Attaining Fairness in Communication for Omniscience

This paper studies how to attain fairness in communication for omniscience that models the multi-terminal compress sensing problem and the coded cooperative data exchange problem where a set of users exchange their observations of a discrete multiple random source to attain omniscience—the state that all users recover the entire source. The optimal rate region containing all source coding rate vectors that achieve omniscience with the minimum sum rate is shown to coincide with the core (the solution set) of a coalitional game. Two game-theoretic fairness solutions are studied: the Shapley value and the egalitarian solution. It is shown that the Shapley value assigns each user the source coding rate measured by their remaining information of the multiple source given the common randomness that is shared by all users, while the egalitarian solution simply distributes the rates as evenly as possible in the core. To avoid the exponentially growing complexity of obtaining the Shapley value, a polynomial-time approximation method is proposed which utilizes the fact that the Shapley value is the mean value over all extreme points in the core. In addition, a steepest descent algorithm is proposed that converges in polynomial time on the fractional egalitarian solution in the core, which can be implemented by network coding schemes. Finally, it is shown that the game can be decomposed into subgames so that both the Shapley value and the egalitarian solution can be obtained within each subgame in a distributed manner with reduced complexity.

Mathematical indices for the influence of risk factors on the lethality of a disease

We develop a theoretical model to measure the relative relevance of different pathologies of the lethality of a disease in society. This approach allows a ranking of diseases to be determined, which can assist in establishing priorities for vaccination campaigns or prevention strategies. Among all possible measurements, we identify three families of rules that satisfy a combination of relevant properties: neutrality, irrelevance, and one of three composition concepts. One of these families includes, for instance, the Shapley value of the associated cooperative game. The other two families also include simple and intuitive indices. As an illustration, we measure the relative relevance of several pathologies in lethality due to COVID-19.

Conceptual Solution Decision Based on Rough Sets and Shapley Value for Product-Service System: Customer Value-Economic Objective Trade-Off Perspective

The product service system (PSS), as a design concept for integrated products and services, needs to be evaluated in the early design stage to maximize the value for stakeholders of the PSS concept, which is a crucial task for enterprises. However, existing methods focus on the ranking and value assessment of PSS evaluation criteria (e.g., quality, sustainability, cost), ignoring the needs conflict between customer value and economic objectives in PSS design, resulting in decision results that are not applicable to industrial enterprises. Furthermore, the influence of weight preference and uncertain information on solution evaluation is seldom considered when calculating the weight of each criterion. To fill this gap, integrating rough sets and the Shapley value decision approach for product-service system design considering customer value-economic objective trade-off is proposed, which mainly includes two parts: firstly, the best worst method (BWM) and the entropy weight method are integrated to obtain the comprehensive weight of evaluation criteria in the customer value and economic objectives; secondly, the Shapley value method in the coalition game is used to solve the optimal expectation allocation of the two objectives, so as to select the solution closest to the allocation, i.e., the optimal solution. In addition, rough set techniques are used to capture and integrate subjective assessment information originating from DMs under uncertainty. Finally, a case study of the electric forklift design is illustrated to verify the proposed decision model. The decision results show that this approach is more reliable through sensitivity and comparison analysis, and provide a valuable recommendation for enterprises to consider product service in forklift design.

A Novel Algorithm for Profit Distribution of Sustainable Development Using E-Commerce Supply Chain

E-commerce supply chain actually deals with the acquisition of the raw materials, their timely processing, and on-time delivery to the right place. It deals with a number of processes such as supply and demand, managing order entry, and inventory tracking. Now profit distribution models are actually stochastic models that are used to optimize the gains and profits in a particular business. They actually generate modern time solutions to the existing problems in a sustainable environment. However, in order to solve the problems existing in the traditional profit distribution algorithm of the e-commerce supply chain, such as low distribution accuracy and large time cost, a profit distribution algorithm of the e-commerce supply chain under the concept of sustainable development was designed. It was supported by the concept of sustainable development, and the coefficient of income distribution is calculated according to the equilibrium bidding strategy of supply chain alliance and its members, net present value of income distribution, total investment, minimum expected rate of return on investment, and other parameters. First, calculate the Shapley value of the profit distribution of the power supply chain, and obtain the correction coefficient through the correction matrix, dimensionless processing, and analytic hierarchy process. Use the correction coefficient to correct the Shapley value and the income distribution coefficient to realize the design of the profit distribution algorithm for the power supply chain. The experimental results show that the algorithm has low relative error rate, high precision, and short time cost of profit distribution coefficient calculation.

Hart–Mas-Colell consistency and the core in convex games

This paper formally introduces Hart–Mas-Colell consistency for general (possibly multi-valued) solutions for cooperative games with transferable utility. This notion is used to axiomatically characterize the core on the domain of convex games. Moreover, we characterize all nonempty solutions satisfying individual rationality, anonymity, scale covariance, superadditivity, weak Hart–Mas-Colell consistency, and converse Hart–Mas-Colell consistency. This family consists of (a) the Shapley value, (b) all homothetic images of the core with the Shapley value as center of homothety and with positive ratios of homothety not larger than one, and (c) their relative interiors.

Application of Choquet Integral-Fuzzy Measures for Aggregating Customers’ Satisfaction

Choquet integral is a type of aggregation operator that is commonly used to aggregate the interrelated information. Nowadays, this operator has been successfully embedded with fuzzy measures in solving various evaluation problems. Inspired from this new development, this paper aims to introduce a combined Choquet integral-fuzzy measures (CI-FM) operator that uses the Shapley value standard and interaction index to deal with the interactions between elements of information. The proposed operator takes into account not only the importance of elements or their ordered positions but also the interaction among criteria during the evaluation process. A case of customers’ satisfaction over two fast restaurants in Malaysia is presented to illustrate the application of the proposed aggregation operator. Based on three customers’ satisfaction criteria, restaurant 1 and restaurant 2 received CI-FM scores of 0.711011 and 0.704945, respectively. Interestingly, the criterion “services” constantly received the highest rating across both restaurants. In addition, the proposed aggregation operator successfully identified which restaurant is superior in the eyes of customers. Finally, this study offers some research ideas for the future.