Abstract:
A situation in which a finite set of players can obtain certain grey payoffs by cooperation can be described by a cooperative grey game. In this paper, we consider some grey division rules, called the grey equal surplus sharing solutions. Further, we focus on a class of the grey equal surplus sharing solutions consisting of all convex combinations of these solutions. Finally, an application of Operations Research (OR) situations is given.
Machine summary:
com On the Grey Equal Surplus Sharing Solutions Uzeyir Alper Yilmaz a, Sırma Zeynep Alparslan Goka,*, Mustafa Ekici b and Osman Palanci a a Süleyman Demirel University, Isparta, Turkey b Usak University, Usak, Turkey Abstract A situation in which a finite set of players can obtain certain grey payoffs by cooperation can be described by acooperative grey game.
Cooperative games; Grey uncertainty; Equal surplus sharing solutions; Facility location situations.
Since these games are defined by using special substraction operator, we apply equal surplus sharing solutions to facility grey situations.
The CIS-value, the ENSC-value, and the ED-solution are defined by as follows: (View the image of this page)A grey number that a number whose exact value is known but a range within that the value lies is known.
But, (View the image of this page) A cooperative grey game is an ordered pair < N , w' > , where N = {1,K, n} is the set of players, and w' : 2N ® G(R ) is the characteristic function such that w' (Æ) Î[0,0] , grey payoff function w' (S )Î[ A , A ] S S refers to the value of the grey expectation benefit belonging to a coalition S Î 2N , where AS and AS represent possible maximum and minimum profits of the coalition S.
The grey equal surplus sharing solutions In this section, we introduce some game-theoretic solutions by using grey calculus which are inspired by van den Brink and Funaki (2009).
1. (View the image of this page) In this paper we propose different equal surplus sharing solutions by using grey numbers.