Cooperative Grey Games: An Application on Transportation Situations

Introduction

Game theory is a modern section of decision theory, having various applications in socio-economic, political, organizational, ecological processes. The subject of this study is conflict and cooperation. The situations in which the interests of participants collide. Essentially all aspects of human activities affect to some extent the interests of different parties and therefore belong to the field of game theory. However, at present methods theory of games in real control procedures (primarily in the construction of organizational systems, the formation of economic mechanism and procedures political negotiations, socio-economic planning and forecasting) are not widely used. This is due to both the lack of theoretical and game training of management experts, and the fact that classic game models are too abstract and difficult to adapt to real processes of management and decision-making. Currently, various sections of the theory of games are included in the programs compulsory and special courses of many higher educational institutions. The study and teaching of this discipline entail serious difficulties, associated with a lack of necessary literature. This report is an exposition of transportation situations under grey games. By and large, makers and retailers are going to minimize their costs or maximizing their benefits. Makers and retailers can shape coalitions to get however much as possible. Constitutionally, a transportation situation comprises two sets of agents called makers and retailers which deliver/request merchandises. The transport of the merchandise from the makers to the retailers must be beneficial. Thusly, the primary goal is to transport the products from the makers to the retailers at greatest benefit (Aparicio et al. 2010). Such a participation can happen in transportation situations (Aziz et al. 2014; Frisk et al. 2010; Zener and Ergun 2008; Snchez-Soriano 2006; Snchez-Soriano et al. 2002, 2001; Soons 2011; Theys et al. 2008). Be that as it may, when the agents included concurring on a coalition, the subject of conveying the acquired benefit or expenses among the specialists emerges. The cooperative game theory is broadly utilized on intriguing sharing cost/benefit issues in numerous regions of Operational Research, for example, association, steering, planning, creation, stock, transportation, and so forth. (See Borm et al. 2001 for a survey on Operational Research Games). Transportation games are inspected in Sanchez-Soriano et al. (2001). Our paper studies the core of the transportation games and illustrates the non-emptiness of the core of transportation games. Also, Sanchez-Soriano et al. (2001) give a few outcomes about the connection between the core and dual optimal solutions of the transportation issue. The paper Sanchez-Soriano (2003) presents a specially appointed solution idea for transportation games called the pairwise egalitarian solution. In the continuation, the article Sanchez-Soriano (2006) looks at the relationship between the pairwise solutions and the core of transportation games. Besides, Sanchez-Soriano (2006) demonstrates that each core component of a transportation game is contained in a pairwise solution with a particular weight framework. In the traditional way to deal with the issue, the parameters are precisely known. In this case, the issue is completely understood utilizing the results of Sanchez-Soriano et al. (2001). However, in real-life transportation situations, issue parameters are not known precisely. Agents considering cooperation can rather figure lower and upper limits on the result of their cooperation. In this manner, we have a transportation interval situation and to solve the related sharing benefit issues, we require suitable sets of solutions. To deal with transportation situations with interval information, the theory of cooperative interval games is appropriate (Alparslan Gok et al. 2008, 2009a, b). The per-user is alluded to Branzei et al. (2010a, b) for a short study on cooperative solution concepts and for a guide for utilizing interval solutions when uncertainty about information is deleted Alparslan Gok et al. 2011). This paper broadens the examination of two-sided transportation situations (Sanchez-Soriano et al. 2001). Furthermore, their related cooperative games to a setting with interval information, i.e., the benefit b_ij of goods j by a maker i, the generation p_i of products of the maker i, and the request q_i of goods retailer j, in the transportation model now lie in intervals of genuine numbers acquired by forecasting their values from the viewpoint of a specialist see. This report consists of five sections which as follows: In the first section, we will review basic concepts and definitions from grey numbers and game theory. In the second section, we consider special classes of cooperative grey games, classification and mathematical models of decision-making problems. The third section, we study transportation interval situations, where we present transportation interval situations and related games, we will give some properties of the grey Shapley value on transportation interval situations and we use transportation situations dealing with the application of scientific methods for making a decision, and especially to the allocation of connections and routing games. Subsequent sections show our new results. In the fourth section, we introduce the transportation grey situations and related games, we will calculate both of the grey Shapley value and the core of the transportation grey game. The main purpose of transportation situations is to provide a rational basis for decisions making in the absence of complete information, because the systems composed of human, machine, and procedures may do not have complete information.