Continuous Stability TS Fuzzy Systems Novel Frame Controlled by a Discrete Approach and Based on SOS Methodology

Generally, the continuous and discrete TS fuzzy systems’ control is studied independently. Unlike the discrete systems, stability results for the continuous systems suffer from conservatism because it is still quite difficult to apply non-quadratic Lyapunov functions, something which is much easier for the discrete systems. In this paper and in order to obtain new results for the continuous case, we proposed to connect the continuous with the discrete cases and then check the stability of the continuous TS fuzzy systems by means of the discrete design approach. To this end, a novel frame was proposed using the sum of square approach (SOS) to check the stability of the continuous Takagi Sugeno (TS) fuzzy models based on the discrete controller. Indeed, the control of the continuous TS fuzzy models is ensured by the discrete gains obtained from the Euler discrete form and based on the non-quadratic Lyapunov function. The simulation examples applied for various models, by modifying the order of the Euler discrete fuzzy system, are presented to show the effectiveness of the proposed methodology.

On Optimal Test Signal Design and Parameter Identification Schemes for Dynamic Takagi-Sugeno Fuzzy Models Using the Fisher Information Matrix

This paper is concerned with the analysis of optimization procedures for optimal experiment design for locally affine Takagi-Sugeno (TS) fuzzy models based on the Fisher Information Matrix (FIM). The FIM is used to estimate the covariance matrix of a parameter estimate. It depends on the model parameters as well as the regression variables. Due to the dependency on the model parameters good initial models are required. Since the FIM is a matrix, a scalar measure of the FIM is optimized. Different measures and optimization goals are investigated in three case studies.

New Concepts of Intuitionistic Fuzzy Trees with Applications

It is known that Intuitionistic fuzzy models give more precision, flexibility and compatibility to the system as compared to the classic and fuzzy models. Intuitionistic fuzzy tree has an important role in neural networks, computer networks, and clustering. In the design of a network, it is important to analyze connections between the levels. In addition, the intuitionistic fuzzy tree is becoming increasingly significant as it is applied to different areas in real life. The study proposes the novel concepts of intuitionistic fuzzy graph (IFG) and some basic definitions. We investigate the types of arcs, for example, $$\alpha _{\mu }$$ α μ -strong, $$\beta _{\mu }$$ β μ -strong, and $$\delta _{\mu }$$ δ μ -arc in an intuitionistic fuzzy graph, and introduce some of their properties. In particular, the present work develops the concepts of intuitionistic fuzzy bridge (IFB), intuitionistic fuzzy cut nodes (IFCN) and some important properties of an intuitionistic fuzzy bridge. Next, we define an intuitionistic fuzzy cycle (IFC) and an intuitionistic fuzzy tree (IFT). Likewise, we discuss some properties of the IFT and the relationship between an intuitionistic fuzzy tree and an intuitionistic fuzzy cycle. Finally, an application of intuitionistic fuzzy tree is illustrated in other sciences.

PREDIKSI INFLOW DAN OUTFLOW UANG KARTAL DI PROVINSI BALI DENGAN METODE NEURO-FUZZY

In this paper, we present a novel approach to data-driven neuro-fuzzy modeling, which aims to create accurate monthly inflow and outflow forecast of money (M0) in Bali Province. The data is monthly time series included some religious ceremony identification variables and a monthly dummy variable from January 2011 to March 2019. Well known, Bali Province has unique cultures, the only one province which Hinduism majority religion in Indonesia, and listed as top tourism destination in the world. The neuro-fuzzy models were created using ANFIS architecture and sliding window time series analysis, then simulated using walk forward validation, interpreted using MAPE, and NRMSE. Based on the simulation of the last 24 months, the model of inflow obtained MAPE 23.33% (worth considering) and NRMSE 18.68% (accurate). Meanwhile, the model of outflow obtained MAPE 19.24% (accurate) and NRMSE 8.71% (very accurate). These models and their pieces of information could assist the central bank in Bali Province to prepare cash for money (M0) outflow and managed technic for counting money (M0) inflow.