Fuzzy GMDH and its application to forecasting financial processes

This paper is devoted to the investigation and application of the fuzzy inductive modeling method known as Group Method of Data Handling (GMDH) in problems of Data Mining, in particularly its application to solving the forecasting tasks in financial sphere. The advantage of the inductive modeling method GMDH is a possibility of constructing an adequate model directly in the process of algorithm run. The generalization of GMDH in case of uncertainty — a new method fuzzy GMDH is described which enables to construct fuzzy models almost automatically. The algorithm of fuzzy GMDH is considered. Fuzzy GMDH with Gaussian and bell-wise membership functions MF are considered and their similarity with triangular MF is shown. Fuzzy GMDH with different partial descriptions orthogonal polynomials of Chebyshev and Fourier are considered. The problem of adaptation of fuzzy models obtained by FGMDH is considered and the corresponding adaptation algorithm is described. The extension and generalization of fuzzy GMDH in case of fuzzy inputs is considered and its properties are analyzed. The experimental investigations of the suggested FGMDH were carried out

Energy performance forecasting of residential buildings using fuzzy approaches

The energy consumption used for domestic purposes in Europe is, to a considerable extent, due to heating and cooling. This energy is produced mostly by burning fossil fuels, which has a high negative environmental impact. The characteristics of a building are an important factor to determine the necessities of heating and cooling loads. Therefore, the study of the relevant characteristics of the buildings, regarding the heating and cooling needed to maintain comfortable indoor air conditions, could be very useful in order to design and construct energy-efficient buildings. In previous studies, different machine-learning approaches have been used to predict heating and cooling loads from the set of variables: relative compactness, surface area, wall area, roof area, overall height, orientation, glazing area and glazing area distribution. However, none of these methods are based on fuzzy logic. In this research, we study two fuzzy logic approaches, i.e., fuzzy inductive reasoning (FIR) and adaptive neuro fuzzy inference system (ANFIS), to deal with the same problem. Fuzzy approaches obtain very good results, outperforming all the methods described in previous studies except one. In this work, we also study the feature selection process of FIR methodology as a pre-processing tool to select the more relevant variables before the use of any predictive modelling methodology. It is proven that FIR feature selection provides interesting insights into the main building variables causally related to heating and cooling loads. This allows better decision making and design strategies, since accurate cooling and heating load estimations and correct identification of parameters that affect building energy demands are of high importance to optimize building designs and equipment specifications.Peer ReviewedPostprint (published version

Uncertainty and Interpretability Studies in Soft Computing with an Application to Complex Manufacturing Systems

In systems modelling and control theory, the benefits of applying neural networks have been extensively studied. Particularly in manufacturing processes, such as the prediction of mechanical properties of heat treated steels. However, modern industrial processes usually involve large amounts of data and a range of non-linear effects and interactions that might hinder their model interpretation. For example, in steel manufacturing the understanding of complex mechanisms that lead to the mechanical properties which are generated by the heat treatment process is vital. This knowledge is not available via numerical models, therefore an experienced metallurgist estimates the model parameters to obtain the required properties. This human knowledge and perception sometimes can be imprecise leading to a kind of cognitive uncertainty such as vagueness and ambiguity when making decisions. In system classification, this may be translated into a system deficiency - for example, small input changes in system attributes may result in a sudden and inappropriate change for class assignation. In order to address this issue, practitioners and researches have developed systems that are functional equivalent to fuzzy systems and neural networks. Such systems provide a morphology that mimics the human ability of reasoning via the qualitative aspects of fuzzy information rather by its quantitative analysis. Furthermore, these models are able to learn from data sets and to describe the associated interactions and non-linearities in the data. However, in a like-manner to neural networks, a neural fuzzy system may suffer from a lost of interpretability and transparency when making decisions. This is mainly due to the application of adaptive approaches for its parameter identification. Since the RBF-NN can be treated as a fuzzy inference engine, this thesis presents several methodologies that quantify different types of uncertainty and its influence on the model interpretability and transparency of the RBF-NN during its parameter identification. Particularly, three kind of uncertainty sources in relation to the RBF-NN are studied, namely: entropy, fuzziness and ambiguity. First, a methodology based on Granular Computing (GrC), neutrosophic sets and the RBF-NN is presented. The objective of this methodology is to quantify the hesitation produced during the granular compression at the low level of interpretability of the RBF-NN via the use of neutrosophic sets. This study also aims to enhance the disitnguishability and hence the transparency of the initial fuzzy partition. The effectiveness of the proposed methodology is tested against a real case study for the prediction of the properties of heat-treated steels. Secondly, a new Interval Type-2 Radial Basis Function Neural Network (IT2-RBF-NN) is introduced as a new modelling framework. The IT2-RBF-NN takes advantage of the functional equivalence between FLSs of type-1 and the RBF-NN so as to construct an Interval Type-2 Fuzzy Logic System (IT2-FLS) that is able to deal with linguistic uncertainty and perceptions in the RBF-NN rule base. This gave raise to different combinations when optimising the IT2-RBF-NN parameters. Finally, a twofold study for uncertainty assessment at the high-level of interpretability of the RBF-NN is provided. On the one hand, the first study proposes a new methodology to quantify the a) fuzziness and the b) ambiguity at each RU, and during the formation of the rule base via the use of neutrosophic sets theory. The aim of this methodology is to calculate the associated fuzziness of each rule and then the ambiguity related to each normalised consequence of the fuzzy rules that result from the overlapping and to the choice with one-to-many decisions respectively. On the other hand, a second study proposes a new methodology to quantify the entropy and the fuzziness that come out from the redundancy phenomenon during the parameter identification. To conclude this work, the experimental results obtained through the application of the proposed methodologies for modelling two well-known benchmark data sets and for the prediction of mechanical properties of heat-treated steels conducted to publication of three articles in two peer-reviewed journals and one international conference

Context dependent fuzzy modelling and its applications

Fuzzy rule-based systems (FRBS) use the principle of fuzzy sets and fuzzy logic to describe vague and imprecise statements and provide a facility to express the behaviours of the system with a human-understandable language. Fuzzy information, once defined by a fuzzy system, is fixed regardless of the circumstances and therefore makes it very difficult to capture the effect of context on the meaning of the fuzzy terms. While efforts have been made to integrate contextual information into the representation of fuzzy sets, it remains the case that often the context model is very restrictive and/or problem specific. The work reported in this thesis is our attempt to create a practical frame work to integrate contextual information into the representation of fuzzy sets so as to improve the interpretability as well as the accuracy of the fuzzy system. Throughout this thesis, we have looked at the capability of the proposed context dependent fuzzy sets as a stand alone as well as in combination with other methods in various application scenarios ranging from time series forecasting to complicated car racing control systems. In all of the applications, the highly competitive performance nature of our approach has proven its effectiveness and efficiency compared with existing techniques in the literature

Context dependent fuzzy modelling and its applications

Fuzzy rule-based systems (FRBS) use the principle of fuzzy sets and fuzzy logic to describe vague and imprecise statements and provide a facility to express the behaviours of the system with a human-understandable language. Fuzzy information, once defined by a fuzzy system, is fixed regardless of the circumstances and therefore makes it very difficult to capture the effect of context on the meaning of the fuzzy terms. While efforts have been made to integrate contextual information into the representation of fuzzy sets, it remains the case that often the context model is very restrictive and/or problem specific. The work reported in this thesis is our attempt to create a practical frame work to integrate contextual information into the representation of fuzzy sets so as to improve the interpretability as well as the accuracy of the fuzzy system. Throughout this thesis, we have looked at the capability of the proposed context dependent fuzzy sets as a stand alone as well as in combination with other methods in various application scenarios ranging from time series forecasting to complicated car racing control systems. In all of the applications, the highly competitive performance nature of our approach has proven its effectiveness and efficiency compared with existing techniques in the literature

A domain transformation approach for addressing staff scheduling problems

Staff scheduling is a complex combinatorial optimisation problem concerning allocation of staff to duty rosters in a wide range of industries and settings. This thesis presents a novel approach to solving staff scheduling problems, and in particular nurse scheduling, by simplifying the problem space through information granulation. The complexity of the problem is due to a large solution space and the many constraints that need to be satisfied. Published research indicates that methods based on random searches of the solution space did not produce good-quality results consistently. In this study, we have avoided random searching and proposed a systematic hierarchical method of granulation of the problem domain through pre-processing of constraints. The approach is general and can be applied to a wide range of staff scheduling problems. The novel approach proposed here involves a simplification of the original problem by a judicious grouping of shift types and a grouping of individual shifts into weekly sequences. The schedule construction is done systematically, while assuring its feasibility and minimising the cost of the solution in the reduced problem space of weekly sequences. Subsequently, the schedules from the reduced problem space are translated into the original problem space by taking into account the constraints that could not be represented in the reduced space. This two-stage approach to solving the scheduling problem is referred to here as a domain-transformation approach. The thesis reports computational results on both standard benchmark problems and a specific scheduling problem from Kajang Hospital in Malaysia. The results confirm that the proposed method delivers high-quality results consistently and is computationally efficient

Uncertain Multi-Criteria Optimization Problems

Most real-world search and optimization problems naturally involve multiple criteria as objectives. Generally, symmetry, asymmetry, and anti-symmetry are basic characteristics of binary relationships used when modeling optimization problems. Moreover, the notion of symmetry has appeared in many articles about uncertainty theories that are employed in multi-criteria problems. Different solutions may produce trade-offs (conflicting scenarios) among different objectives. A better solution with respect to one objective may compromise other objectives. There are various factors that need to be considered to address the problems in multidisciplinary research, which is critical for the overall sustainability of human development and activity. In this regard, in recent decades, decision-making theory has been the subject of intense research activities due to its wide applications in different areas. The decision-making theory approach has become an important means to provide real-time solutions to uncertainty problems. Theories such as probability theory, fuzzy set theory, type-2 fuzzy set theory, rough set, and uncertainty theory, available in the existing literature, deal with such uncertainties. Nevertheless, the uncertain multi-criteria characteristics in such problems have not yet been explored in depth, and there is much left to be achieved in this direction. Hence, different mathematical models of real-life multi-criteria optimization problems can be developed in various uncertain frameworks with special emphasis on optimization problems