Fuzzy Bayesian inference

Bayesian methods provide formalism for reasoning about partial beliefs under conditions of uncertainty. Given a set of exhaustive and mutually exclusive hypotheses, one can compute the probability of a hypothesis for a given evidence using the Bayesian inversion formula. In Bayesian's inference, the evidence could be a single atomic proposition or multi-valued one. For the multi-valued evidence, these values could be discrete, continuous, or fuzzy. For the continuous-valued evidence, the density functions used in the Bayesian inference are difficult to be determined in many practical situations. Complicated laboratory testing and advance statistical techniques are required to estimate the parameters of the assumed type of distribution. Using the proposed fuzzy Bayesian approach, a formulation is derived to estimate the density function from the conditional probabilities of the fuzzy-supported values. It avoids the complicated testing and analysis, and it does not require the assumption of a particular type of distribution. The estimated density function in our approach is proved to conform to two axioms in the theorem of probability. Example is provided in the paper.published_or_final_versio

After the Twitter X-pocalypse: Approaches to Characterising Human Behaviour in Agent-based Models and Beyond

Characterising human behaviour is challenging, and datasets about people often suffer from issues of misrepresentation. To account for misrepresentation, researchers have turned to data synthesis. Here, we implement a straightforward data synthesis approach that does not rely upon knowledge of dataset uncertainty and use it to parametrise predictors used in an agent-based model (ABM) to estimate visits by people to greenspaces in Glasgow. The predicted visits follow expected patterns, with more visits on weekends, during daylight, and to popular tourist destinations. The approach is easy to implement and allows researchers to combine datasets of varying veracity to predict human behaviour

Fuzzy Bayesian inference for mapping vague and place-based regions:a case study of sectarian territory

The problem of mapping regions with socially-derived boundaries has been a topic of discussion in the GIS literature for many years. Fuzzy approaches have frequently been suggested as solutions, but none have been adopted. This is likely due to difficulties associated with determining suitable membership functions, which are often as arbitrary as the crisp boundaries that they seek to replace. This paper presents a novel approach to fuzzy geographical modelling that replaces the membership function with a possibility distribution that is estimated using Bayesian inference. In this method, data from multiple sources are combined to estimate the degree to which a given location is a member of a given set and the level of uncertainty associated with that estimate. The Fuzzy Bayesian Inference approach is demonstrated through a case study in which census data are combined with perceptual and behavioural evidence to model the territory of two segregated groups (Catholics and Protestants) in Belfast, Northern Ireland, UK. This novel method provides a robust empirical basis for the use of fuzzy models in GIS, and therefore has applications for mapping a range of socially-derived and otherwise vague boundaries

Development of Fuzzy Hybrid Approaches to Project Delivery Method Selection in Highway Construction

Selection of project delivery methods is a success factor in delivering highway construction projects because it has a substantial impact on the project performance, such as cost, time, and quality. Project delivery decision-making processes have been heavily relied on experts’ opinions and subjective judgements of professionals to evaluate quantitative and qualitative decision variables. Although current quantitative and probabilistic methods provide a robust means to analyze quantitative variables, they are not ideally suited for treating uncertainties encountered in qualitative variables. Fuzzy set theory is a mathematical approach that can accommodate a combination of quantitative and qualitative variables. This dissertation aimed at investigating the applications of fuzzy set theory and fuzzy logic to support decision-making processes in project delivery method selections. Using an empirical dataset of 254 completed highway construction projects, three fuzzy-based applications, including fuzzy cluster analysis, fuzzy pattern recognition, and fuzzy Bayesian inference system were developed, trained, and tested. As a result, fuzzy cluster analysis was used to establish seven common project clusters that share high similarities in project characteristics, project complexity, delivery risks, cost growth, and project delivery methods. Fuzzy pattern recognition was used to develop a fuzzy rule-based inference system based on the seven identified project clusters to help recognize an appropriate project delivery method associated with potential cost growth for new highway projects. Fuzzy Bayesian networks were used to develop the theoretical framework of fuzzy Bayesian inference system which is able to depict the causal relationships between project characteristics, project complexity, delivery risks, and project delivery methods. The flexibility of fuzzy membership functions in the developed applications helps leverage the evaluation of a combination of quantitative and qualitative variables in highway project delivery method selection. In addition, these data-driven fuzzy applications also allow for multiple decision scenarios based on the decision maker’s judgements of delivery risks and project complexity. This dissertation contributes to the body of knowledge by demonstrating quantitative approaches derived from fuzzy set theory and fuzzy logic to support the selection of project delivery methods in highway construction. Additionally, the results from the developed fuzzy-based applications also provide insights regarding cost performance comparisons between project delivery methods. This study may assist highway agencies in making project delivery decisions based on project attributes, historical data and their relevant experience

"The Great Blackbury Pie" ~ or ~ Focal Area Bias in Geographically Weighted Analysis

Focal and geographically weighted analyses are commonplace in GIS applications across many fields and disciplines. However, where such analyses are based on ‘dense’ datasets (e.g., a raster surface), they can suffer from an unintended bias towards the periphery of the focal zone (neighbourhood), which (counterintuitively) is exacerbated by the use of distance weighting functions. This paper serves to characterise this problem, which we call focal area bias (FAB), present a proposed correction, and point to extensive simulation-based analysis, which demonstrates both the impact that this effect can have on analyses and the efficacy of our proposed solution

Data Fusion through Fuzzy-Bayesian Networks for Belief Generation in Cognitive Agents

Situation Awareness provides a theory for agents decision making to allow perception and comprehension of his environment. However, the transformation of the sensory stimulus in beliefs to favor the BDI reasoning cycle is still an unexplored subject. Autonomous agent projects often require the use of multiple sensors to capture environmental aspects. The natural variability of the physical world and the imprecision contained in linguistic concepts used by humans mean that sensory data contain different types of uncertainty in their measurements. Thus, to obtain the Situational Awareness for Agents with physical sensors, it is necessary to define a data fusion process to perform uncertainty treatment. This paper presents a model to beliefs generation using fuzzy-bayesian inference. An example in robotics navigation and location is used to illustrate the proposal

Fuzzy Bayesian inference for mapping vague and place-based regions: a case study of sectarian territory

The problem of mapping regions with socially-derived boundaries has been a topic of discussion in the GIS literature for many years. Fuzzy approaches have frequently been suggested as solutions, but none have been adopted. This is likely due to difficulties associated with determining suitable membership functions, which are often as arbitrary as the crisp boundaries that they seek to replace. This paper presents a novel approach to fuzzy geographical modelling that replaces the membership function with a possibility distribution that is estimated using Bayesian inference. In this method, data from multiple sources are combined to estimate the degree to which a given location is a member of a given set and the level of uncertainty associated with that estimate. The Fuzzy Bayesian Inference approach is demonstrated through a case study in which census data are combined with perceptual and behavioural evidence to model the territory of two segregated groups (Catholics and Protestants) in Belfast, Northern Ireland, UK. This novel method provides a robust empirical basis for the use of fuzzy models in GIS, and therefore has applications for mapping a range of socially-derived and otherwise vague boundaries

Predicting combined sewer overflows chamber depth using artificial neural networks with rainfall radar data

Combined sewer overflows (CSOs) represent a common feature in combined urban drainage systems and are used to discharge excess water to the environment during heavy storms. To better understand the performance of CSOs, the UK water industry has installed a large number of monitoring systems that provide data for these assets. This paper presents research into the prediction of the hydraulic performance of CSOs using artificial neural networks (ANN) as an alternative to hydraulic models. Previous work has explored using an ANN model for the prediction of chamber depth using time series for depth and rain gauge data. Rainfall intensity data that can be provided by rainfall radar devices can be used to improve on this approach. Results are presented using real data from a CSO for a catchment in the North of England, UK. An ANN model trained with the pseudo-inverse rule was shown to be capable of providing prediction of CSO depth with less than 5% error for predictions more than one hour ahead for unseen data. Such predictive approaches are important to the future management of combined sewer systems