Type-Reduction of the Discretised Interval Type-2 Fuzzy Set: Approaching the Continuous Case through Progressively Finer Discretisation.

The defuzzification of a type-2 fuzzy set is a two stage process consisting of firstly type-reduction, and secondly defuzzification of the resultant type-1 set. This paper considers three approaches to discrete interval type-reduction: 1. The exhaustive method which produces the Type-Reduced Set, 2. the Greenfield-Chiclana Collapsing Defuzzifier which gives rise to the Representative Embedded Set Approximation, and 3. the Nie-Tan Method from which the Nie-Tan Set is derived. In the discrete case these three type-1 sets are distinct. The behavior of the three sets under fine discretisation is investigated experimentally, in order to shed light on the relationships between the continuous versions of these type-1 sets

Higher order fuzzy logic in controlling selective catalytic reduction systems

This paper presents research on applications of fuzzy logic and higher-order fuzzy logic systems to control filters reducing air pollution [1]. The filters use Selective Catalytic Reduction (SCR) method and, as for now, this process is controlled manually by a human expert. The goal of the research is to control an SCR system responsible for emission of nitrogen oxide (NO) and nitrogen dioxide (NO2) to the air, using SCR with ammonia (NH3). There are two higher-order fuzzy logic systems presented, applying interval-valued fuzzy sets and type-2 fuzzy sets, respectively. Fuzzy sets and higher order fuzzy sets describe linguistically levels of nitrogen oxides as the input, and settings of ammonia valve in the air filter as the output. The obtained results are consistent with data provided by experts. Besides, we show that the type-2 fuzzy logic controllers allows us to obtain results much closer to desired parameters of the ammonia valve, than traditional FLS

Comments on: Interval Type-2 Fuzzy Sets are generalization of Interval-Valued Fuzzy Sets: Towards a Wider view on their relationship

This Letter makes some observations about [2] that further support the distinction between an interval type-2 fuzzy set (IT2 FS) and an interval-valued fuzzy set (IV FS), points out that all operations, methods and systems that have been developed and published about IT2 FSs are, so far, only valid in the special case when IT2 FS = IVFS, and suggests some research opportunities

A Bibliometric Overview of the Field of Type-2 Fuzzy Sets and Systems [Discussion Forum]

© 2005-2012 IEEE. Fuzzy Sets and Systems is an area of computational intelligence, pioneered by Lotfi Zadeh over 50 years ago in a seminal paper in Information and Control. Fuzzy Sets (FSs) deal with uncertainty in our knowledge of a particular situation. Research and applications in FSs have grown steadily over 50 years. More recently, we have seen a growth in Type-2 Fuzzy Set (T2 FS) related papers, where T2 FSs are utilized to handle uncertainty in realworld problems. In this paper, we have used bibliometric methods to obtain a broad overview of the area of T2 FSs. This method analyzes information on the bibliographic details of published journal papers, which includes title, authors, author address, journals and citations, extracted from the Science and Social Science Citation Indices in the Web of Science (WoS) database for the last 20 years (1997-2017). We have compared the growth of publications in the field of FSs, and its subset T2 FSs, identified highly cited papers in T2 FSs, highly cited authors, key institutions, and main countries with researchers involved in T2 FS related research

Vehicle Trajectory Tracking Through Magnetic Sensors

Traffic surveillance is an important issue in Intelligent Transportation Systems(ITS). In this paper, we propose a novel surveillance system to detect and track vehicles using ubiquitously deployed magnetic sensors. That is, multiple magnetic sensors, mounted roadside and along lane boundary lines, are used to track various vehicles. Real-time vehicle detection data are reported from magnetic sensors, collected into data center via base stations, and processed to depict vehicle trajectories including vehicle position, timestamp, speed and type. We first define a vehicle trajectory tracking problem. We then propose a graph-based data association algorithm to track each detected vehicle, and design a related online algorithm framework respectively. We finally validate the performance via both experimental simulation and real-world road test. The experimental results demonstrate that the proposed solution provides a cost-effective solution to capture the driving status of vehicles and on that basis form various traffic safety and efficiency applications

A support vector-based interval type-2 fuzzy system

In this paper, a new fuzzy regression model that is supported by support vector regression is presented. Type-2 fuzzy systems are able to tackle applications that have significant uncertainty. However general type-2 fuzzy systems are more complex than type-1 fuzzy systems. Support vector machines are similar to fuzzy systems in that they can also model systems that are non-linear in nature. In the proposed model the consequent parameters of type-2 fuzzy rules are learnt using support vector regression and an efficient closed-form type reduction strategy is used to simplify the computations. Support vector regression improved the generalisation performance of the fuzzy rule-based system in which the fuzzy rules were a set of interpretable IF-THEN rules. The performance of the proposed model was demonstrated by conducting case studies for the non-linear system approximation and prediction of chaotic time series. The model yielded promising results and the simulation results are compared to the results published in the area

Exploring Constrained Type-2 fuzzy sets

Fuzzy logic has been widely used to model human reasoning thanks to its inherent capability of handling uncertainty. In particular, the introduction of Type-2 fuzzy sets added the possibility of expressing uncertainty even on the definition of the membership functions. Type-2 sets, however, don’t pose any restrictions on the continuity or convexity of their embedded sets while these properties may be desirable in certain contexts. To overcome this problem, Constrained Type-2 fuzzy sets have been proposed. In this paper, we focus on Interval Constrained Type-2 sets to see how their unique structure can be exploited to build a new inference process. This will set some ground work for future developments, such as the design of a new defuzzification process for Constrained Type-2 fuzzy systems

Comparación entre el Índice de Yager y el Centroide para Reducción de tipo de un Número Difuso Tipo-2 de Intervalo

Context: There is a need for ranking and defuzzification of Interval Type-2 fuzzy sets (IT2FS), in particular Interval Type-2 fuzzy numbers (IT2FN). To do so, we use the classical Yager Index Rank (YIR) for fuzzy sets to IT2FNs in order to find an alternative to the centroid of an IT2FN.Method: We use a simulation strategy to compare the results of the centroid and the YIR of an IT2FN. This way, we simulate 1000 IT2FNs of the following three kinds: gaussian, triangular, and non symmetrical in order to compare their centroids and YIRs.Results: After performing the simulations, we compute some statistics about its behavior such as the degree of subsethood, equality and the size of the Footprint of Uncertainty (FOU) of an IT2FN. A description of the obtained results shows that the YIR is less wide than centroid of an IT2FN.Conclusions: In general, YIR is less complex to obtain than the centroid of an IT2FN, which is highly desirable in practical applications such as fuzzy decision making and control. Some other properties regarding its size and location are also discussed.Contexto: Hay una necesidad por defuzzificar y rankear Conjuntos Difusos Tipo-2 de Intervalo (IT2FS), en particular Números Difusos Tipo-2 de Intervalo (IT2FN). Para ello, usamos el Índice de Yager (YIR) para conjuntos difusos aplicado a IT2FNs con el fin de encontrar una alternativa al centroide de un IT2FN.Método: Usamos una estrategia de simulación para comparar los resultados del centroide y del YIR de un IT2FN. Así pues, simulamos 1000 IT2FNs de cada uno de los siguientes tres tipos: gausianos, triangulares y asimétricos para comparar sus centroides y YIRs.Resultados: Después de realizar las simulaciones, se calculan algunas estadísticas de su comportamiento como el grado de cobertura y de igualdad relativas del YIR respecto al centroide así como el tamaño de la Huella de Incertidumbre (FOU) de un IT2FN. La descripción de los resultados obtenidos muestra que el YIR es menos amplio que el centroide.Conclusiones: En general, el YIR es menos complejo de obtener que el centroide de un IT2FN, lo cual es altamente deseable en aplicaciones prácticas como toma de decisiones y control. Otras propiedades relacionadas con su tamaño y ubicación también son discutidas

A support vector-based interval type-2 fuzzy system

In this paper, a new fuzzy regression model that is supported by support vector regression is presented. Type-2 fuzzy systems are able to tackle applications that have significant uncertainty. However general type-2 fuzzy systems are more complex than type-1 fuzzy systems. Support vector machines are similar to fuzzy systems in that they can also model systems that are non-linear in nature. In the proposed model the consequent parameters of type-2 fuzzy rules are learnt using support vector regression and an efficient closed-form type reduction strategy is used to simplify the computations. Support vector regression improved the generalisation performance of the fuzzy rule-based system in which the fuzzy rules were a set of interpretable IF-THEN rules. The performance of the proposed model was demonstrated by conducting case studies for the non-linear system approximation and prediction of chaotic time series. The model yielded promising results and the simulation results are compared to the results published in the area