Fuzzy Optimizing Multi-Dimensional Multi-Objective Dynamic Programming And Its Application For Resources Allocation

In recent years, with social economic development, resources allocation problem has been extended to every social area and become the important contents of management decision. The decision is a kind of alternative behavior existing in politics, economy, science and technology and daily life. About the decision, Simon, the Nobel prize winner, said:" the management is a decision". This means the core of the management is the decision. The decision is a kind of behavior. The most simple choice is an answer of Yes or No. But in real life, this kind of problem is seldom, and usually hard to make a judgment to every kind of indefinite and fuzzy factor, especially in the aspects of the importance of describing every kind of alternative projects opposing to the final decision, which is hard to be depicted with accurate figures.The Fuzzy Optimization Programming originated from the 70's of 20 century and based on the Fuzzy Sets Theory provided the valid method and technique for this kind of problem. When the deciders believe some probability distribution is incorrect, or the deciders have no clear boundary information, or some information are related to human language or behavior, or some information can't be defined and expressed clearly because of human knowledge and cognition being limited, and etc,whose behaviors and factors can't be depicted actually with optimization programming of actual mathematic and random optimization programming based probability theory, we can use Fuzzy Optimization Programming to resolve these problems. Now, Fuzzy Optimization Programming has been applied widely, and approached to many areas of the natural science and the social science. The scholars of the many areas have made the extensive research to Fuzzy Optimization Programming when they apply to and practice it, which develop Fuzzy Optimization Programming.The multi-stage decision problem is a kind of active process, which can be divided into many related stages, and we need make decision in each stage. This decision not only decides the profits of this stage, but also decides the beginning state of the next stage. The multi-stage decision problem is to get a strategy, making the total profit of each stage is optimal. If there is only a quantitative assessment target, the allocation problem of the limited resources can use the dynamic of the classic optimal theory to resolve these problems. But, if there are many quantitative assessment objectives or many with both quantitative and qualitative objectives, the general dynamic planning method can't resolve them. One of the difficulties of the multi-objective decision is that the objectives can't be measured with one norm, which is said that these objectives have not uniform norm. While resolving this kind of problem, the author of this article tries to combine Fuzzy Optimization Programming with dynamic planning optima theory. So before solution, we should turn quantitative or qualitative index into the index can be measured with uniformed norm through relative membership degree of definitive index number. Settling a quantity of complex qualitative factor, we can use the person's experience and knowledge to do two elements comparison and quantification of the importance and superiority. And according to our country language and thought habits, reciprocal principle will be the norm of two elements comparison. The two elements comparison in decisions has two steps: quality and quantity. The fore step do the qualitative arrangement in decisions (factors) to get a qualitative arrangement in the condition of uniform, and the second step is to decide relative membership degree of the decision which is relative to superiority. According to effective demand of resources allocation, usually the problems needed to be resolved are not only one dimension, but multi-dimension, for this reason the theme expand the theory of one dimensional fuzzy dynamic planning to multi-dimension and built the model. Currently there are some methods of resolving the multi-dimensional dynamic planni...