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With numerous and ambiguous sets of information and often conflicting requirements, construction management is a complex process involving much uncertainty. Decision makers may be challenged with satisfying multiple criteria using vague information. Fuzzy multi-criteria decision-making (FMCDM) provides an innovative approach for addressing complex problems featuring diverse decision makers’ interests, conflicting objectives and numerous but uncertain bits of information. FMCDM has therefore been widely applied in construction management. With the increase in information complexity, extensions of fuzzy set (FS) theory have been generated and adopted to improve its capacity to address this complexity. Examples include hesitant FSs (HFSs), intuitionistic FSs (IFSs) and type-2 FSs (T2FSs). This chapter introduces commonly used FMCDM methods, examines their applications in construction management and discusses trends in future research and application. The chapter first introduces the MCDM process as well as FS theory and its three main extensions, namely, HFSs, IFSs and T2FSs. The chapter then explores the linkage between FS theory and its extensions and MCDM approaches. In total, 17 FMCDM methods are reviewed and two FMCDM methods (i.e. T2FS-TOPSIS and T2FS-PROMETHEE) are further improved based on the literature. These 19 FMCDM methods with their corresponding applications in construction management are discussed in a systematic manner. This review and development of FS theory and its extensions should help both researchers and practitioners better understand and handle information uncertainty in complex decision problems.

This paper aims to propose two portfolio selection models with hesitant value-at-risk (HVaR) – HVaR fuzzy portfolio selection model (HVaR-FPSM) and HVaR-score fuzzy portfolio selection model (HVaR-S-FPSM) – to help investors solve the problem that how bad a portfolio can be under probabilistic hesitant fuzzy environment.

It is strictly proved that the higher the probability threshold, the higher the HVaR in HVaR-S-FPSM. Numerical examples and a case study are used to illustrate the steps of building the proposed models and the importance of the HVaR and score constraint. In case study, the authors conduct a sensitivity analysis and compare the proposed models with decision-making models and hesitant fuzzy portfolio models.

The score constraint can make sure that the portfolio selected is profitable, but will not cause the HVaR to decrease dramatically. The investment proportions of stocks are mainly affected by their HVaRs, which is consistent with the fact that the stock having good performance is usually desirable in portfolio selection. The HVaR-S-FPSM can find portfolios with higher HVaR than each single stock and has little sacrifice of extreme returns.

This paper fulfills a need to construct portfolio selection models with HVaR under probabilistic hesitant fuzzy environment. As a downside risk, the HVaR is more consistent with investors’ intuitions about risks. Moreover, the score constraint makes sure that undesirable portfolios will not be selected.

The purpose of this paper is to develop some weight determining methods for hesitant fuzzy multi-criterion decision making (MCDM) in which the preference information on attributes is collected over different periods.

Based on the proposed weight determining methods and dynamic hesitant fuzzy aggregation operators, an approach is developed to solve the hesitant fuzzy multi-stage multi-attribute decision-making problem where all the preference information of attributes over different periods is represented in hesitant fuzzy values.

In order to determine the weights associated with dynamic hesitant fuzzy operators, the authors propose the improved maximum entropy method and the minimum average deviation method.

This paper does not consider the multi-stage multi-criteria group decision-making problem.

An example concerning the evaluation of rangelands is given to illustrate the validation and efficiency of the proposed approach. It should be stated that the proposed approach can also be implemented into other multi-stage MCDM problems.

The concept of hesitant fuzzy variable (HFV) is defined. Some operational laws and properties of the HFVs are given. Moreover, to fuse the multi-stage hesitant fuzzy information, the aggregation operators of hesitant fuzzy sets are extended to that of the HFVs.

This study aims to carry out an analysis for flow and heat transfer of a new hybrid nanofluid over a vertical flat surface embedded in a saturated porous medium with anisotropic permeability at high Rayleigh number. Here the hybrid nanofluid is considered as the working fluid, with different kinds of small particles in nanoscale being suspended.

The generalized homogenous model is introduced to describe the behaviors of hybrid nanofluid. Within the framework of the boundary layer approximations, the governing equations embodying the conservation equations of total mass, momentum and thermal energy are reduced to a set of fully coupled ordinary differential equations via relevant scaling transformations. A flow stability analysis is performed to examine the behavior of convective heat energy. Accurate solutions are obtained by means of a very efficient homotopy-based package BVPh 2.0.

Results show that the linear correlations of physical quantities among the base fluid and its suspended nanoparticles are adequate to give accurate results for simulation of behaviors of hybrid nanofluids. Heat enhancement can be also fulfilled by hybrid nanofluids. A flow stability analysis suggests the heat-related power index m > −1/3 for satisfying the increasing behavior of convective heat energy.

Free convection of a hybrid nanofluid near a vertical flat surface embedded in a saturated porous medium with anisotropic permeability is investigated for the first time. The simplified hybrid nanofluid model is proposed for describing nanofluid behaviors. The results of this proposed approach agree well with those given by the traditional hybrid nanofluid model and experiment. It is expected that, by using different combinations of various kinds of nanoparticles, the new generation of heat transfer fluids can be fabricated, which possess similar thermal-physical properties as regular nanofluids but with lower cost.

Based on the context of the Internet of Things (IoT), the territorial public emergency supplies will be networked, platform-based management, unified emergency dispatch. The problem of supplies dispatching in the “last kilometer” of emergency is solved, and the supplies needed in the disaster area are promptly delivered to the hands of the victims so that they can quickly be rescued after the disaster and to save valuable time for rapid rescue, which can greatly decrease casualties and property losses. This paper aims to discuss these issues.

By analyzing the shortage of existing emergency supplies dispatching research and taking all factors such as disaster area demand, social reserve, road conditions, mode of transport, loading limit, disaster area satisfaction rate and road capacity into consideration under the background of IoT, a variety of the territorial emergency supplies dispatching model with more rescue points, more affected areas are constructed. The objective function of the model is to aim in finding the shortest rescue time, giving the solution algorithm, and finally simulating the simulation case.

Based on the context of the IoT, the territorial public emergency supplies will be networked, platform-based management, unified emergency dispatch. Considering factors such as road conditions, modes of transport and road capacity, the authors construct a number of emergency rescue plans, multiple disaster scenarios and various emergency supplies dispatching models. The authors simulate the situation through simulation cases with the shortest time being the ultimate goal. The problem of supplies dispatching in the “last kilometer” of emergency is solved, and the supplies needed in the disaster area are promptly delivered to the hands of the victims so that they can quickly be rescued after the disaster and to save valuable time for rapid rescue, which can greatly decrease casualties and property losses.

This paper provides little research on the dispatch of emergency supplies. The problems of direct dispatch from the rescue point to the affected area and dispatch of supplies without relying on the arrival of emergency supplies at the rear are addressed. Therefore, this study does not focus on the arrival of emergency supplies at the rear but on direct dispatching issues during territorial public emergency supplies from the rescue point to the disaster point.

The purpose of this paper is to find an accurate, efficient and easy-to-implement point estimate method (PEM) for the statistical moments of random systems.

First, by the theoretical and numerical analysis, the approximate reference variables for the frequently used nine types of random variables are obtained; then by combining with the dimension-reduction method (DRM), a new method which consists of four sub-methods is proposed; and finally, several examples are investigated to verify the characteristics of the proposed method.

Two types of reference variables for the frequently used nine types of variables are proposed, and four sub-methods for estimating the moments of responses are presented by combining with the univariate and bivariate DRM.

In this paper, the number of nodes of one-dimensional integrals is determined subjectively and empirically; therefore, determining the number of nodes rationally is still a challenge.

Through the linear transformation, the optimal reference variables of random variables are presented, and a PEM based on the linear transformation is proposed which is efficient and easy to implement. By the numerical method, the quasi-optimal reference variables are given, which is the basis of the proposed PEM based on the quasi-optimal reference variables, together with high efficiency and ease of implementation.

The purpose of the paper is to design a robust control system for a generic hypersonic vehicle which includes dynamic nonlinear, open loop unstable and parametric uncertainties.

For a complex longitudinal model of a generic hypersonic vehicle which includes dynamic nonlinear, open loop unstable and parametric uncertainties, a nonlinear dynamic inverse (NDI) approach combined with proportional differential (PD) control is used to design a strong robust control system to deal with the sensitivity to changes of atmosphere condition. In this way, a simple genetic algorithm is used to search a group of parameters of the control system to satisfy the specific performance indices. Then parametric uncertainties are considered to verify the robustness of the control system.

The PD hypersonic vehicle control system using NDI approach can satisfy the specific flight performance. And it has strong robustness under the parametric uncertainties.

The paper fulfills a complete process of the nonlinear control system design for a generic hypersonic vehicle. And, the simulation results show the efficiency and robustness of the control system.

The purpose of this paper is to present some dynamic hesitant fuzzy aggregation operators to tackle with the multi-period decision-making problems where all decision information is provided by decision makers in hesitant fuzzy information from different periods.

First, the notions and operational laws of the hesitant fuzzy variable are defined. Then, some dynamic hesitant fuzzy aggregation operators involve the dynamic hesitant fuzzy weighted averaging (DHFWA) operator, the dynamic hesitant fuzzy weighted geometric (DHFWG) operator, and their generalized versions are presented. Some desirable properties of these proposed operators are established. Furthermore, two linguistic quantifier-based methods are introduced to determine the weights of periods. Next, the paper extends the results to the interval-valued hesitant fuzzy situation. Furthermore, the authors develop an approach to solve the multi-period multiple criteria decision making (MPMCDM) problems. Finally, an illustrative example is given.

The presented hesitant fuzzy aggregation operators are very suitable for aggregating the hesitant fuzzy information collected at different periods. The developed approach can solve the MPMCDM problems where all decision information takes the form of hesitant fuzzy information collected at different periods.

The presented hesitant fuzzy aggregation operators and decision-making approach can widely apply to dynamic decision analysis, multi-stage decision analysis in real life.

The paper presents the useful way to aggregate the hesitant fuzzy information collected at different periods in MPMCDM situations.

This paper aims to present a direct analysis to demonstrate why markedly different tensile and compressive behaviors of concretes could not be simulated with the Drucker–Prager yield criterion.

This study proposed an extended form of the latter for establishing a new elastoplasticity model with evolving yield strengths.

Explicit closed-form solutions to non-symmetric tensile and compressive responses of uniaxial specimens at finite strain are for the first time obtained from hardening to softening.

With such exact solutions, the yield strengths in tension and compression can be explicitly prescribed by uniaxial tensile and compressive stress-strain functions. Then, the latter two are further provided in explicit forms toward accurately simulating tensile and compressive behaviors. Numerical examples are supplied for meso-scale heterogeneous concrete (MSHC) and high-performance concrete (HPC), etc. Model predictions are in good agreement with test data.