Properties of interval type-2 fuzzy sets in decision support systems

Definitions and methods of designing interval type-2 fuzzy sets in fuzzy inference systems for control problems of complex technical objects in conditions of uncertainty are considered. The main types of uncertainties, that arise when designing fuzzy inference systems and depend on the number of expert assessments, are described. Methods for assessing intra-uncertainty and inter-uncertainty are proposed, taking into account the different number of expert assessments at the stage of determining the types and number of membership functions. Factors influencing the parameters and properties of interval type-2 fuzzy during experimental studies are determined. Such factors include the number of experiments performed, external factors, technical parameters of the control object, and the reliability of the components of the computer system decision support system. The properties of the lower and upper membership functions of interval type-2 fuzzy sets are investigated on the example of the Gaussian membership function, which is one of the most used in the problems of fuzzy inference systems design. The main features and differences in the methods of determining the lower and upper membership functions of interval type-2 fuzzy sets for different types of uncertainties are taken into account. Methods for determining the footprint of uncertainty, as well as the dependence of its size on the number of expert assessments, are considered. The footprint of uncertainty is characterized by the lower and upper membership functions, and its size directly affects the accuracy of the obtained solutions. Methods for determining interval type-2 fuzzy sets using regulation factors of membership function parameters for intra-uncertainty and weighting factors of membership functions for inter-uncertainties have been developed. The regulation factor of the function parameters can be used to describe the lower and upper membership functions while determining the size of the footprint of uncertainty. Complex interval type-2 sets are determined to take into account inter-uncertainties in the problems of fuzzy inference systems design.

Kendali Posisi Motor DC Menggunakan Logika Fuzzy Interval Tipe 2

Kendali posisi motor DC sangat diperlukan dalam berbagai sistem dinamik. Karaketristik kekokohan pengendalian menjadi salah satu hal yang harus dipertimbangkan dalam pengendalian posisi motor DC. Makalah ini bertujuan untuk mengusulkan metode pengendalian posisi motor DC menggunakan kendali Interval Type 2 Fuzzy Logic (IT2FL). Berbeda dengan pengendali logika fuzzy tipe 1, pengendali ini memiliki fungsi keanggotaan dengan Footprint of Uncertainty (FoU) di setiap variabel linguistik. Kelebihan inilah yang menyebabkan kendali logika fuzzy tipe 2 memiliki karakteristik kekokohan terhadap ketidakpastian parameter sistem. Penelitian ini menggunakan simulasi Matlab/Simulink untuk menunjukkan respon pengendalian dengan penambahan sinyal derau dan dua skenario FoU. Hasil simulasi menunjukkan bahwa pengendali IT2FL menghasilkan performa lebih baik dibandingkan pengendali logika fuzzy tipe 1 dalam mengatasi derau pengukuran. Pada pengendali IT2FL, FoU 0,2 menghasilkan integral error yang lebih kecil dibandingkan FoU 0,1 dengan selisih terkecil sebesar 0,001. Position control of DC motor is indispensable in various dynamic systems. Control robustness characteristics are one of the things that must be considered in controlling the position of a DC motor. This paper aims to propose a DC motor position control method using an Interval Type 2 Fuzzy Logic (IT2FL) controller. Unlike the type 1 fuzzy logic controller, this controller has a membership function with a Footprint of Uncertainty (FoU) in each linguistic variable. The benefits of it cause the type 2 fuzzy logic control to have robust characteristics against the uncertainty of system parameters. This study uses a Matlab / Simulink simulation to show the control response with the addition of a noise signal and two FoU scenarios. The simulation results show that the IT2FL controller produces better performance than the type 1 fuzzy logic controller in overcoming measurement noise. In the IT2FL controller, FoU 0.2 produces an integral error that is smaller than FoU 0.1 with the smallest difference of 0.001.

Analysis of Footprint of Uncertainty of the IT2 Mamdani Controllers Using Different Type-Reducers

Appropriate Footprint of Uncertainties (FOUs) are beneficial to the performance of Interval Type-2 (IT2) fuzzy controller, revealing the effect of FOUs is a key problem. In our published work, as the FOUs increase, the IT2 Mamdani and TS fuzzy controllers, using KM or EKM type-reducer (TR), approach the constant and piecewise linear controllers, respectively, while they finally become constant and piecewise linear controllers. To verify the validation of the above results, when a different TR is used, in this study, the effects of other popular TRs (i.e., Nie-Tan, Wu-Mendel, Iterative Algorithm with Stop Condition) on output of IT2 Mamdani fuzzy controller, are explored. We proven that, (1) as the FOUs increase, irrespectively of the TRs used, the IT2 Mamdani fuzzy controllers approach constant controllers, (2) when all the FOUs are equal to 1 (i.e., at their maximum ), the fuzzy controllers using Nie-Tan and Iterative Algorithm with Stop Condition TR become constant controllers. The FOUs of the controllers using Wu-Mendel TR can be infinitely approaching 1 and cannot be equal to 1 (otherwise, the denominator of the TR output expression are equal to 0), hence when FOUs are infinitely approaching 1, the controller will approach the constant controller infinitely. These results imply regardless of which popular TR is used, the IT2 Mamdani fuzzy controller, when using larger FOUs, the fluctuation of the input variables have a limited impact on the output, the ability to deal with system uncertainties will deteriorate. Laboratory control experiments are provided to demonstrate these findings.

Classification with Fuzzification Optimization Combining Fuzzy Information Systems and Type-2 Fuzzy Inference

In this research, we introduce a classification procedure based on rule induction and fuzzy reasoning. The classifier generalizes attribute information to handle uncertainty, which often occurs in real data. To induce fuzzy rules, we define the corresponding fuzzy information system. A transformation of the derived rules into interval type-2 fuzzy rules is provided as well. The fuzzification applied is optimized with respect to the footprint of uncertainty of the corresponding type-2 fuzzy sets. The classification process is related to a Mamdani type fuzzy inference. The method proposed was evaluated by the F-score measure on benchmark data.

Modeling Words for Qualitative Distance Based on Interval Type-2 Fuzzy Sets

Modeling qualitative distance words is important for natural language understanding, scene reconstruction and many decision support systems (DSSs) based on a geographic information system (GIS). However, it is difficult to establish the relationship between qualitative distance words and quantitative distance for special applications since the meanings of these words are influenced by both subjective and objective factors. Some existing methods are reviewed, and the Hao–Mendel approach (HMA) is improved to model qualitative distance words for four travel modes by using interval type-2 fuzzy sets (IT2 FSs), aiming at addressing the individual and interpersonal uncertainty among qualitative distance words. The area of the footprint of uncertainty (FOU), fuzziness (entropy), and variance are adopted to measure the uncertainties of qualitative distance words. The experimental results show that the improved HMA algorithm is better than the original HMA algorithm and can be used in spatial information retrieval and GIS-based DSSs.

Robust Wavelet Stabilized ‘Footprints of Uncertainty’ for Fuzzy System Classifiers to Automatically Detect Sharp Waves in the EEG after Hypoxia Ischemia

Currently, there are no developed methods to detect sharp wave transients that exist in the latent phase after hypoxia-ischemia (HI) in the electroencephalogram (EEG) in order to determine if these micro-scale transients are potential biomarkers of HI. A major issue with sharp waves in the HI-EEG is that they possess a large variability in their sharp wave profile making it difficult to build a compact ‘footprint of uncertainty’ (FOU) required for ideal performance of a Type-2 fuzzy logic system (FLS) classifier. In this paper, we develop a novel computational EEG analysis method to robustly detect sharp waves using over 30[Formula: see text]h of post occlusion HI-EEG from an equivalent, in utero, preterm fetal sheep model cohort. We demonstrate that initial wavelet transform (WT) of the sharp waves stabilizes the variation in their profile and thus permits a highly compact FOU to be built, hence, optimizing the performance of a Type-2 FLS. We demonstrate that this method leads to higher overall performance of [Formula: see text] for the clinical [Formula: see text] sampled EEG and [Formula: see text] for the high resolution [Formula: see text] sampled EEG that is improved upon over conventional standard wavelet [Formula: see text] and [Formula: see text], respectively, and fuzzy approaches [Formula: see text] and [Formula: see text], respectively, when performed in isolation.