Application of decision trees and multivariate regression trees in design and optimization

Induction of decision trees and regression trees is a powerful technique not only for performing ordinary classification and regression analysis but also for discovering the often complex knowledge which describes the input-output behavior of a learning system in qualitative forms;In the area of classification (discrimination analysis), a new technique called IDea is presented for performing incremental learning with decision trees. It is demonstrated that IDea\u27s incremental learning can greatly reduce the spatial complexity of a given set of training examples. Furthermore, it is shown that this reduction in complexity can also be used as an effective tool for improving the learning efficiency of other types of inductive learners such as standard backpropagation neural networks;In the area of regression analysis, a new methodology for performing multiobjective optimization has been developed. Specifically, we demonstrate that muitiple-objective optimization through induction of multivariate regression trees is a powerful alternative to the conventional vector optimization techniques. Furthermore, in an attempt to investigate the effect of various types of splitting rules on the overall performance of the optimizing system, we present a tree partitioning algorithm which utilizes a number of techniques derived from diverse fields of statistics and fuzzy logic. These include: two multivariate statistical approaches based on dispersion matrices, an information-theoretic measure of covariance complexity which is typically used for obtaining multivariate linear models, two newly-formulated fuzzy splitting rules based on Pearson\u27s parametric and Kendall\u27s nonparametric measures of association, Bellman and Zadeh\u27s fuzzy decision-maximizing approach within an inductive framework, and finally, the multidimensional extension of a widely-used fuzzy entropy measure. The advantages of this new approach to optimization are highlighted by presenting three examples which respectively deal with design of a three-bar truss, a beam, and an electric discharge machining (EDM) process

Linguistic probability theory

In recent years probabilistic knowledge-based systems such as Bayesian networks and influence diagrams have come to the fore as a means of representing and reasoning about complex real-world situations. Although some of the probabilities used in these models may be obtained statistically, where this is impossible or simply inconvenient, modellers rely on expert knowledge. Experts, however, typically find it difficult to specify exact probabilities and conventional representations cannot reflect any uncertainty they may have. In this way, the use of conventional point probabilities can damage the accuracy, robustness and interpretability of acquired models. With these concerns in mind, psychometric researchers have demonstrated that fuzzy numbers are good candidates for representing the inherent vagueness of probability estimates, and the fuzzy community has responded with two distinct theories of fuzzy probabilities.This thesis, however, identifies formal and presentational problems with these theories which render them unable to represent even very simple scenarios. This analysis leads to the development of a novel and intuitively appealing alternative - a theory of linguistic probabilities patterned after the standard Kolmogorov axioms of probability theory. Since fuzzy numbers lack algebraic inverses, the resulting theory is weaker than, but generalises its classical counterpart. Nevertheless, it is demonstrated that analogues for classical probabilistic concepts such as conditional probability and random variables can be constructed. In the classical theory, representation theorems mean that most of the time the distinction between mass/density distributions and probability measures can be ignored. Similar results are proven for linguistic probabiliities.From these results it is shown that directed acyclic graphs annotated with linguistic probabilities (under certain identified conditions) represent systems of linguistic random variables. It is then demonstrated these linguistic Bayesian networks can utilise adapted best-of-breed Bayesian network algorithms (junction tree based inference and Bayes' ball irrelevancy calculation). These algorithms are implemented in ARBOR, an interactive design, editing and querying tool for linguistic Bayesian networks.To explore the applications of these techniques, a realistic example drawn from the domain of forensic statistics is developed. In this domain the knowledge engineering problems cited above are especially pronounced and expert estimates are commonplace. Moreover, robust conclusions are of unusually critical importance. An analysis of the resulting linguistic Bayesian network for assessing evidential support in glass-transfer scenarios highlights the potential utility of the approach

Pricing options in a fuzzy environment

Includes abstract.Includes bibliographical references (leaves 114-116).Although Fuzzy Logic is not new, it is however only since 2004 that an axiomatic theory has been created that has all the desirable effects of Fuzzy Logic. This theory, named Credibility theory was proposed by Dr. Liu. Within this thesis we aim to utilize credibility theory to model the psychological impacts of market participants on European options. Specifically this is done by modifying the approach that was originally taken by Black and Scholes. The Hew model, which is known as the fuzzy drift parameter model, begins by replacing the deterministic drift within Brownian motion with a fuzzy parameter. This fuzzy parameter models the psychological impacts of market participants. Naturally as we are dealing in Chance theory 1 the risk neutral dynamics change from that of Black and Scholes and thus so does the price of European call options

Fuzzy approach to construction activity estimation

Past experience has shown that variations in production rate value for the same work item is attributed to a wide range of factors. The relationships between these factors and the production rates are often very complex. It is impossible to describe an exact mathematical causal relationship between the qualitative factors(QF) and production rates. Various subjective approaches have been attempted to quantify the uncertainties contained in these causal relationships. This thesis presents one such approach by adopting a fuzzy set theory in conjunction with a fuzzy rule based system that could improve the quantification of the qualitative factors in estimating construction activity durations and costs. A method to generate a Standard Activity Unit Rate(SAUR) is presented. A construction activity can be defined by combining the Design Breakdown Structure, Trade Breakdown Structure and Work Section Breakdown Structure. By establishing the data structure of an activity, it is possible to synthesis the SAUR from published estimating sources in a systematic way. After the SAUR is defined, it is then used as a standard value from which an appropriate Activity Unit Rate(AUR) can be determined. A proto-type fuzzy rule based system called 'Fuzzy Activity Unit Rate Analyser(FAURA)' was developed to formalise a systematic framework for the QF quantification process in determining the most likely activity duration/cost. The compatibility measurement method proposed by Nafarieh and Keller has been applied as an inference strategy for FAURA. A computer program was developed to implement FAURA using Turbo Prolog. FAURA was tested and analysed by using a hypothetical bricklayer's activity in conjunction with five major QF as the input variables. The results produced by FAURA iii show that it can be applied usefully to overcome many of the problems encountered in the QF quantification process. In addition, the analysis shows that a fuzzy rule base approach provides the means to model and study the variability of AUR. Although the domain problem of this research was in estimation of activity duration/cost, the principles and system presented in this study are not limited to this specific area, and can be applied to a wide range of other disciplines involving uncertainty quantification problems. Further, this research highlights how the existing subjective methods in activity duration/cost estimation can be enhanced by utilising fuzzy set theory and fuzzy logic

Control optimization, stabilization and computer algorithms for space applications

Research of control optimization, stochastic stability, and air traffic control problem

Science as a growing system: A cybernetic essay

This thesis was submitted for the degree of Doctor of Philosophy and awarded by Brunel University.Direct and significant narrations of the Human's past subsume so complex a multitude of problems (historical, anthropological, psychological, epistemological, etc) that, taking exception for some few areas, no formal, quantified and predictive theory of historical reconstitutions (understood in the classical, paradigmatic, sense of physical, quasi-physical or engineering disciplines) has, so far, been constructed. A first step towards overcoming this situation is outlined in the essay. The work is primarily (though not exclusively) devoted to historical/ scientific reconstitutions; special emphasis is laid upon the so called "domain of Natural Science". Throughout it a rather unconventional way of looking upon human's past achievements in that area is proposed, discussed and progressively developed: not as a mere repository of inventions and discoveries (as the usual historical approaches do), not as a simple reproduction of the possible cognitive processes which their authors used' (as the logistic reconstitutions seek) but rather as a cybernetic adaptative learning process (in the sense of G. PASK and H. VON FOESTER). The use of this approach allows, in particular: - to demonstrate that Science may be globally regarded as a (time-"space") growing system; - to give expression to this growth in terms, of an evolutionary model binding the approaches of PIAGET, WALLON, FREUD, HARTMANN etc (in which epistemological, contextual (social), psychological (conscious, unconscious) affective and cognitive paradigms are involved); - to describe this evolution in formal and quantifiable terms (using for it fuzzy "conditioned" automata theories); - to reproduce it in a special purpose cybernetic device (PASK's THOUGHTSTICKER system); - to perform historical experimentation (varying the value of the parameters, relationships and constraints by means of which the system is described). The essay ends with a practical application: the construction of an entailment-mesh of the First (or Greek) Image of Nature.Financial support was obtained from NATO's Research Grants, INIC (Instituto Nacional de Investigaccao Cientifica) and GULBENKIAN Foundation