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The purpose of this paper is to propose a unified optimization design method and apply it to handle the brake squeal instability involving various uncertainties in a unified framework.

Fuzzy random variables are taken as equivalent variables of conventional uncertain variables, and a unified response analysis method is first derived based on level-cut technique, Taylor expansion and central difference scheme. Next, a unified reliability analysis method is developed by integrating the unified response analysis and fuzzy possibility theory. Finally, based on the unified reliability analysis method, a unified reliability-based optimization model is established, which is capable of optimizing uncertain responses in a unified way for different uncertainty cases.

The proposed method is extended to perform squeal instability analysis and optimization involving various uncertainties. Numerical examples under eight uncertainty cases are provided and the results demonstrate the effectiveness of the proposed method.

Most of the existing methods of uncertainty analysis and optimization are merely effective in tackling one uncertainty case. The proposed method is able to handle the uncertain problems involving various types of uncertainties in a unified way.

This paper proposes a fuzzy random multi-objective portfolio model with different entropy measures and designs a hybrid algorithm to solve the proposed model.

Because random uncertainty and fuzzy uncertainty are often combined in a real-world setting, the security returns are considered as fuzzy random numbers. In the model, the authors also consider the effects of different entropy measures, including Yager's entropy, Shannon's entropy and min-max entropy. During the process of solving the model, the authors use a ranking method to convert the expected return into a crisp number. To find the optimal solution efficiently, a fuzzy programming technique based on artificial bee colony (ABC) algorithm is also proposed.

(1) The return of optimal portfolio increases while the level of investor risk aversion increases. (2) The difference of the investment weights of the optimal portfolio obtained with Yager's entropy are much smaller than that of the min–max entropy. (3) The performance of the ABC algorithm on solving the proposed model is superior than other intelligent algorithms such as the genetic algorithm, differential evolution and particle swarm optimization.

To the best of the authors' knowledge, no effect has been made to consider a fuzzy random portfolio model with different entropy measures. Thus, the novelty of the research is constructing a fuzzy random multi-objective portfolio model with different entropy measures and designing a hybrid fuzzy programming-ABC algorithm to solve the proposed model.

Due to the increasing size and complexity of construction projects, construction engineering and management involves the coordination of many complex and dynamic processes and relies on the analysis of uncertain, imprecise and incomplete information, including subjective and linguistically expressed information. Various modelling and computing techniques have been used by construction researchers and applied to practical construction problems in order to overcome these challenges, including fuzzy hybrid techniques. Fuzzy hybrid techniques combine the human-like reasoning capabilities of fuzzy logic with the capabilities of other techniques, such as optimization, machine learning, multi-criteria decision-making (MCDM) and simulation, to capitalise on their strengths and overcome their limitations. Based on a review of construction literature, this chapter identifies the most common types of fuzzy hybrid techniques applied to construction problems and reviews selected papers in each category of fuzzy hybrid technique to illustrate their capabilities for addressing construction challenges. Finally, this chapter discusses areas for future development of fuzzy hybrid techniques that will increase their capabilities for solving construction-related problems. The contributions of this chapter are threefold: (1) the limitations of some standard techniques for solving construction problems are discussed, as are the ways that fuzzy methods have been hybridized with these techniques in order to address their limitations; (2) a review of existing applications of fuzzy hybrid techniques in construction is provided in order to illustrate the capabilities of these techniques for solving a variety of construction problems and (3) potential improvements in each category of fuzzy hybrid technique in construction are provided, as areas for future research.

This paper aims to cover the development of a methodology for hybrid fuzzy Monte Carlo agent-based simulation (FMCABS) and its implementation on a parametric study of construction crew performance.

The developed methodology uses fuzzy logic, Monte Carlo simulation and agent-based modeling to simulate the behavior of construction crews and predict their performance. Both random and subjective uncertainties are considered in model variables.

The developed methodology was implemented on a real case involving the parametric study of construction crew performance to assess its applicability and suitability for this context.

This parametric study demonstrates a practical application for the hybrid FMCABS methodology. Though findings from this study are limited to the context of construction crew motivation and performance, the applicability of the developed methodology extends beyond the construction domain.

This paper will help construction practitioners to predict and improve crew performance by taking into account both random and subjective uncertainties.

This paper will advance construction modeling by allowing for the assessment of social interactions among crews and their effects on crew performance.

The developed hybrid FMCABS methodology represents an original contribution, as it allows agent-based models to simultaneously process all types of variables (i.e. deterministic, random and subjective) in the same simulation experiment while accounting for interactions among different agents. In addition, the developed methodology is implemented in a novel and extensive parametric study of construction crew performance.

The purpose of this research is to introduce a class of FRC (fuzzy random coefficient) volatility models and to study their moment properties. Fuzzy option values and the superiority of fuzzy forecasts over minimum mean‐square forecasts are also discussed in some detail.

Fuzzy components are assumed to be triangular fuzzy numbers. Buckley's data‐driven method is used to determine the spread of the triangular fuzzy numbers by using standard errors of the estimated parameters.

The fuzzy kurtosis of various volatility models is obtained in terms of fuzzy coefficients. Fuzzy option values and fuzzy forecasts are illustrated with examples. Fuzzy forecast intervals are narrower than the corresponding MMSE forecast intervals.

This paper will be of value to econometricians and to anyone with an interest in financial volatility models.

Coal and power generation are related upstream and downstream industries. Coal price marketization and electricity price regulation have caused the price of coal to be sensitive to the benefits of generators. The paper aims to discuss these issues.

As a financial tool, contracts for differences can both help balance interests and reduce risks caused by spot price fluctuation. This thesis regards coal demand as a triangular fuzzy stochastic variable while directing a levelling consideration towards risk returns for coal and power enterprises that are involved in coal generation contracts for differences. Risk and benefit measurement models were established between coal suppliers and power generators, and risk and benefit balance optimization models for contract negotiation were constructed.

A numerical example showed that the above models can be effectively used to avoid the risks of coal-electricity parties.

This thesis regards coal demand as a triangular fuzzy random variable while directing a levelling consideration towards the risk return to coal and power enterprises that are involved with coal generation contracts for differences. The features of this thesis are the following: demand information is regarded as a fuzzy random variable instead of a random variable. With historical data, sales experience and increasingly clear macro-economic conditions, coal and power enterprises are able to make a fuzzy decision – to a certain extent – when the transaction approaches. Accurate market information enables the supply chain system to satisfy the clients’ needs better, improve the profit level or avoid severe financial damages; by developing a feasible set of contracts for different parameters, it is possible to estimate whether the price difference enables supply chain coordination, requires changes or gives accounts to all involved parties of the supply chain; and without the assumption that the traditional M-V rule is unfavourable to decision makers, this thesis proposes the prospect M-V rule, which involves decision makers’ projections of future coal generation prices and enables wide applicability of the response method to contracts for differences.

In the present literature on fuzzy sets and fuzzy information, there is much confusion between entropies of fuzzy sets and fuzzy sets of entropies. After a thorough critical review of this question, proposes a unified approach based on the theory of deterministic functions. One must carefully distinguish between index of fuzziness, uncertainty of fuzziness and uncertainty of randomness on the one hand; and uncertainty of fuzzy sets and uncertainty of possibility on the other hand. This new framework could provide new approaches to management of uncertainty originating from both probability and possibility distributions.

The purpose of this paper is to explore new ways and lay a solid foundation to solve the problem of reliability growth analysis of major aerospace equipment with various uncertainty data through propose new concepts of general uncertainty data (GUD) and general uncertainty variable (GUV) and build the operation system of GUVs.

The characteristics of reliability growth data of major aerospace equipment and the limitations of current reliability growth models have been analyzed at first. The most commonly used uncertainty system analysis methods of probability statistics, fuzzy mathematics, grey system theory and rough set theory have been introduced. The concepts of GUD and GUV for reliability growth data analysis of major aerospace equipment are proposed. The simplified form of GUV based on the “kernel” and the degree of uncertainty of GUV is defined. Then an operation system of GUVs is built.

(1) The concept of GUD; (2) the concept of GUV; (3) The novel operation rules of GUVs with simplified form.

The method exposed in this paper can be used to integrate complex reliability growth data of major aerospace equipment. The reliability growth models based on GUV can be built for reliability growth evaluation and forecasting of major aerospace equipment in practice. The reliability evaluation example of a solid rocket motor shows that the concept and idea proposed in this paper are feasible. The research of this paper opens up a new way for the analysis of complex uncertainty data of reliability growth of major aerospace equipment. Moreover, the operation of GUVs could be extended to the case of algebraic equation, differential equation and matrix which including GUVs.

The new concepts of GUD and GUV are given for the first time. The novel operation rules of GUVs with simplified form were constructed.

With respect to multiple attribute group decision-making (MAGDM) in which the assessment values of alternatives are denoted by normal discrete fuzzy variables (NDFVs) and the weight information of attributes is incompletely known, this paper aims to develop a novel fuzzy stochastic MAGDM method based on credibility theory and fuzzy stochastic dominance, and then applies the proposed method for selecting the most desirable investment alternative under uncertain environment.

First, by aggregating the membership degrees of an alternative to a scale provided by all decision-makers into a triangular fuzzy number, the credibility degree and expect the value of a triangular fuzzy number are calculated to construct the group fuzzy stochastic decision matrix. Second, based on determining the credibility distribution functions of NDFVs, the fuzzy stochastic dominance relations between alternatives on each attribute are obtained and the fuzzy stochastic dominance degree matrices are constructed by calculating the dominance degrees that one alternative dominates another on each attribute. Subsequently, calculating the overall fuzzy stochastic dominance degrees of an alternative on each attribute, a single objective non-linear optimization model is established to determine the weights of attributes by maximizing the relative closeness coefficients of all alternatives to positive ideal solution. If the information about attribute weights is completely unknown, the idea of maximizing deviation is used to determine the weights of attributes. Finally, the ranking order of alternatives is determined according to the descending order of corresponding relative closeness coefficients and the best alternative is determined.

This paper proposes a novel fuzzy stochastic MAGDM method based on credibility theory and fuzzy stochastic dominance, and a case study of investment alternative selection problem is provided to illustrate the applicability and sensitivity of the proposed method and its effectiveness is demonstrated by comparison analysis with the proposed method with the existing fuzzy stochastic MAGDM method. The result shows that the proposed method is useful to solve the MAGDM problems in which the assessment values of alternatives are denoted by NDFVs and the weight information of attributes is incompletely known.

The contributions of this paper are that to describe the dominance relations between fuzzy variables reasonably and quantitatively, the fuzzy stochastic dominance relations between any two fuzzy variables are redefined and the concept of fuzzy stochastic dominance degree is proposed to measure the dominance degree that one fuzzy variable dominate another; Based on credibility theory and fuzzy stochastic dominance, a novel fuzzy stochastic MAGDM method is proposed to solve MAGDM problems in which the assessment values of alternatives are denoted by NDFVs and the weight information of attributes is incompletely known. The proposed method has a clear logic, which not only can enrich and develop the theories and methods of MAGDM but also provides decision-makers a novel method for solving fuzzy stochastic MAGDM problems.

The purpose of this paper is to present a fault tree (FT)-based approach for quantitative risk analysis in the construction industry that can take into account both objective and subjective uncertainties.

In this research, the identified basic events (BEs) are first categorized based on the availability of historical data into probabilistic and possibilistic. The probabilistic and possibilistic events are represented by probability distributions and fuzzy numbers, respectively. Hybrid uncertainty analysis is then performed through a combination of Monte Carlo simulation and fuzzy set theory. The probability of occurrence of the top event is finally calculated using the proposed FT-based hybrid uncertainty analysis method.

The efficiency of the proposed method is demonstrated by implementing in a real steel structure project. A quantitative risk assessment is performed for weld cracks, taking into account of both types of uncertainties. An importance analysis is finally performed to evaluate the contribution of each BE to the probability of occurrence of weld cracks and adopt appropriate response strategies.

In this research, the impact of objective (aleatory) dependence between the occurrences of different BEs and subjective (epistemic) dependence between estimates of the epistemically uncertain probabilities of some BEs are not considered. Moreover, there exist limitations to the application of fuzzy set rules, which were used for aggregating experts’ opinions and ranking purposes of the BEs in the FT model. These limitations can be investigated through further research.

It is believed that the proposed hybrid uncertainty analysis method presents a robust and powerful tool for quantitative risk analysis, as both types of uncertainties are taken into account appropriately.