(R1958) On Deferred Statistical Convergence of Fuzzy Variables

In this paper, within framework credibility theory, we examine several notions of convergence and statistical convergence of fuzzy variable sequences. The convergence of fuzzy variable sequences such as the notion of convergence in credibility, convergence in distribution, convergence in mean, and convergence uniformly virtually certainly via postponed Cesàro mean and a regular matrix are researched using fuzzy variables. We investigate the connections between these concepts. Significant results on deferred statistical convergence for fuzzy variable sequences are thoroughly investigated

Empirical statistical modelling for crop yields predictions: bayesian and uncertainty approaches

Includes bibliographical referencesThis thesis explores uncertainty statistics to model agricultural crop yields, in a situation where there are neither sampling observations nor historical record. The Bayesian approach to a linear regression model is useful for predict ion of crop yield when there are quantity data issue s and the model structure uncertainty and the regression model involves a large number of explanatory variables. Data quantity issues might occur when a farmer is cultivating a new crop variety, moving to a new farming location or when introducing a new farming technology, where the situation may warrant a change in the current farming practice. The first part of this thesis involved the collection of data from experts' domain and the elicitation of the probability distributions. Uncertainty statistics, the foundation of uncertainty theory and the data gathering procedures were discussed in detail. We proposed an estimation procedure for the estimation of uncertainty distributions. The procedure was then implemented on agricultural data to fit some uncertainty distributions to five cereal crop yields. A Delphi method was introduced and used to fit uncertainty distributions for multiple experts' data of sesame seed yield. The thesis defined an uncertainty distance and derived a distance for a difference between two uncertainty distributions. We lastly estimated the distance between a hypothesized distribution and an uncertainty normal distribution. Although, the applicability of uncertainty statistics is limited to one sample model, the approach provides a fast approach to establish a standard for process parameters. Where no sampling observation exists or it is very expensive to acquire, the approach provides an opportunity to engage experts and come up with a model for guiding decision making. In the second part, we fitted a full dataset obtained from an agricultural survey of small-scale farmers to a linear regression model using direct Markov Chain Monte Carlo (MCMC), Bayesian estimation (with uniform prior) and maximum likelihood estimation (MLE) method. The results obtained from the three procedures yielded similar mean estimates, but the credible intervals were found to be narrower in Bayesian estimates than confidence intervals in MLE method. The predictive outcome of the estimated model was then assessed using simulated data for a set of covariates. Furthermore, the dataset was then randomly split into two data sets. The informative prior was later estimated from one-half called the "old data" using Ordinary Least Squares (OLS) method. Three models were then fitted onto the second half called the "new data": General Linear Model (GLM) (M1), Bayesian model with a non-informative prior (M2) and Bayesian model with informative prior (M3). A leave-one-outcross validation (LOOCV) method was used to compare the predictive performance of these models. It was found that the Bayesian models showed better predictive performance than M1. M3 (with a prior) had moderate average Cross Validation (CV) error and Cross Validation (CV) standard error. GLM performed worst with least average CV error and highest (CV) standard error among the models. In Model M3 (expert prior), the predictor variables were found to be significant at 95% credible intervals. In contrast, most variables were not significant under models M1 and M2. Also, The model with informative prior had narrower credible intervals compared to the non-information prior and GLM model. The results indicated that variability and uncertainty in the data was reasonably reduced due to the incorporation of expert prior / information prior. We lastly investigated the residual plots of these models to assess their prediction performance. Bayesian Model Average (BMA) was later introduced to address the issue of model structure uncertainty of a single model. BMA allows the computation of weighted average over possible model combinations of predictors. An approximate AIC weight was then proposed for model selection instead of frequentist alternative hypothesis testing (or models comparison in a set of competing candidate models). The method is flexible and easy to interpret instead of raw AIC or Bayesian information criterion (BIC), which approximates the Bayes factor. Zellner's g-prior was considered appropriate as it has widely been used in linear models. It preserves the correlation structure among predictors in its prior covariance. The method also yields closed-form marginal likelihoods which lead to huge computational savings by avoiding sampling in the parameter space as in BMA. We lastly determined a single optimal model from all possible combination of models and also computed the log-likelihood of each model

Facilitating Brownfield Redevelopment Projects: Evaluation, Negotiation, and Policy

A risky project evaluation technique called the fuzzy real options analysis is developed to evaluate brownfield redevelopment projects. Other decision making techniques, such as multiple criteria analysis and conflict analysis, can be incorporated into fuzzy real options analysis to facilitate negotiations on brownfield redevelopment among decision makers (DMs). The value of managerial flexibility, which is important in negotiations and policy making for brownfield redevelopment, is overlooked when the traditional evaluation method, net present value (NPV), is employed. Findings of this thesis can be used to promote brownfield redevelopment, thereby helping to eliminate environmental threats and enhance regional sustainability. A brownfield is an abandoned or underutilized property that contains, or may contain, pollutants, hazardous substances, or contaminants from previous usage, typically industrial activity. Brownfields often occur when the local economy transits from industrial to service-oriented seeking more profit. Governments actively promote brownfield redevelopment to eliminate public health threats, help economic transition, and enhance sustainability. However, developers are reluctant to participate in brownfield redevelopment because they often regard these projects as unprofitable when using classic evaluation techniques. On the other hand, case studies show that brownfield redevelopment projects can be good business opportunities for developers. An improved evaluation method is developed in order to estimate the value of a brownfield more accurately. The main reason that makes the difference between estimates and ''actual'' values lies in the failure of the deterministic project evaluation tool to price the value of uncertainty, which leads to efforts to enhance the decision making under uncertainty. Real options modelling, which extends the ability of option pricing models in real asset evaluation, is employed in risky project evaluation because of its capacity to handle uncertainties. However, brownfield redevelopment projects contain uncertain factors that have no market price, thus violating the assumption of option pricing models for which all risks have been reflected in the market. This problem, called private risk, is addressed by incorporating fuzzy numbers into real options in this thesis, which can be called fuzzy real options. Fuzzy real options are shown to generalize the original model to deal with additional kinds of uncertainties, making them more suitable for project evaluation. A numerical technique based on hybrid variables is developed to price fuzzy real options. We proposed an extension of Least Squares Monte-Carlo simulation (LSM) that produces numerical evaluations of options. A major advantage of this methodology lies in its ability to produce results regardless of whether or not an analytic solution exists. Tests show that the generalized LSM produces similar results to the analytic valuation of fuzzy real options, when this is possible. To facilitate parameter estimation for the fuzzy real options model, another numerical method is proposed to represent the likelihood of contamination of a brownfield using fuzzy boundaries. Linguistic quantifiers and ordered weighted averaging (OWA) techniques are utilized to determine the likelihood of pollution at sample locations based on multiple environmental indicators, acting as a fuzzy deduction rule to calculate the triangle membership functions of the fuzzy parameters. Risk preferences of DMs are expressed as different ''ORness'' levels of OWA operators, which affect likelihood estimates. When the fuzzy boundaries of a brownfield are generated by interpolation of sample points, the parameters of fuzzy real options, drift rate and volatility, can be calculated as fuzzy numbers. Hence, this proposed method can act as an intermediary between DMs and the fuzzy real options models, making this model much easier to apply. The values of DMs to a brownfield can be input to the graph model for conflict resolution (GMCR) to identify possible resolutions during brownfield redevelopment negotiation among all possible states, or combinations of DMs' choices. Major redevelopment policies are studied using a brownfield redevelopment case, Ralgreen Community in Kitchener, Ontario, Canada. The fuzzy preference framework and probability-based comparison method to rank fuzzy variables are employed to integrate fuzzy real options and GMCR. Insights into this conflict and general policy suggestions are provided. A potential negotiation support system (NSS) implementing these numerical methods is discussed in the context of negotiating brownfield redevelopment projects. The NSS combines the computational modules, decision support system (DSS) prototypes, and geographic information systems (GIS), and message systems. A public-private partnership (PPP) will be enhanced through information sharing, scenario generation, and conflict analysis provided by the NSS, encouraging more efficient brownfield redevelopment and leading to greater regional sustainability. The integrated usage of fuzzy real options, OWA, and GMCR takes advantage of fuzziness and randomness, making better evaluation technique available in a multiple DMs negotiation setting. Decision techniques expand their range from decision analysis, multiple criteria analysis, to a game-theoretic approach, contributing to a big picture on decision making under uncertainty. When these methods are used to study brownfield redevelopment, we found that creating better business opportunities, such as allowing land use change to raise net income, are more important in determining equilibria than remediation cost refunding. Better redevelopment policies can be proposed to aid negotiations among stakeholders