Constant Weight Analysis And Variable Weight Theory

In this paper, we have discussed weight vectors w =(w1 ……,wm) problem in multi-objective decision-making. And discuss two different type of the problem. I.e. the first case vv = c1,, where c1 ∈ R1 and c = (c1,……,cM) is constant, the second case is that w1 =w1(x1,x2,……,xm), where w= (w1(x1,x2,……,xm),w2(x1,x2,……,xm),……,wn(x1,x2,……,xm), and w1 is a function of the multi-objective decision-making vectors x = (x1 , ……,xn).In chapter l,we put forward the problem of multi-objective decision-making, the definition of multi-objective decision-making solution, and the concept of weight that is correlative with the multi-objective decision-making.Chapter 2 and Chapter 3 are devoted to the constant weight problem.In chapter 2, we find the weight vectors of multi-objective decision-making problem by using the p-series method, and put the idea of hierarchy onto the ascertainment of function power .To solve the MOP problem is changed into plot the problem of hierarchical multi-objective problems LSP. Then using p -series method to solve the single-objective function, if the result is not the ideal weakly Pareto optima to decision-maker. We change the primary power of the multi-objective optima .to interactive and yield to one solution.In chapter 3,we put forward one method to solve the multi-objective decision-making problem on the ground that the decider has provided the feasible region and constraint set of each sub-objective function. We can check out the same number Pareto solutions of multi-objective programming problem as the number of multi-objective vectors .Use the Pareto solutions and Lagrange function, we can get the power vector.In chapter 4, we discuss the variable weight principle. We improve the theory of variable weight principle based on the previous documents, discuss the case of penalty/incentive variable weights, penalty/incentive state variable weights, and penalty/incentive balance function. At last we give the sufficient and necessary conditions that ∑g(x1) and ∏g(x1) are balance functions.