, is proposed.The weighting parameters approach is used to optimize local and global modelling capability of T-S fuzzy model.The global stability of the controlled system is guaranteed.A fuzzy switching function is added as an additional fuzzy variable. In this paper, a fuzzy logic controller (FLC) based variable structure control (VSC) with guaranteed stability for multivariable systems is presented. It is aimed at obtaining an improved performance of nonlinear multivariable systems. The main contribution of this work is firstly developing a generic matrix formulation of the FLC-VSC algorithm for nonlinear multivariable systems, with a special attention to non-zero final state. Secondly, ensuring the global stability of the controlled system. The multivariable nonlinear system is represented by T-S fuzzy model. The identification of the T-S model parameters has been improved using the well known weighting parameters approach to optimize local and global approximation and modeling capability of T-S fuzzy model. The main problem encountered is that T-S identification method cannot be applied when the membership functions (MFs) are overlapped by pairs. This in turn restricts the application of the T-S method because this type of membership function has been widely used in control applications. In order to overcome the chattering problem a switching function is added as an additional fuzzy variable and will be introduced in the premise part of the fuzzy rules together with the state variables. A two-link robot system and a mixing thermal system are chosen to evaluate the robustness, effectiveness, accuracy and remarkable performance of proposed FLC-VSC method.

An Approach for Solving Fuzzy Game Problem

Abstract: In this paper we consider a two person zero sum game with imprecise values in payoff matrix. All the imprecise values are assumed to be triangular or trapezoidal Fuzzy Numbers. An approach for solving problems by using ranking of the fuzzy numbers has been considered to solve the fuzzy game problem. By using ranking to the payoffs we convert the fuzzy valued game problem to crisp valued game problem, which can be solved using the traditional method.