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

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

Fuzzy Knowledge Based Reliability Evaluation and Its Application to Power Generating System

PhDThe method of using Fuzzy Sets Theory(FST) and Fuzzy Reasoning(FR) to aid reliability evaluation in a complex and uncertain environment is studied, with special reference to electrical power generating system reliability evaluation. Device(component) reliability prediction contributes significantly to a system's reliability through their ability to identify source and causes of unreliability. The main factors which affect reliability are identified in Reliability Prediction Process(RPP). However, the relation between reliability and each affecting factor is not a necessary and sufficient one. It is difficult to express this kind of relation precisely in terms of quantitative mathematics. It is acknowledged that human experts possesses some special characteristics that enable them to learn and reason in a vague and fuzzy environment based on their experience. Therefore, reliability prediction can be classified as a human engineer oriented decision process. A fuzzy knowledge based reliability prediction framework, in which speciality rather than generality is emphasised, is proposed in the first part of the thesis. For this purpose, various factors affected device reliability are investigated and the knowledge trees for predicting three reliability indices, i.e. failure rate, maintenance time and human error rate are presented. Human experts' empirical and heuristic knowledge are represented by fuzzy linguistic rules and fuzzy compositional rule of inference is employed as inference tool. Two approaches to system reliability evaluation are presented in the second part of this thesis. In first approach, fuzzy arithmetic are conducted as the foundation for system reliability evaluation under the fuzzy envimnment The objective is to extend the underlying fuzzy concept into strict mathematics framework in order to arrive at decision on system adequacy based on imprecise and qualitative information. To achieve this, various reliability indices are modelled as Trapezoidal Fuzzy Numbers(TFN) and are proceeded by extended fuzzy arithmetic operators. In second approach, the knowledge of system reliability evaluation are modelled in the form of fuzzy combination production rules and device combination sequence control algorithm. System reliability are evaluated by using fuzzy inference system. Comparison of two approaches are carried out through case studies. As an application, power generating system reliability adequacy is studied. Under the assumption that both unit reliability data and load data are subjectively estimated, these fuzzy data are modelled as triangular fuzzy numbers, fuzzy capacity outage model and fuzzy load model are developed by using fuzzy arithmetic operations. Power generating system adequacy is evaluated by convoluting fuzzy capacity outage model with fuzzy load model. A fuzzy risk index named "Possibility Of Load Loss" (POLL) is defined based on the concept of fuzzy containment The proposed new index is tested on IEEE Reliability Test System (RTS) and satisfactory results are obtained Finally, the implementation issues of Fuzzy Rule Based Expert System Shell (FRBESS) are reported. The application of ERBESS to device reliability prediction and system reliability evaluation is discussed

Quality control charts under random fuzzy measurements

Includes bibliographical references. .We consider statistical process control charts as tools that statistical process control utilizes for monitoring changes; identifying process variations and their causes in industrial processes (manufacturing processes) and which help manufacturers to take the appropriate action, rectify problems or improve manufacturing processes so as to produce good quality products. As an essential tool, researchers have always paid attention to the development of process control charts. Also, the sample sizes required for establishing control charts are often under discussion depending on the field of study. Of late, the problem of Fuzziness and Randomness often brought into modern manufacturing processes by the shortening product life cycles and diversification (in product designs, raw material supply etc) has compelled researchers to invoke quality control methodologies in their search for high customer satisfaction and better market shares (Guo et al 2006). We herein focus our attention on small sample sizes and focus on the development of quality control charts in terms of the Economic Design of Quality Control Charts; based on credibility measure theory under Random Fuzzy Measurements and Small Sample Asymptotic Distribution Theory. Economic process data will be collected from the study of Duncan (1956) in terms of these new developments as an illustrative example. or/Producer, otherwise they are undertaken with respect to the market as a whole. The techniques used for tackling the complex issues are diverse and wide-ranging as ascertained from the existing literature on the subject. The global ideology focuses on combining two streams of thought: the production optimisation and equilibrium techniques of the old monopolistic, cost-saving industry and; the new dynamic profit-maximising and risk-mitigating competitive industry. Financial engineering in a new and poorly understood market for electrical power must now take place in conjunction with - yet also constrained by - the physical production and distribution of the commodity

Unsupervised and Supervised Fuzzy Neural Network Architecture, with Applications in Machine Vision Fuzzy Object Recognition and Inspection

Mechanical Engineerin

A practical development of multi-attribute decision making using fuzzy set theory

The foundations of multi-attribute utility theory are reviewed and compared with the author's practical experience and other psychological studies of decision-making. The case is presented for a new approach to decision-making, moving away from the strictly numerical techniques. Instead of concentrating on the normative or descriptive aspects of decision-making, themed-problem of decision-making is studied, thereby giving the decision-maker more control over the decision-making process and ensuring a more truly participative approach to design and decision-making. The problem of uncertainty is also tackled by considering it from both the stochastic and fuzzy standpoints. A revised approach to the assessment of uncertainty and its incorporation in the decision-making process is advocated. The theoretical framework behind these ideas is expressed using fuzzy set theory. Previous attempts to apply fuzzy set theory to multi-attribute decision-making are reviewed and criticised for their failure to tackle the basic assumptions of multi-attribute utility theory. A practical methodology for using verbal descriptions is derived, and illustrated with a worked example. A practical description of how to apply the method is included, and the results of some applications are presented

A methodology for the selection of a paradigm of reasoning under uncertainty in expert system development

The aim of this thesis is to develop a methodology for the selection of a paradigm of reasoning under uncertainty for the expert system developer. This is important since practical information on how to select a paradigm of reasoning under uncertainty is not generally available. The thesis explores the role of uncertainty in an expert system and considers the process of reasoning under uncertainty. The possible sources of uncertainty are investigated and prove to be crucial to some aspects of the methodology. A variety of Uncertainty Management Techniques (UMTs) are considered, including numeric, symbolic and hybrid methods. Considerably more information is found in the literature on numeric methods, than the latter two. Methods that have been proposed for comparing UMTs are studied and comparisons reported in the literature are summarised. Again this concentrates on numeric methods, since there is more literature available. The requirements of a methodology for the selection of a UMT are considered. A manual approach to the selection process is developed. The possibility of extending the boundaries of knowledge stored in the expert system by including meta-data to describe the handling of uncertainty in an expert system is then considered. This is followed by suggestions taken from the literature for automating the process of selection. Finally consideration is given to whether the objectives of the research have been met and recommendations are made for the next stage in researching a methodology for the selection of a paradigm of reasoning under uncertainty in expert system development