Time series forecasting with interval type-2 intuitionistic fuzzy logic systems

Conventional fuzzy time series approaches make use of type-1 or type-2 fuzzy models. Type-1 models with one index (membership grade) cannot fully handle the level of uncertainty inherent in many real world applications. The type-2 models with upper and lower membership functions do handle uncertainties in many applications better than its type-1 counterparts. This study proposes the use of interval type-2 intuitionistic fuzzy logic system of Takagi-Sugeno-Kang (IT2IFLS-TSK) fuzzy inference that utilises more parameters than type-2 fuzzy models in time series forecasting. The IT2IFLS utilises more indexes namely upper and lower non-membership functions. These additional parameters of IT2IFLS serve to refine the fuzzy relationships obtained from type-2 fuzzy models and ultimately improve the forecasting performance. Evaluation is made on the proposed system using three real world benchmark time series problems namely: Santa Fe, tree ring and Canadian lynx datasets. The empirical analyses show improvements of prediction of IT2IFLS over other approaches on these datasets

Interval type-2 intuitionistic fuzzy logic system for time series and identification problems - a comparative study

This paper proposes a sliding mode control-based learning of interval type-2 intuitionistic fuzzy logic system for time series and identification problems. Until now, derivative-based algorithms such as gradient descent back propagation, extended Kalman filter, decoupled extended Kalman filter and hybrid method of decoupled extended Kalman filter and gradient descent methods have been utilized for the optimization of the parameters of interval type-2 intuitionistic fuzzy logic systems. The proposed model is based on a Takagi-Sugeno-Kang inference system. The evaluations of the model are conducted using both real world and artificially generated datasets. Analysis of results reveals that the proposed interval type-2 intuitionistic fuzzy logic system trained with sliding mode control learning algorithm (derivative-free) do outperforms some existing models in terms of the test root mean squared error while competing favourable with other models in the literature. Moreover, the proposed model may stand as a good choice for real time applications where running time is paramount compared to the derivative-based models

Hybrid learning for interval type-2 intuitionistic fuzzy logic systems as applied to identification and prediction problems

This paper presents a novel application of a hybrid learning approach to the optimisation of membership and non-membership functions of a newly developed interval type-2 intuitionistic fuzzy logic system (IT2 IFLS) of a Takagi-Sugeno-Kang (TSK) fuzzy inference system with neural network learning capability. The hybrid algorithms consisting of decou- pled extended Kalman filter (DEKF) and gradient descent (GD) are used to tune the parameters of the IT2 IFLS for the first time. The DEKF is used to tune the consequent parameters in the forward pass while the GD method is used to tune the antecedents parts during the backward pass of the hybrid learning. The hybrid algorithm is described and evaluated, prediction and identification results together with the runtime are compared with similar existing studies in the literature. Performance comparison is made between the proposed hybrid learning model of IT2 IFLS, a TSK-type-1 intuitionistic fuzzy logic system (IFLS-TSK) and a TSK-type interval type-2 fuzzy logic system (IT2 FLS-TSK) on two instances of the datasets under investigation. The empirical comparison is made on the designed systems using three artificially generated datasets and three real world datasets. Analysis of results reveal that IT2 IFLS outperforms its type-1 variants, IT2 FLS and most of the existing models in the literature. Moreover, the minimal run time of the proposed hybrid learning model for IT2 IFLS also puts this model forward as a good candidate for application in real time systems

Extended Kalman filter-based learning of interval type-2 intuitionistic fuzzy logic system

Fuzzy logic systems have been extensively applied for solving many real world application problems because they are found to be universal approximators and many methods, particularly, gradient descent (GD) methods have been widely adopted for the optimization of fuzzy membership functions. Despite its popularity, GD still suffers some drawbacks in terms of its slow learning and convergence. In this study, the use of decoupled extended Kalman filter (DEKF) to optimize the parameters of an interval type-2 intuitionistic fuzzy logic system of Tagagi-Sugeno-Kang (IT2IFLS-TSK) fuzzy inference is proposed and results compared with IT2IFLS gradient descent learning. The resulting systems are evaluated on a real world dataset from Australia’s electricity market. The IT2IFLS-DEKF is also compared with its type-1 variant and interval type-2 fuzzy logic system (IT2FLS). Analysis of results reveal performance superiority of IT2IFLS trained with DEKF (IT2IFLS-DEKF) over IT2IFLS trained with gradient descent (IT2IFLS-GD). The proposed IT2IFLS-DEKF also outperforms its type-1 variant and IT2FLS on the same learning platform

Interval type-2 intuitionistic fuzzy logic system for non-linear system prediction

This paper presents an approach to prediction based on a new interval type-2 intuitionistic fuzzy logic system (IT2IFLS) of Takagi-Sugeno-Kang (TSK) fuzzy inference. The gradient descent algorithm (GDA) is used to adapt the parame- ters of the IT2IFLS. The empirical comparison is made on the designed system using two synthetic datasets. Analysis of our results reveal that the presence of additional degrees of freedom in terms of non-membership functions and hesitation indexes in IT2IFLS tend to reduce the root mean square error (RMSE) of the system compared to a type-1 fuzzy logic approach and some interval type-2 fuzzy systems

“Fuzzy time”, a Solution of Unexpected Hanging Paradox (a Fuzzy interpretation of Quantum Mechanics)

Although Fuzzy logic and Fuzzy Mathematics is a widespread subject and there is a vast literature about it, yet the use of Fuzzy issues like Fuzzy sets and Fuzzy numbers was relatively rare in time concept. This could be seen in the Fuzzy time series. In addition, some attempts are done in fuzzing Turing Machines but seemingly there is no need to fuzzy time. Throughout this article, we try to change this picture and show why it is helpful to consider the instants of time as Fuzzy numbers. In physics, though there are revolutionary ideas on the time concept like B theories in contrast to A theory also about central concepts like space, momentum… it is a long time that these concepts are changed, but time is considered classically in all well-known and established physics theories. Seemingly, we stick to the classical time concept in all fields of science and we have a vast inertia to change it. Our goal in this article is to provide some bases why it is rational and reasonable to change and modify this picture. Here, the central point is the modified version of “Unexpected Hanging” paradox as it is described in "Is classical Mathematics appropriate for theory of Computation".This modified version leads us to a contradiction and based on that it is presented there why some problems in Theory of Computation are not solved yet. To resolve the difficulties arising there, we have two choices. Either “choosing” a new type of Logic like “Para-consistent Logic” to tolerate contradiction or changing and improving the time concept and consequently to modify the “Turing Computational Model”. Throughout this paper, we select the second way for benefiting from saving some aspects of Classical Logic. In chapter 2, by applying quantum Mechanics and Schrodinger equation we compute the associated fuzzy number to time

“Fuzzy time”, from paradox to paradox (Does it solve the contradiction between Quantum Mechanics & General Relativity?)

Although Fuzzy logic and Fuzzy Mathematics is a widespread subject and there is a vast literature about it, yet the use of Fuzzy issues like Fuzzy sets and Fuzzy numbers was relatively rare in time concept. This could be seen in the Fuzzy time series. In addition, some attempts are done in fuzzing Turing Machines but seemingly there is no need to fuzzy time. Throughout this article, we try to change this picture and show why it is helpful to consider the instants of time as Fuzzy numbers. In physics, though there are revolutionary ideas on the time concept like B theories in contrast to A theory also about central concepts like space, momentum… it is a long time that these concepts are changed, but time is considered classically in all well-known and established physics theories. Seemingly, we stick to the classical time concept in all fields of science and we have a vast inertia to change it. Our goal in this article is to provide some bases why it is rational and reasonable to change and modify this picture. Here, the central point is the modified version of “Unexpected Hanging” paradox as it is described in "Is classical Mathematics appropriate for theory of Computation".This modified version leads us to a contradiction and based on that it is presented there why some problems in Theory of Computation are not solved yet. To resolve the difficulties arising there, we have two choices. Either “choosing” a new type of Logic like “Para-consistent Logic” to tolerate contradiction or changing and improving the time concept and consequently to modify the “Turing Computational Model”. Throughout this paper, we select the second way for benefiting from saving some aspects of Classical Logic. In chapter 2, by applying quantum Mechanics and Schrodinger equation we compute the associated fuzzy number to time. These, provides a new interpretation of Quantum Mechanics.More exactly what we see here is "Particle-Fuzzy time" interpretation of quantum Mechanics, in contrast to some other interpretations of Quantum Mechanics like " Wave-Particle" interpretation. At the end, we propound a question about the possible solution of a paradox in Physics, the contradiction between General Relativity and Quantum Mechanics

Fuzzy Logic in Decision Support: Methods, Applications and Future Trends

During the last decades, the art and science of fuzzy logic have witnessed significant developments and have found applications in many active areas, such as pattern recognition, classification, control systems, etc. A lot of research has demonstrated the ability of fuzzy logic in dealing with vague and uncertain linguistic information. For the purpose of representing human perception, fuzzy logic has been employed as an effective tool in intelligent decision making. Due to the emergence of various studies on fuzzy logic-based decision-making methods, it is necessary to make a comprehensive overview of published papers in this field and their applications. This paper covers a wide range of both theoretical and practical applications of fuzzy logic in decision making. It has been grouped into five parts: to explain the role of fuzzy logic in decision making, we first present some basic ideas underlying different types of fuzzy logic and the structure of the fuzzy logic system. Then, we make a review of evaluation methods, prediction methods, decision support algorithms, group decision-making methods based on fuzzy logic. Applications of these methods are further reviewed. Finally, some challenges and future trends are given from different perspectives. This paper illustrates that the combination of fuzzy logic and decision making method has an extensive research prospect. It can help researchers to identify the frontiers of fuzzy logic in the field of decision making

Kapılı tekrarlayan hücreler tabanlı bulanık zaman serileri tahminleme modeli

Time series forecasting and prediction are utilized in various industries, such as e-commerce, stock markets, wind power, and energy demand forecasting. An accurate forecast in these applications is an essential and challenging task because of the complexity and uncertainty of time series. Nowadays, deep learning methods are popular in time series forecasting and show better performance than classical methods. However, in the literature, only some studies use deep learning methods in fuzzy time series (FTS) forecasting. In this study, we propose a novel FTS forecasting model based upon the hybridization of Recurrent Neural Networks with FTS to deal with the complexity and uncertainty of these series. The proposed model utilizes Gated Recurrent Unit (GRU) to make predictions using a combination of membership values and past values from original time series data as model input and produce real forecast value. Moreover, the proposed model can handle first-order fuzzy relations and high-order ones. In experiments, we have compared our model results with state-of-art methods by using two real-world datasets; The Taiwan Stock Exchange Capitalization Weighted Stock Index (TAIEX) and Nikkei Stock Average. The results indicate that our model outperforms or performs similarly to other methods. The proposed model is validated using the Covid-19 active case dataset and BIST100 Index dataset and performs better than Long Short-term Memory (LSTM) networks.Zaman serisi tahminleme hava durumu, iş dünyası, satış verileri ve enerji tüketimi tahminleme gibi bir çok alanda uygulama alanına sahiptir. Bu alanlarda tahminleme yaparken kesin sonuçlar elde etmek çok önemlidir ama aynı zamanda zaman serilerinin karmaşık ve de belirsizlik içeren veriler olması nedeniyle çok zordur. Günümüzde, derin öğrenme metotları bu alanda klasik metotlara göre daha iyi sonuçlar vermektedir. Fakat literatürde bulanık zaman serileri tahminleme konusunda çok az çalışma vardır. Bu çalışmada, zaman serilerindeki karmaşıklığın ve belirsizliğin doğurduğu problemleri yok etmek için Yinelemeli sinir Ağları ile bulanık zaman serilerini bir arada kullanan bir model ortaya konumuştur. Bu çalışmada, Kapılı Tekrarlayan Hücreler kullanarak geçmiş veriler ile bulanık verilerin üyelik değerleri birleştirilerek tahminleme değeri hesaplanmıştır. Ayrıca, bu çalışmadaki model ilk seviye bulanık ilişkileri ele alabildiği gibi, çoklu seviye bulanık ilişkileri de kapsamaktadır. Testlerde literatürde var olan çalışmalar ilgili model ile iki açık veri seti ile karşılaştırılmış olup bahsi geçen modelin daha iyi veya benzer sonuçlar verdiği gözlemlenmiştir. Ayrıca model Covid-19 ve BIST100 borsa verileri kullanılarak da test edilmiş ve Uzun-Kısa Süreli Bellek modellerinden daha iyi sonuç vermiştir