Research On Uncertainty Multi-attribute Decision-making Method Based On Soft Set Theory

With the continuous progress of the society and development of science and technology, human's understands of the objective world being more and more deep, and the activities of human society are becoming more and more diversified, colorful and complicated. As a basic human activity, decisions generally exist in every aspect of society and daily life; the size of the decision problem is becoming bigger, so more factors need to be taken into consideration and decision goal is becoming more and more complex. Decision-making methods based on a single criterion are hard to meet the needs of social development in many cases; Multi-Criteria Decision-Making has become a focus research field of many experts and scholars. As an important branch of Multi-Criteria Decision-Making, Multiple-Attribute Decision-Making (MADM) has important application value and broad application fields. However MADM itself is faced with a lot of problems which need to be further studied and settled. This paper focus on the uncertainty led by such matters as participants' lacking of prior knowledge, unable to acquiring data accurately, difficult to quantify attribute values and different knowledge-background and so on, then tries to make a further study of the uncertain MADM problem.This paper makes an in-depth analysis about the characteristic of the uncertain MADM problem. On the basis of retrieving domestic and foreign relevant results, the frontier theory, and the latest technology, this paper gives full play to the advantage of subject crossing, and then integrates the soft set theory, multi-attribute decision making theory, group decision theory with each other. Under the guidance of system concept, together with the management, behavior science, statistics, set theory, information science and other related knowledge, the research mainly focuses on the expression and information processing by the Soft Set theory, Soft Set attribute reduction, the decision model based on Soft Set and the group decision-making model based on Soft Set, and finally puts forward a set of MADM model and group-decision method based on Soft Set. In the process of the research, in order to verify the feasibility, validity, rationality, and applicability of such methods and models, this paper adopts the method of example computation, mathematical derivation to analyze the results. The main research work can be summarized as follows:Firstly, the paper systematically studies the expression and processing of uncertainty information by Soft Set. After introducing the classic soft set definition, representation and basic operation which putted by Molodtsov, the expansion research is summarized, including Fuzzy Soft Set, Intuitionist Fuzzy Soft Set, Interval-Value Fuzzy Soft Set, Vague Soft Set etc. The paper expounds Parameterization characteristics of the Soft Set, and described the rationality and validity when soft sets used as an uncertainty information expression, and the processing tools, by combining the Gradualness, Gramilarity and Parameterization characteristics.Secondly, the paper studies the attribute reduction problem of Soft Set. Attribute reduction is very important in MADM. In principle, MADM requires minimum attribute set, and this also can simplify the calculation for complex decision parameter reduction. By combing parameter reduction of Soft Set research results, the paper puts forward a new heuristic algorithm based on the classical Soft Set, which improves the efficiency of parameter reduction calculation. Furthermore, by combining with rough set, the paper proposes the parameter reduction of Soft Set method based on similarity relations.Thirdly, this paper proposes a unified decision method based on Soft Set theory. With the continuous development of the soft set theory, the decision-making method based on Choice Value is also in constant evolution, based on Classical Soft Set, Fuzzy Soft Set and Vague Soft Set, different decision-making theory and methods appear. At the same time there are a lot of application achievements constantly emerges. By analyzing the essence of these decision-making methods, this paper establishes a unified decision rules and decision making method of Soft Sets, explores a more consistent approach for decision-making method of Soft Sets, widens the research channel and ideals of the soft set applied to the decision-making problem.Lastly, this paper studies a Group Decision-Making method based on soft set theory. In many fields such as society, economy, management and the project, Group Decision-Making has a very wide application range. By taking advantage of information carrier and processing functions of Soft Set, this article uses Soft Set as a group decision tool for preference aggregation, proposes a Soft Set Group Decision method based on Satisfaction Theory, and different knowledge-background decision participants' Group Decision methods. The results explore the basic thinking and methods of Soft Set Group Decision; widen the application field of Soft Set.