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The article discusses the task of assessing the contribution of individual specialists working in the consulting services group. To date, such problems are solved mainly using the expert method. The article proposes a quantitative solution to this problem, based on the application of the mathematical apparatus of the theory of cooperative games and the theory of fuzzy sets

In DEA production models the technology is assumed to be implicit in the input-output data given by a set of recorded observations. DEA production games assess the benefits to different firms of pooling their resources and sharing their technology. The crisp version of this type of problems has been studied in the literature and methods to obtain stable solutions have been proposed. However, no solution approach exists when there is uncertainty in the unit output prices, a situation that can clearly occur in practice. This paper extends DEA production games to the case of fuzzy unit output prices. In that scenario the total revenue is uncertain and therefore the corresponding allocation among the players is also necessarily uncertain. A core-like solution concept is introduced for these fuzzy games, the Preference Least Core. The computational burden of obtaining allocations of the fuzzy total profit reached through cooperation that belong to the preference least core is high. However, the results presented in the paper permit us to compute the fuzzy total revenue obtained by the grand coalition and a fuzzy allocation in the preference least core by solving a single linear programming model. The application of the proposed approach is illustrated with the analysis of two cooperative production situations originated by data sets from the literature. [ABSTRACT FROM AUTHOR]

Purpose: Alliance between manufacturing and logistics industry is a new model of the joint development of the two industries. A reasonable profit allocation mechanism is the key to ensure the stable operation of the alliance, as well as to achieve the desired objectives. Based on uncertainty of alliance expected return as well as the inherent features of the alliance, this research establishes an improved model of profit allocation in manufacturing and logistics industry alliance. Design/methodology/approach: This article studies how to introduce comprehensive correction factors to improve interval Shapley value method, which is based on the fact that had been proved by exiting studies. In this study, interval Shapley value method is first applied to calculate the initial allocation of fuzzy cooperative games. Next AHP-GEM method and fuzzy comprehensive evaluation method are incorporated. Based on those results, an improved model of profit allocation is established. After that, a case study is demonstrated the practicality and feasibility of the improved model. Findings: Profit allocation is a complex issue in fuzzy cooperative games. There're impacts from partner risk sharing, collaborative effort, market competition, innovative contribution as well as resource investment. All these factors should be involved in the profit allocation, and different factors have different weight in importance. Practical implications: The new model established in the paper is more scientific and reasonable, and more in line with the actual situation. This method also provides good incentives to each enterprise to ensure the healthy and stable development of the alliance. Originality/value: Based on alliance characteristics, this paper establishes an indicator system and a new model for profit allocation in manufacturing and logistics industry alliance, using AHP-GEM method. [ABSTRACT FROM AUTHOR]

Fuzzy cooperative games with interval payoffs are discussed by defining subtraction operation for internal numbers. A Shapley function axiomatic system for fuzzy games with interval payoffs is given, which is an extension of the Shapley function axiomatic system for traditional fuzzy games. The existence and uniqueness of the given interval Shapley function are proved. Finally, a numerical example is offered to illustrate the utility of the given interval Shapley function [ABSTRACT FROM AUTHOR]