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The purpose of this paper is to propose a model for a target searching problem in a two-dimensional region with time constraints. The proposed model facilitates the search operation by minimizing the mission time and fuel usage, and the search operation is performed by a set of agents divided into a number of groups.

The authors have applied optimization techniques, Cartesian product, inclusion–exclusion principle, cooperative strategy, Shapley value, fuzzy Shapley function and Choquet integral to model the problem.

The proposed technique optimizes the placement of base stations that minimizes the sortie length of the agents. The results show that the cooperative strategy outperforms the non-cooperative strategy. The Shapley values quantify the rewards of each group based on their contributions to the search operation, whereas the fuzzy Shapley values determine the rewards of each group based on their contributions and level of cooperation in the search operation.

The proposed model can be applied to model many real-time problems such as patrolling in international borders, urban areas, forests and managing rescue operations after natural calamities, etc. Therefore, defence organizations, police departments and other operation management sectors will be benefitted by applying the proposed approach.

To the best of the authors’ knowledge, determining the optimal locations of base stations in a region is not explored in the existing works on target searching problems with fuel constraints. The proposed approach to cooperatively search the targets in a region is new. Introducing the Shapley function and fuzzy Shapley function is a novel idea to quantify the rewards of each group based on their contributions and level of cooperation in the search operation. This paper addresses these unexplored areas.

This paper examines the profit distribution of engineering projects in the integrated project delivery (IPD) mode. IPD is a new delivery method that can ameliorate many of the disadvantages of traditional delivery methods and improve project results. In the implementation of IPD, the profit distribution is key for ensuring the success of IPD projects.

This paper described a new method for characterizing profit distribution in the IPD mode. The payment function and Shapley value of the cooperative fuzzy game of fuzzy alliance were defined by considering the Choquet integral of the fuzzy measure. The participation of each player was considered, and the influence of participation on the profit distribution was discussed. Lastly, changes in the profit distribution of core participants under different alliance combinations were studied.

A case from a report of The American Institute of Architects (AIA) was used to verify the fuzzy alliance model. There was a significant correlation between the degree of participation of the owner, architect and builder and the profit distribution among these three participants.

The theoretical research in this paper has some limitations. Initially, this paper selects a case with only three key participants in order to simplify the research. When there are many core participants, how to establish the alliance in the IPD mode and how to establish the corresponding profit distribution model, further work is certainly required to disentangle these complexities in models. Second, in this case, BIM technology has little impact on the income of the whole project. Therefore, this paper does not consider the impact of BIM technology on the marginal effect of the IPD project. Third, the contract type in the case is a custom tri-party based on IFOA. There is no classified discussion of the impact of different contracts on the profit distribute in the paper.

Based on the in-depth study of cooperative game with alliance structure, this paper promotes the classic cooperative game with alliance structure. The authors define the payoff function of fuzzy cooperative games by Choquet integral of fuzzy measure, and introduce the idea into the field of IPD. It aims at extending the solution to a cooperative game without a core. It can be obtained through a simple calculation. In the IPD alliance, the fuzziness and uncertainty of the participation degree of each participant will affect the profit of the whole project. The authors find that the higher the participation rate of players, the more profit each participant has. The greater the influence weight of the designer on the alliance, the lower the influence weight of the contractor on the alliance, the lower the participation of the contractor and the designer, and the lower the income distribution value of the three core participants. It shows a monotonous decline status.

For any construction enterprise, it can make more profits if it joins the grand alliance. In the IPD alliance, each participant can maximize their own interests, which can also promote the enthusiasm of construction enterprises to participate in the alliance and increase the application of IPD mode in AEC industry. This research method provides a new fast, effective, and more realistic solution method for cooperative countermeasures. It can be further extended to other cooperative game fields and advance a new research perspective and solution for the distribution of cooperative interests.

The contribution of this paper is the development of a fuzzy alliance model that provides a tool for measuring the profit distribution in IPD. This is the first quantitative model to connect the degree of participation with the profit distribution in IPD using fuzzy alliance.

The purpose of this paper is to develop a novel recommendation method using online reviews with emotional preferences for facilitating online purchase decisions. This leads to better use of information-rich online reviews for providing users with personalized recommendations.

A novel method is developed for producing personalized recommendations in online purchase decision-making. Such a method fuses the belief structure and the Shapley function together to effectively deal with the emotional preferences in online reviews and adequately tackle the interaction existent between product criteria with the use of a modified combination rule for making better online recommendations for making online purchase decisions.

An example is presented for demonstrating the applicability of the method for facilitating online purchase. The results show that the recommendation using the proposed method can effectively improve customer satisfaction with better purchase decisions.

The proposed method can better utilize online reviews for satisfying personalized needs of consumers. The use of such a method can optimize interface design, refine customer needs, reduce recommendation errors and provide personalized recommendations.

The proposed method adequately considers the characteristics of online reviews and the personalized needs of customers for providing customers with appropriate recommendations. It can help businesses better manage online reviews for improving customer satisfaction and create greater value for both businesses and customers.

This paper aims to solve the problem of public resource allocation among vulnerable groups by proposing a new method called uncertain α-coordination value based on uncertain cooperative game.

First, explicit forms of uncertain Shapley value with Chouqet integral form and uncertain centre-of-gravity of imputation-set (CIS) value are defined separately on the basis of uncertainty theory and cooperative game. Then, a convex combination of the two values above called the uncertain α-coordination value is used as the best solution. This study proves that the proposed methods meet the basic properties of cooperative game.

The uncertain α-coordination value is used to solve a public medical resource allocation problem in fuzzy coalitions and uncertain payoffs. Compared with other methods, the α-coordination value can solve such problem effectively because it balances the worries of vulnerable group’s further development and group fairness.

In this paper, an extension of classical cooperative game called uncertain cooperative game is proposed, in which players choose any level of participation in a game and relate uncertainty with the value of the game. A new function called uncertain α-Coordination value is proposed to allocate public resources amongst vulnerable groups in an uncertain environment, a topic that has not been explored yet. The definitions of uncertain Shapley value with Choquet integral form and uncertain CIS value are proposed separately to establish uncertain α-Coordination value.

The paper aims to build the connections between game theory and the resource allocation problem with general uncertainty. It proposes modeling the distributed resource allocation problem by Bayesian game. During this paper, three basic kinds of uncertainties are discussed. Therefore, the purpose of this paper is to build the connections between game theory and the resource allocation problem with general uncertainty.

In this paper, the Bayesian game is proposed for modeling the resource allocation problem with uncertainty. The basic game theoretical model contains three parts: agents, utility function, and decision-making process. Therefore, the probabilistic weighted Shapley value (WSV) is applied to design the utility function of the agents. For achieving the Bayesian Nash equilibrium point, the rational learning method is introduced for optimizing the decision-making process of the agents.

The paper provides empirical insights about how the game theoretical model deals with the resource allocation problem uncertainty. A probabilistic WSV function was proposed to design the utility function of agents. Moreover, the rational learning was used to optimize the decision-making process of agents for achieving Bayesian Nash equilibrium point. By comparing with the models with full information, the simulation results illustrated the effectiveness of the Bayesian game theoretical methods for the resource allocation problem under uncertainty.

This paper designs a Bayesian theoretical model for the resource allocation problem under uncertainty. The relationships between the Bayesian game and the resource allocation problem are discussed.

This chapter discusses a collaborative strategy for noncompetitive small- and medium-sized enterprises (SME's) aiming to reduce their logistics costs by means of a joint replenishment of multiple items. The proposed approach is an extension of the classical joint replenishment problem, named as a Stochastic Collaborative Joint Replenishment problem (S-CJRP) because it considers stochastic demand, warehouse and transport capacity constraints, and multiple buyers and vendors. Operating this method implies three main challenges: (1) determining the frequency with which each buyer should replenish the products; (2) allocating investments and benefits between partnering buyers; and (3) deciding whether to coordinate the supply chain internally or outsource its coordination. The S-CJRP is solved through a heuristic approach, which deals with uses of the Shapley Value Function to allocate the investments and benefits, and it explores the coordination through several simulation scenarios, all of which exhibit prospective cost reductions in inventory management. Preliminary results show that third-party logistics providers could be a valuable resource in coordinating SMEs along a supply chain.

The purpose of this paper is to develop a probabilistic uncertain linguistic (PUL) TODIM method based on the generalized Choquet integral, with respect to the interdependencies between criteria, for the selection of the best alternate in the context of multiple criteria group decision-making (MCGDM).

Owing to decision makers (DMs) do not always show completely rational and may have the preference of bounded rational behavior, this may affect the result of the MCGDM. At the same time, criteria interaction is a focused issue in MCGDM. Hence, a novel TODIM method based on the generalized Choquet integral selects the best alternate using PUL evaluation, where the generalized Choquet integral is used to calculate the weight of criterion. The generalized PUL distance measure between two probabilistic uncertain linguistic elements (PULEs) is calculated and the perceived dominance degree matrices for each alternate relative to other alternates are obtained. Furthermore, the comprehensive perceived dominance degree of each alternate can be calculated to get the ranking.

Potential application of the PUL-TODIM method is demonstrated through an evaluation example with sensitivity and comparative analysis.

As per author's concern, there are no TODIM methods with probabilistic uncertain linguistic sets (PULTSs) to solve MCGDM problems under uncertainty. Compared with the result of existing methods, the final judgment value of alternates using the extended TODIM methodology is highly corroborated, which proves its potential in solving MCGDM problems under qualitative and quantitative environments.

Construction projects have become increasingly long, complex and costly with waste and inefficiencies and often fail to achieve the desired results. Integrated project delivery (IPD) is believed to change these problems. A reasonable and fair profit distribution mechanism is a critical factor for ensuring the success of the IPD projects. This study aims to investigate the strategies of all participants in the profit distribution of an IPD project with respect to the factor of the effort level.

This study describes the influence of owners and participants on profit distribution due to their respective efforts in the IPD project alliance. The influence of effort level on profit distribution is discussed based on the Holmstrom-Milgrom model of asymmetric information game theory and principal-agent theory, combined with incentive compatibility (IC) constraints and individual rationality (IR) constraints.

The results show that the optimal level of effort by each participant optimizes the profit distribution of an IPD project. At the same time, in the revenue incentive contract, the effort level of the participants is positively correlated with the profit distribution, proportional to their contribution coefficient and inversely proportional to the square of the cost of their creative activities in terms of effort. Each party of an IPD project can adopt a series of measures to improve their own effort level and choose the optimal level of effort based on the profit distribution, while satisfying their own utility maximization.

This study introduces the Holmstrom-Milgrom model in the principal-agent theory to explore the influence of the effort level on profit distribution in IPD projects. The quantitative model can contribute to establish a fair and efficient profit distribution scheme for the IPD projects.

Cross-layer approach in media access control (MAC) layer will address interference and jamming problems. Hybrid distributed MAC can be used for simultaneous voice, data transmissions in wireless sensor network (WSN) and Internet of Things (IoT) applications. Choosing the correct objective function in Nash equilibrium for game theory will address fairness index and resource allocation to the nodes. Game theory optimization for distributed may increase the network performance. The purpose of this study is to survey the various operations that can be carried out using distributive and adaptive MAC protocol. Hill climbing distributed MAC does not need a central coordination system and location-based transmission with neighbor awareness reduces transmission power.

Distributed MAC in wireless networks is used to address the challenges like network lifetime, reduced energy consumption and for improving delay performance. In this paper, a survey is made on various cooperative communications in MAC protocols, optimization techniques used to improve MAC performance in various applications and mathematical approaches involved in game theory optimization for MAC protocol.

Spatial reuse of channel improved by 3%–29%, and multichannel improves throughput by 8% using distributed MAC protocol. Nash equilibrium is found to perform well, which focuses on energy utility in the network by individual players. Fuzzy logic improves channel selection by 17% and secondary users’ involvement by 8%. Cross-layer approach in MAC layer will address interference and jamming problems. Hybrid distributed MAC can be used for simultaneous voice, data transmissions in WSN and IoT applications. Cross-layer and cooperative communication give energy savings of 27% and reduces hop distance by 4.7%. Choosing the correct objective function in Nash equilibrium for game theory will address fairness index and resource allocation to the nodes.

Other optimization techniques can be applied for WSN to analyze the performance.

Game theory optimization for distributed may increase the network performance. Optimal cuckoo search improves throughput by 90% and reduces delay by 91%. Stochastic approaches detect 80% attacks even in 90% malicious nodes.

Channel allocations in centralized or static manner must be based on traffic demands whether dynamic traffic or fluctuated traffic. Usage of multimedia devices also increased which in turn increased the demand for high throughput. Cochannel interference keep on changing or mitigations occur which can be handled by proper resource allocations. Network survival is by efficient usage of valid patis in the network by avoiding transmission failures and time slots’ effective usage.

Literature survey is carried out to find the methods which give better performance.

Intuitionistic linguistic fuzzy information (ILFI), characterized by linguistic terms and intuitionistic fuzzy sets (IFSs), can easily express the fuzzy information in the process of muticriteria decision making (MCDM) and muticriteria group decision making (MCGDM) problems. The purpose of this paper is to provide an overview of aggregation operators (AOs) and applications of ILFI.

First, some meaningful AOs for ILFI are summarized, and some extended MCDM approaches for intuitionistic uncertain linguistic variables (IULVs), such as extended TOPSIS, extended TODIM, extended VIKOR, are discussed. Then, the authors summarize and analyze the applications about the AOs of IULVs.

IULVs, characterized by linguistic terms and IFSs, can more detailed and comprehensively express the criteria values in the process of MCDM and MCGDM. Therefore, lots of researchers pay more and more attention to the MCDM or MCGDM methods with IULVs.

The authors summarize and analyze the applications about the AOs of IULVs Finally, the authors point out some possible directions for future research.