Computational intelligence techniques in asset risk analysis

This thesis was submitted for the degree of Doctor of Philosophy and awarded by Brunel University.The problem of asset risk analysis is positioned within the computational intelligence paradigm. We suggest an algorithm for reformulating asset pricing, which involves incorporating imprecise information into the pricing factors through fuzzy variables as well as a calibration procedure for their possibility distributions. Then fuzzy mathematics is used to process the imprecise factors and obtain an asset evaluation. This evaluation is further automated using neural networks with sign restrictions on their weights. While such type of networks has been only used for up to two network inputs and hypothetical data, here we apply thirty-six inputs and empirical data. To achieve successful training, we modify the Levenberg-Marquart backpropagation algorithm. The intermediate result achieved is that the fuzzy asset evaluation inherits features of the factor imprecision and provides the basis for risk analysis. Next, we formulate a risk measure and a risk robustness measure based on the fuzzy asset evaluation under different characteristics of the pricing factors as well as different calibrations. Our database, extracted from DataStream, includes thirty-five companies traded on the London Stock Exchange. For each company, the risk and robustness measures are evaluated and an asset risk analysis is carried out through these values, indicating the implications they have on company performance. A comparative company risk analysis is also provided. Then, we employ both risk measures to formulate a two-step asset ranking method. The assets are initially rated according to the investors' risk preference. In addition, an algorithm is suggested to incorporate the asset robustness information and refine further the ranking benefiting market analysts. The rationale provided by the ranking technique serves as a point of departure in designing an asset risk classifier. We identify the fuzzy neural network structure of the classifier and develop an evolutionary training algorithm. The algorithm starts with suggesting preliminary heuristics in constructing a sufficient training set of assets with various characteristics revealed by the values of the pricing factors and the asset risk values. Then, the training algorithm works at two levels, the inner level targets weight optimization, while the outer level efficiently guides the exploration of the search space. The latter is achieved by automatically decomposing the training set into subsets of decreasing complexity and then incrementing backward the corresponding subpopulations of partially trained networks. The empirical results prove that the developed algorithm is capable of training the identified fuzzy network structure. This is a problem of such complexity that prevents single-level evolution from attaining meaningful results. The final outcome is an automatic asset classifier, based on the investors’ perceptions of acceptable risk. All the steps described above constitute our approach to reformulating asset risk analysis within the approximate reasoning framework through the fusion of various computational intelligence techniques

Robust regression with imprecise data

We consider the problem of regression analysis with imprecise data. By imprecise data we mean imprecise observations of precise quantities in the form of sets of values. In this paper, we explore a recently introduced likelihood-based approach to regression with such data. The approach is very general, since it covers all kinds of imprecise data (i.e. not only intervals) and it is not restricted to linear regression. Its result consists of a set of functions, reflecting the entire uncertainty of the regression problem. Here we study in particular a robust special case of the likelihood-based imprecise regression, which can be interpreted as a generalization of the method of least median of squares. Moreover, we apply it to data from a social survey, and compare it with other approaches to regression with imprecise data. It turns out that the likelihood-based approach is the most generally applicable one and is the only approach accounting for multiple sources of uncertainty at the same time

Design and implementation of fuzzy logic controllers

The main objectives of our research are to present a self-contained overview of fuzzy sets and fuzzy logic, develop a methodology for control system design using fuzzy logic controllers, and to design and implement a fuzzy logic controller for a real system. We first present the fundamental concepts of fuzzy sets and fuzzy logic. Fuzzy sets and basic fuzzy operations are defined. In addition, for control systems, it is important to understand the concepts of linguistic values, term sets, fuzzy rule base, inference methods, and defuzzification methods. Second, we introduce a four-step fuzzy logic control system design procedure. The design procedure is illustrated via four examples, showing the capabilities and robustness of fuzzy logic control systems. This is followed by a tuning procedure that we developed from our design experience. Third, we present two Lyapunov based techniques for stability analysis. Finally, we present our design and implementation of a fuzzy logic controller for a linear actuator to be used to control the direction of the Free Flight Rotorcraft Research Vehicle at LaRC

A spatial-type interval-valued median for random intervals

© 2018 Informa UK Limited, trading as Taylor & Francis Group. To estimate the central tendency or location of a sample of interval-valued data, a standard statistic is the interval-valued sample mean. Its strong sensitivity to outliers or data changes motivates the search for more robust alternatives. In this respect, a more robust location statistic is studied in this paper. This measure is inspired by the concept of spatial median and makes use of the versatile generalized Bertoluzza's metric between intervals, the so-called dθ distance. The problem of minimizing the mean dθ distance to the values the random interval takes, which defines the spatial-type dθ-median, is analysed. Existence and uniqueness of the sample version are shown. Furthermore, the robustness of this proposal is investigated by deriving its finite sample breakdown point. Finally, a real-life example from the Economics field illustrates the robustness of the sample dθ-median, and simulation studies show some comparisons with respect to the mean and several recently introduced robust location measures for interval-valued data.status: publishe

Symmetric implicational restriction method of fuzzy inference

summary:The symmetric implicational method is revealed from a different perspective based upon the restriction theory, which results in a novel fuzzy inference scheme called the symmetric implicational restriction method. Initially, the SIR-principles are put forward, which constitute optimized versions of the triple I restriction inference mechanism. Next, the existential requirements of basic solutions are given. The supremum (or infimum) of its basic solutions is achieved from some properties of fuzzy implications. The conditions are obtained for the supremum to become the maximum (or the infimum to be the minimum). Lastly, four concrete examples are provided, and it is shown that the new method is better than the triple I restriction method, because the former is able to let the inference more compact, and lead to more and superior particular inference schemes

Possibilistic and fuzzy clustering methods for robust analysis of non-precise data

This work focuses on robust clustering of data affected by imprecision. The imprecision is managed in terms of fuzzy sets. The clustering process is based on the fuzzy and possibilistic approaches. In both approaches the observations are assigned to the clusters by means of membership degrees. In fuzzy clustering the membership degrees express the degrees of sharing of the observations to the clusters. In contrast, in possibilistic clustering the membership degrees are degrees of typicality. These two sources of information are complementary because the former helps to discover the best fuzzy partition of the observations while the latter reflects how well the observations are described by the centroids and, therefore, is helpful to identify outliers. First, a fully possibilistic k-means clustering procedure is suggested. Then, in order to exploit the benefits of both the approaches, a joint possibilistic and fuzzy clustering method for fuzzy data is proposed. A selection procedure for choosing the parameters of the new clustering method is introduced. The effectiveness of the proposal is investigated by means of simulated and real-life data