Real-world problems especially the ones that involve natural systems are complex and they are composed of many non-deterministic components. Uncertainties associated with these non-deterministic components may originate from randomness or from imprecision due to lack of information. Until recently, uncertainty, regardless of its nature or source has been treated by probability concepts. However, uncertainties associated with real-world systems are not limited to randomness. Imprecise, vague or incomplete information may better be represented by other mathematical tools, such as fuzzy set theory, possibility theory, belief functions, etc. New approaches which allow utilization of probability theory in combination with these new mathematical tools found applications in various engineering fields. Uncertainty modeling in human health risk assessment and groundwater resources management areas are investigated in this thesis. In the first part of this thesis two new approaches which utilize both probability theory and fuzzy set theory concepts to treat parameter uncertainties in carcinogenic risk assessment are proposed. As a result of these approaches fuzzy health risks are generated. For the fuzzy risk to be useful for practical purposes its acceptability with respect to compliance guideline has to be evaluated. A new fuzzy measure, the risk tolerance measure, is proposed for this purpose. The risk tolerance measure is a weighed average of the possibility and the necessity measures which are currently used for decision making purposes. In the second part of this thesis two decision making frameworks are proposed to determine the best groundwater resources management strategy in the Savannah region, Georgia. Groundwater resources management problems, especially ones in the coastal areas are complex and require treatment of various uncertain inputs. The first decision making framework proposed in this study is composed of a coupled simulation-optimization model followed by a fuzzy multi-objective decision making approach while the second framework includes a groundwater flow model in which the parameters of the flow equation are characterized by fuzzy numbers and a decision making approach which utilizes the risk tolerance measure proposed in the first part of this thesis.

The research focuses on the application of site selection for cage aquaculture in Taiwan by developing the site evaluation DSS (Decision Support System). The modeling aspect of the system belongs to the domain of multi-criteria decision theories, which AHP (Analytic Hierarchy Process) and Fuzzy Set theory were used. Two case studies based on real world and hypothetical data were conducted to verify the integrity of the system. According to the literature review and the interview with several domain experts, various impact factors were identified first. The corresponding weights of each factor were then decided by analyzing the questionnaires designed based on the concept of AHP. The following work was to evaluate those impact factors based on the experience of domain experts using some appropriate approaches. To represent the domain knowledge, it is appropriate to use rule based inference system. Besides, fuzzy set theory was chosen to describe the antecedent and consequence of the rule base due to the considerations of uncertainty from human experts and ocean field data. Several related mythologies derived from the fuzzy set theory were used, such as the operation of fuzzy composition, determination of suitable membership function, fuzzy relationship matrix, fuzzy inference, defuzzification, and fuzzy pattern classification. All impact factors were categorized into three different types of membership functions that were designed specifically for the site selection of cage aquaculture. The consequence in the rule base, which is the site suitability, was also represented as the unique membership function. To calculate the fuzzy relationship matrix, the current research found that the operation of ¡§algebraic product and bounder sum¡¨ would produce better results than the commonly used ¡§max-min¡¨ operation. Each impact factor would have the associated fuzzy relationship matrix derived from the rule base. The site suitability in term of a fuzzy set can then be inferred by the fuzzy composition of current situation of the factor and the relationship matrix. By multiplying the AHP weight and the fuzzy suitability, the final site suitability index, taking all the impact factors into consideration, can therefore be derived. The real data in Feng-Gang, located in the southern Taiwan, were collected and evaluated using the site selection DSS. The results show Feng-Gang is suitable for the development of cage aquaculture, which is validated by the current prosperous business locally in cage aquaculture. As for the evaluation of multiple sites, 18 hypothetical sites near shore around Taiwan were chosen to calculate the corresponding suitability indexes, which were then be partitioned into several groups using the fuzzy pattern classification. Based on the results, the sites that were classified in the same group have similar cultivation conditions, which also proves the applicability of the site evaluation DSS.

By means of fuzzy set theory as well as Takagi-Sugeno and Mamdani fuzzy controller, this paper presents the investigation of a Resort Management System implemented by a combination of a T-S model and a Mamdani model. It demonstrates the procedure of the specific premise parameters identification and consequence parameters identification performed by regression knowledge in the T-S model, and the process of the fuzzification, the rule base creation and the defuzzification with COG technique in the Mamdani model. Therefore, an aggregation between T-S controller and Mamdani controller applied in the field of management by a novel angle is illustrated, which, as a result, devotes an improved management system that shares great convenience in the control process when combined with mathematics. Moreover, a modification of the conventional Takagi-Sugeno and Mamdani controller is demonstrated in conjunction with fuzzy operations t-norms and OWA by adjusting the -value, which is used in the calculation of final outputs in the T-S model and the computation of rule consequences in the Mamdani model. The algebraic intersection, bounded intersection as well as the -parameter t-norm are the t-norms which are going to be introduced. Besides, we have tested that t-norms generate the same alpha values when the membership degrees meet the boundary with the value of 1 or 0 while OWA can still yield a well-balanced result different from the one computing by minimum operation. Nevertheless both t-norms and OWA are able to shift the alpha-value in a well-adjusted way when the membership degrees lie in the interval [0,1]. A tendency has been shown that alpha-value tends to decrease by means of t-norms and OWA operations and consequently, the final outputs appear to be reduced.

This dissertation provides experimental evidence for the validity of an intonational phonology. The widely used Autosegmental-Metrical theory con- tends that the phonological structure of intonation can be expressed with two tonal targets (L/H tones and derivatives) and retrieved from its phonetic im- plementations. However, it has not been specifically demonstrated so far in a systematic way. This dissertation argues that this view on intonational phonol- ogy considers the phonetic forms of intonation as instances of phonologically structured intonational units forming functionally discrete categories (tones and derivatives). The model of Pattern Recognition for Intonation (PRInt) applies the concepts of categorization (vagueness, prototype, degrees of typicality) to in- tonation in order to abstract the phonological structure of intonational cate- gories from the ranking, by degree of typicality, of their variations in phonetic implementation. First, instances belonging to an intonation category are collected. Sec- ond, a pattern recognition module, relying on the 4-layer structure protocol, extracts a feature vector from the phonetic data of each instance: a sequence of structurally organized tones (L/H tones and derivatives). Third, a fuzzy classifier, using two functions (frequency and similar- ity), organizes the data from the feature vectors of all instances by degree of typicality (grade of membership of values in multisets) and generates the phonological structure of the intonation category, the prototypical pattern, ex- tracted from all instances, and that subsumes them all. It also re-creates the phonetic implementations of the phonological structure but with their features ranked by degree of typicality. This allows the model to distinguish phono- logically distinct structures from phonetic variations of the same phonological structure. The model successfully extracted the phonological intonation structure associated to three modalities of closed questions in French: neutral, doubt- ful, and surprised. It found that neutral and doubtful closed questions are phonologically distinct while surprise is a phonetic allocontour of the neutral modality, in line with prior characterizations of these patterns. It demon- strated that a bi-tonal phonological structure of intonation can be retrieved from phonetic variations. A versatile modeling tool, PRInt will be developed to use its acquired knowledge to evaluate the categorical status of novel instances and to extract multiple phonological units from mixed corpora. / text

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Ease of use differentiates products in a highly competitive market place. It also brings an added value that culminates in a higher degree of customer satisfaction, repeated business, increased sales, and higher revenue. User-centered design is a strategic asset that companies can use to improve their customer relationships by learning more about their customers, and increase their sales. In today's economy, the measurement of intangible assets such as user experience has become a major need for industries because of the relationship between user-centered design and organizational benefits such as customer loyalty. As companies realize that the inclusion of user-centered design concepts in product or system design are a key component of attracting and maintaining customers, as well as increasing revenue, the need for quantitative methods to describe these benefits has become more urgent. The goal of this research is to develop a methodology to characterize user-centered design features, customer benefits and organizational benefits resulting from developing products using user-centered design principles through the use of an integrated framework of critical factors. Therefore, this research focuses on the identification of the most significant variables required to assess and measure the degree of user-centered design (UCD) characteristics included in the various aspects of product development such as physical design features, cognitive design attributes, industrial design aspects and user experience design considerations. Also this research focuses on the development of assessment tools for developers to use when evaluating the incorporation of user-centered design features in the creation of products and systems. In addition, a mathematical model to quantify the inclusion of UCD factors considered in the design of a product and systems is presented in this research. The results obtained using the assessment tools and the mathematical model can be employed to assess the customer benefits and organizational benefits resulting from including user-centered design features in the creation of products and systems. Overall, organizational benefits such as customer loyalty, company image, and profitability are expected to be impacted by the company's capability to meet or exceed stated design claims and performance consistency while maintaining aesthetic appeal, long product life, and product usefulness. The successful completion of this research has produced many beneficial research findings. For example, it has helped characterize and develop descriptors for estimating critical quantitative and qualitative components, sub-components, and factors influencing user-centered design that are related to customer and organizational benefits through the use of fuzzy set modeling. In addition, the development of specific tools, methods, and techniques for evaluating and quantifying UCD components resulted from this study.

The objective of the research was to develop and validate a multifaceted model such as a fuzzy Analytical Hierarchy Process (AHP) model that considers both qualitative and quantitative elements with relative significance in assessing the likelihood of falls and aid in the design of NASA Ground Support Operations in aerospace environments. The model represented linguistic variables that quantified significant risk factor levels. Multiple risk factors that contribute to falls in NASA Ground Support Operations are task related, human/personal, environmental, and organizational. Six subject matter experts were asked to participate in a voting system involving a survey where they judge risk factors using the fundamental pairwise comparison scale. The results were analyzed and synthesize using Expert Choice Software, which produced the relative weights for the risk factors. The following are relative weights for these risk factors: Task Related (0.314), Human/Personal (0.307), Environmental (0.248), and Organizational (0.130). The overall inconsistency ratio for all risk factors was 0.07, which indicates the model results were acceptable. The results show that task related risk factors are the highest cause for falls and the organizational risk are the lowest cause for falls in NASA Ground Support Operations. The multiple risk factors weights were validated by having two teams of subject matter experts create priority vectors separately and confirm the weights are valid. The fuzzy AHP model usability was utilizing fifteen subjects in a repeated measures analysis. The subjects were asked to evaluate three scenarios in NASA KSC Ground Support Operations regarding various case studies and historical data. The three scenarios were Shuttle Landing Facility (SLF), Launch Complex Payloads (LCP), and Vehicle Assembly Building (VAB). The Kendall Coefficient of Concordance for assessment agreement between and within the subjects was 1.00. Therefore, the appraisers are applying essentially the same standard when evaluating the scenarios. In addition, a NASA subject matter expert was requested to evaluate the three scenarios also. The predicted value was compared to accepted value. The results from the subject matter expert for the model usability confirmed that the predicted value and accepted value for the likelihood rating were similar. The percentage error for the three scenarios was 0%, 33%, 0% respectively. Multiple descriptive statistics for a 95% confidence interval and t-test are the following: coefficient of variation (21.36), variance (0.251), mean (2.34), and standard deviation (0.501). Model validation was the guarantee of agreement with the NASA standard. Model validation process was partitioned into three components: reliability, objectivity, and consistency. The model was validated by comparing the fuzzy AHP model to NASA accepted model. The results indicate there was minimal variability with fuzzy AHP modeling. As a result, the fuzzy AHP model is confirmed valid. Future research includes developing fall protection guidelines.

Yes / Quantitative risk assessment (QRA) approaches systematically evaluate the likelihood, impacts, and risk of adverse events. QRA using fault tree analysis (FTA) is based on the assumptions that failure events have crisp probabilities and they are statistically independent. The crisp probabilities of the events are often absent, which leads to data uncertainty. However, the independence assumption leads to model uncertainty. Experts’ knowledge can be utilized to obtain unknown failure data; however, this process itself is subject to different issues such as imprecision, incompleteness, and lack of consensus. For this reason, to minimize the overall uncertainty in QRA, in addition to addressing the uncertainties in the knowledge, it is equally important to combine the opinions of multiple experts and update prior beliefs based on new evidence. In this article, a novel methodology is proposed for QRA by combining fuzzy set theory and evidence theory with Bayesian networks to describe the uncertainties, aggregate experts’ opinions, and update prior probabilities when new evidences become available. Additionally, sensitivity analysis is performed to identify the most critical events in the FTA. The effectiveness of the proposed approach has been demonstrated via application to a practical system. / The research of Sohag Kabir was partly funded by the DEIS project (Grant Agreement 732242).

Yes / Fuzzy data-driven reliability analysis has been used in different safety-critical domains for risk assessment and decision-making where precise failure data is non-existent. Expert judgements and fuzzy set theory have been combined with different variants of fault trees as part of fuzzy data-driven reliability analysis studies. In such fuzzy fault tree analyses, different people represented failure data using different membership functions for the fuzzy set, and different parameters were set differently in the expert opinion elicitation process. Due to the availability of a wide variety of options, it is possible to obtain different outcomes when choosing one option over another. This article performed an analysis in the context of fuzzy data-based temporal fault tree analysis to investigate the effect of choosing different membership functions on the estimated system reliability and criticality ranking of different failure events. Moreover, the effect of using different values for the relaxation factor, a parameter set during the expert elicitation process, was studied on the system reliability and criticality evaluation. The experiments on the fuel distribution system case study show system reliability did not vary when triangular and trapezoidal fuzzy numbers were used with the same upper and lower bounds. However, it was seen that the criticality rankings of a couple of events were changed due to choosing different membership functions and different values of relaxation factor

Yes / Risk assessment methods have been widely used in various industries, and they play a significant role in improving the safety performance of systems. However, the outcomes of risk assessment approaches are subject to uncertainty and ambiguity due to the complexity and variability of system behaviour, scarcity of quantitative data about different system parameters, and human involvement in the analysis, operation, and decision-making processes. The implications for improving system safety are slowly being recognised; however, research on uncertainty handling during both qualitative and quantitative risk assessment procedures is a growing field. This paper presents a review of the state of the art in this field, focusing on uncertainty handling in fault tree analysis (FTA) based risk assessment. Theoretical contributions, aleatory uncertainty, epistemic uncertainty, and integration of both epistemic and aleatory uncertainty handling in the scientific and technical literature are carefully reviewed. The emphasis is on highlighting how assessors can handle uncertainty based on the available evidence as an input to FTA.