Study On The Rules Of Alternative Selection In Group Decision Mking

Group decision making is an important branch of Decision Science. It plays an important role in modern politics,management,military affairs,science,technology and so on. Since the "Impossibility Theorems" was proposed by K.J.Arrow in 1950s,as the important method of modern decision,the research of group decision making theory and methods is attached more important to day and day.There are four chapters work on it.In the first chapter,we mainly introduce the origin and current research situations of group decision making problems.Furthermore,the main contribution of this paper is also listed.In the second chapter,we introduce a new conception called t~*—optimal integral difference solution for group decision making problems,and we show that t~*—optimal integral difference solution equals to the optimal solution to solve another mathematical programming problem.Besides,the relations between t~*-optimal integral difference solution and s*-optimal equilibrium solution is also discussed.In the third chapter,a new kind of decision making rule which is improved fromαk-Major rule known as ,βm-Major rule is given in this paper. It considers the personal weight in order to collect the group presence,and some coefficients of correlation become more extensive. It is proved that the rule satisfies four Axoims of Arrows Axoim. Besides,the properties of group optimal solution based on this rule is also discussed. In the last chapter,we make further research on the penalty mark methods in group decision making and give some properties that it satisfies.