An Application of Cooperative Grey Games to Post-Disaster Housing Problem

This paper shows that cooperative grey game theory can help us to establish a fair cost share between private organizations for supporting the temporary housing problem by using facility location games under uncertainty. Temporary accommodation may be a method that ought to get started before the tragedy happens, as a preventative pre-planning. In spite of being temporary constructions, the housing buildings are one of the most essential parts to produce in emergency situations, to contribute to the reconstruction and to recover better. Our study is based on a default earthquake in Izmir of western Turkey. A number of tents are being built in the following three cities, Aydin, Usak, and Balikesir near Izmir as illustrated in Figure 1. Two companies are selected, one is local and another is foreign to distribute the tents in a fair way between the three cities. For this purpose, we use cooperative grey game theory to help us to define a fair cost allocation between private organizations for supporting the housing problem by using facility location games under uncertainty

On the Grey Equal Surplus Sharing Solutions

The grey uncertainty is a new methodology focusing on the study of problems involving small samples and poor information. It deals with uncertain systems with partially known information through generating, excavating, and extracting useful information from what is available. This paper focuses some division solutions for cooperative games, called the equal surplus sharing solutions. 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, namely the equal surplus sharing grey solutions. Further, we focus on a class of equal surplus sharing grey solutions consisting of all convex combinations of these solutions. An application from Operations Research (OR) situations is also given

Cooperative Grey Games: Grey Solutions and an Optimization Algorithm

In this paper, some set-valued solutions using grey payoffs, namely, the grey core, the grey dominance core and the grey stable sets for cooperative grey games, are introduced and studied. Our main results contained are relations between the grey core, the grey dominance core and the grey stable sets of such a game. Moreover, we present a linear programming (LP) problem for the grey core. On the other hand, we suggest a corresponding optimization-basedalgorithm finding the grey core element of a cooperative grey game. Finally, we give an application how cooperative grey game theory can be used to model users' behaviors in various multimedia social networks. The paper ends with aconclusion and an outlook to future investigations