Fuzzy Coalitions Research Articles

A profit distribution model for the multimodal transport alliance considering participation rate and communication structure

The rationality of profit distribution affects the stability of the multimodal transport alliance. In the multimodal transport alliance, the participation rate of the carrier and the communication structure of the alliance are important influencing factors of profit distribution results. To get a reasonable profit distribution scheme, this paper constructs a profit distribution model considering the characteristics of multimodal transport, called the Choquet Cloud Gravity Center AT model. Firstly, considering the communication structure of the alliance, the Cloud Gravity Center Average Tree method is used as the base model for profit distribution. Secondly, considering the multimodal transport alliance is a fuzzy coalition, the profit for each alliance subset in the base model is calculated by the Choquet integral. Then, the profit distribution model considering participation rate and communication structure is obtained. Finally, a numerical example is given to illustrate the applicability of the model, and comparative analysis is conducted to verify the rationality of the model. This study provides a suitable profit-sharing model for multimodal transport alliances, which is conducive to the stable and efficient operation of alliances.

Decision Making for Connected Automated Vehicles at Urban Intersections Considering Social and Individual Benefits

To address the coordination issue of connected automated vehicles (CAVs) at urban scenarios, a game-theoretic decision-making framework is proposed that can advance social benefits, including the traffic system efficiency and safety, as well as the benefits of individual users. Under the proposed decision-making framework, in this work, a representative urban driving scenario, i.e. the unsignalized intersection, is investigated. Once the vehicle enters the focused zone, it will interact with other CAVs and make collaborative decisions. To evaluate the safety risk of surrounding vehicles and reduce the complexity of the decision-making algorithm, the driving risk assessment algorithm is designed with a Gaussian potential field approach. The decision-making cost function is constructed by considering the driving safety and passing efficiency of CAVs. Additionally, decision-making constraints are designed and include safety, comfort, efficiency, control and stability. Based on the cost function and constraints, the fuzzy coalitional game approach is applied to the decision-making issue of CAVs at unsignalized intersections. Two types of fuzzy coalitions are constructed that reflect both individual and social benefits. The benefit allocation in the two types of fuzzy coalitions is associated with the driving aggressiveness of CAVs. Finally, the effectiveness and feasibility of the proposed decision-making framework are verified with three test cases.

Fuzzy Strong Nash Equilibria in Generalized Fuzzy Games with Application in Urban Public-Sports Services

In this paper, we apply the existence of solutions of the Ky Fan minimax inequality to establish the existence of fuzzy strong Nash equilibria in generalized fuzzy games and strong Nash equilibria in fuzzy coalition generalized games. We then show some applications of our existence results about the strong Nash equilibrium in urban public-sports services.

The Choquet integral-based Shapley function for n-person cooperative games with probabilistic hesitant fuzzy coalitions

The use of probabilistic hesitant fuzzy elements (PHFEs) to represent the alliance status in cooperative games can describe the player's participation levels and associated probability. This paper proposes an effective Shapley function for probabilistic hesitant fuzzy cooperative games based on generalized Choquet integral. We first define the probabilistic hesitant fuzzy coalition of cooperative games. After that, a supplementary model of incomplete probability information is established. Without losing any probability information, an adjustment algorithm is developed to derive the consistent probability of coalitions. Then the characteristic function of probabilistic hesitant fuzzy cooperative games is constructed based on generalized Choquet integral. The Choquet integral-based Shapley function is presented according to the proposed characteristic function. Some desirable properties of Shapley function are discussed in detail. The CIG algorithm is established for generating consistent imputation of cooperative games. Finally, the proposed algorithm is applied to the cooperative production of alloy materials.

Fairness principles for insurance contracts in the presence of default risk

AbstractWe use the theory of cooperative games for the design of fair insurance contracts. An insurance contract needs to specify the premium to be paid and a possible participation in the benefit (or surplus) of the company. We suppose that a convex commonotonic premium functional is used to value the aggregated liability of the insurance company. It results from the analysis that when a contract is exposed to the default risk of the insurance company, ex‐ante equilibrium considerations require a certain participation in the benefit of the company to be specified in the contracts. The fair benefit participation of agents appears as an outcome of a game involving the residual risks induced by the default possibility and using fuzzy coalitions.

Cooperative Games with Multiple Scenarios in Intuitionistic Fuzzy Environment

‎The main aim of this paper is to introduce the core and nucleolus notions of cooperative games with multiple scenarios in uncertain environment‎. ‎Taking imprecision of information into account‎, ‎we incorporate fuzzy coalition values‎, ‎which are represented by intuitionistic fuzzy numbers‎. ‎They can be applied as an appropriate approach to define a fuzzy set in the case that available information is not sufficient for defining an imprecise concept by means of a conventional fuzzy set‎. ‎The characteristic function of such games associates a coalition with a vector containing the intuitionistic fuzzy components‎. ‎The notion of expected interval is defined and computed for the intuitionistic fuzzy numbers‎. ‎Then‎, ‎an approach is proposed to transform the problem into a single-objective cooperative game with interval-valued payoffs‎. ‎The concepts of core and nucleolus are considered‎. ‎It is shown that the core is nonempty in these games‎. ‎A method is proposed to compute the nucleolus of such the problems‎. ‎Finally‎, ‎the validity and applicability of the approach are illustrated by a numerical example.

Use of Fuzzy Coalition Games in Socially Oriented Decision Making During Hospitalization in Pandemic

The problems of organizing medical care in the context of the COVID-19 pandemic, associated with the uncertainty and limitedness of various resources, led to the need to improve decision-making systems for hospitalization of patients. Situational management can improve the decision-making process to fit the current situation better. At the same time, it becomes important to take into account the influence of psychological factors on decisions made during hospitalization. The paper proposes the use of coalition games for situational management during hospitalization of patients. The players and members of the coalition are hospitals, ambulance teams, patients and computed tomography centers. The goal of the game is to form a coalition of participants that provides the maximum benefit in terms of time and cost of hospitalization at the time of decision making. The general scheme of hospitalization, the main sources of information about the situation, the formulation and formalization of the problem are considered. An experiment was carried out in which the formation of a coalition during hospitalization was tested based on data obtained from analyzing the dynamics of the COVID-19 pandemic. Due to the small amount of data and the lack of approved models of the situation development, when carrying out the calculation, some of the parameters were estimated using heuristic models of the development of the situation, based on the analysis of information from open sources of information. The experiment result contains a set of coalitions that provide the maximum benefit under the specified constraints. At the same time, the calculation time of the coalition game allows using the proposed model of decision-making support during hospitalization in the dispatch service of ambulance stations.

Fairness and fuzzy coalitions

In this paper, we study the problem of a fair redistribution of resources among agents in an exchange economy á la Shitovitz (Econometrica 41:467–501, 1973), with agents’ measure space having both atoms and an atomless sector. We proceed by following the idea of Aubin (Mathematical methods of game economic theory. North-Holland, Amsterdam, New York, Oxford, 1979) to allow for partial participation of individuals in coalitions, that induces an enlargement of the set of ordinary coalitions to the so-called fuzzy or generalized coalitions. We propose a notion of fairness which, besides efficiency, imposes absence of envy towards fuzzy coalitions, and which fully characterizes competitive equilibria and Aubin-core allocations.

A cooperative game theory based user-centered medical device design decision approach under uncertainty

The medical device conceptual design decision-making is a process of coordinating pertinent stakeholders, which will significantly affect the quality of follow-up market competitiveness. However, as the most challenging parts of user-centered design, traditional methods are mainly focusing on determining the priorities of the evaluation criteria and forming the comprehensive value (utility) of the conceptual scheme, may not fully deal with the interaction and interdependent between the conflicts of interest among stakeholders and weigh the ambiguous influence on the overall design expectations, which results in the unstable decision-making results. To overcome this drawback, this paper proposes a cooperative game theory based decision model for device conceptual scheme under uncertainty. The proposed approach consists of three parts: first part is to collect and classify needs of end users and professional users based on predefined evaluation criteria; second part is using rough set theory technique to create criteria correlation diagram and scheme value matrix from users; and third part is developing the fuzzy coalition utility model to maximize the overall desirability through the criteria correlation diagram with the conflict of interests of end and professional users considered, and then selecting the optimal scheme. A case study of blood pressure meter is used to illustrate the proposed approach and the result shows that this approach is more robust compared with the widely used the Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS) approach.

Unblocked Imputations of Fuzzy Games. I: Existence

We generalize the well-known Scarf theorem on the nonemptiness of the core to the case of generalized fuzzy cooperative games without side payments provided that the set of blocking coalitions is extended by the so-called fuzzy coalitions. The notion of a balanced family is extended to the case of an arbitrary set of fuzzy blocking coalitions, owing to which it is possible to introduce a natural analogue of balancedness of a fuzzy game for the characteristic function with an arbitrary efficiency domain. Based on an appropriate approximation of a fuzzy game by finitely-generated games, together with the seminal combinatorial Scarf lemma on ordinal and admissible bases, we obtain rather general conditions of the existence of unblocked imputations for F-balanced fuzzy cooperative games. Bibliography: 15 titles.

Profit Allocations for Restricted Coalition With Hesitation Degrees in Cooperative Game Theory

Profit allocation plays an important role in the decision-making field. In this paper, we study an allocation method on restricted coalition cooperation with intuitionistic fuzzy coalitions, in which the partners have some hesitation degree and different risk preferences when they participate in a limited communication structure game. In order to sufficiently analyze the profit allocation strategy, an average tree solution (A-T solution) with Choquet integrals and hesitation degrees is studied. In particular, a simple solving method for the A-T solution is proposed by proving that the characteristic functions of the cooperative game satisfy the monotonicity condition. Using this method, the upper and lower bounds of the A-T solution can be calculated directly from the upper and lower bounds of the interval characteristic functions. This method avoids the subtraction of interval numbers. Furthermore, the properties of the A-T solution according to an axiomatic system are proved in this paper. Finally, the applicability and superiority of the proposed approach are demonstrated through comparison with other methods.

Generalized form solutions of cooperative game with fuzzy coalition structure

A fuzzy coalition structure is a partition of player set under a certain participation level. In this study, a kind of cooperative games with fuzzy coalition structure (i.e., generalized fuzzy game) is proposed, which can be seen as an extension of game in Owen’s coalition structure. The generalized fuzzy game is defined by partition function, which could be used to express several cooperative games with fuzzy coalition structure (i.e., fuzzy coalition structure games). For the fuzzy coalition structure, the generalized cooperative game could denote the coalition interaction under different participation ratios for players. The properties of generalized fuzzy game have been proven, such as inheritance, supperadditivity and convexity. In order to get unified solution for the generalized fuzzy game, fuzzy Owen value is also extended based on the consistent formula of generalized fuzzy game. It is proved that the fuzzy Owen value is a unique value for the generalized fuzzy game based on symmetric within fuzzy coalition, symmetric across fuzzy coalitions, fuzzy null player, linearity and efficiency. Finally, the fuzzy Owen value is represented by crisp one in order to simplify fuzzy solution computation.

A fuzzy cooperative game theoretic approach for multinational water resource spatiotemporal allocation

Water resource allocation in multinational river basins has been a major concern for all riparian countries. From the perspective of cooperative and sustainable water resource development, considering the spatiotemporal characteristics of the water demand, namely, the priority of water use due to the geographic location of each riparian country, the seasonality of water demand, and the differences in the net utility of water utilization, this paper constructs a fuzzy coalition game model for multinational water resource allocation and provides the optimal allocation strategy using the example of the Lancang-Mekong River. The study indicates that considering the geographic locations and the differences in the water utility of each country compared with the initial allocation strategy based on agricultural water demand, the cooperative strategy increases the allocated water resources in high-utility countries (expect countries near the estuary) and the overall water utility in the entire basin. Then, considering the seasonality of the water resource reallocation, the fuzzy coalition among riparian countries further increases the net water utility of each country and achieves the optimal allocation. As the preconditions for the establishment of cooperative relationships, upstream countries need to transfer partial water rights to downstream countries in certain seasons. The basic idea that is presented in this paper, the fuzzy coalition model of water resource allocation with spaciotemporal constraints, can be applied to the water allocation of other multinational rivers.

Public resources allocation using an uncertain cooperative game among vulnerable groups

PurposeThis paper aims to solve the problem of public resource allocation among vulnerable groups by proposing a new method called uncertainα-coordination value based on uncertain cooperative game.Design/methodology/approachFirst, 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 uncertainα-coordination value is used as the best solution. This study proves that the proposed methods meet the basic properties of cooperative game.FindingsThe uncertainα-coordination value is used to solve a public medical resource allocation problem in fuzzy coalitions and uncertain payoffs. Compared with other methods, theα-coordination value can solve such problem effectively because it balances the worries of vulnerable group’s further development and group fairness.Originality/valueIn 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 uncertainα-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 uncertainCISvalue are proposed separately to establish uncertainα-Coordination value.

Cooperative games with multiple attributes

ABSTRACTIn this paper, we introduce the notion of a cooperative game with multiple attributes where players can provide partial participations in multiple attributes and form coalitions. The power or influence of the players due to their multiple attributes is evaluated based on their memberships in the coalitions. Our game therefore, extends the notion of cooperative games with fuzzy coalitions. The Shapley function for this class of games is proposed as a rational and fair solution concept. Every fuzzy game stems out of a specific crisp game under the assumption that the players provide partial memberships in forming multiple coalitions simultaneously. We adopt similar techniques to obtain the cooperative games with multiple attributes from their crisp counterparts and subsequently determine their Shapley functions.

Fuzzy Harsanyi solution for a kind of fuzzy coalition games

The fuzzy linear game in Ref. [32] is a class of fuzzy cooperative games with fuzzy coalition (fuzzy coalition game for short), which admits the difference of interactions for different fuzzy coalitions. The fuzzy Shapley value for fuzzy linear game has been studied. As Shapley value is just one point in the Harsanyi solution, it is interesting to study the explicit form of Harsanyi solution in the fuzzy coalition game. This paper defines the fuzzy Harsanyi solution which distributes the Harsanyi dividends such that the dividend shares of players in each fuzzy coalition are proportional to the corresponding players' participation index. When the fuzzy coalition payoff is average distributed between players in the fuzzy coalition, the fuzzy Harsanyi solution also coincides with the fuzzy Shapley value just as their relationship in a crisp cooperative game. We provide two axiomatic characterizations for the fuzzy Harsanyi solution: one uses axioms, and the other uses distribution matrices. The fuzzy Harsanyi solution is a unique value on the fuzzy linear game that satisfies fuzzy efficiency, fuzzy null player and fuzzy additivity property. Meanwhile, based on probability distribution, fuzzy Harsanyi solution is seen as an expected marginal contribution of each player in the fuzzy coalition, which provides more choices for players in the fuzzy coalition.

A modified position value for communication situations and its fuzzification

Myerson treated various situations of cooperation in the field of cooperative games and proposed the communication structure. In this paper, we define and characterize an allocation rule in terms of the position value, called an average spanning tree solution, for communication situations by introducing a concept of cooperation relationship which says that two players are deemed to possess this relationship if there is a communication path through them. Considering the fact that the extent to what players participate in a coalition may be partially restricted for uncertain possibilities, we construct a graph game in multilinear extension form and continue to explore the fuzzy average spanning tree solution on a framework of communication situation with fuzzy coalition.

An Analog of the Bondareva-Shapley Theorem I. The Non-Emptiness of the Core of a Fuzzy Game

This paper deals with a generalization of the famous Bondareva-Shapley theorem [1, 9] on the core of TU cooperative games to the case of fuzzy blocking. The suggested approach is based on the concept of a balanced collection of fuzzy coalitions. Introduced by the author, this extension of the classical balanced collection of standard coalitions yields a natural analog of balancedness for the so-called fuzzy TU cooperative games. As established below, the general balancedness is a necessary and sufficient condition for the non-emptiness of the core of fuzzy TU cooperative games. The non-emptiness criterion of the core is further refined using the classical Helly's theorem on the intersection of convex sets. The S*-representation of a fuzzy game is studied, which simplifies the existence conditions for non-blocking imputations of this game in a series of cases.

PM2.5 Cooperative Control with Fuzzy Cost and Fuzzy Coalitions.

Haze control cost is hard to value by a crisp number because it is often affected by various factors such as regional uncertain meteorological conditions and topographical features. Furthermore, regions may be involved in different coalitions for haze control with different levels of effort. In this paper, we propose a PM2.5 cooperative control model with fuzzy cost and crisp coalitions or fuzzy coalitions based on the uncertain cross-border transmission factor. We focus on the Beijing–Tianjin–Hebei regions of China and obtain the following major findings. In the case of haze control in the Beijing–Tianjin–Hebei regions of China, local governments in the global crisp coalition can achieve their emission reduction targets with the lowest aggregated cost. However, Hebei fails to satisfy its individual rationality if there is no cost sharing. Therefore, the Hukuhara–Shapley value is used to allocate the aggregated cost among these regions so that the grand coalition is stable. However, the Beijing–Tianjin–Hebei regions cannot achieve their emission reduction targets in the global fuzzy coalition without government subsidies.

A bi-average tree solution for probabilistic communication situations with fuzzy coalition

A bi-average tree solution for probabilistic communication situations with fuzzy coalition