The Research Of Decision-Making Method Based On Decision-Theoretic Rough Sets Under The Fuzzy Environment

When people want to make a reasonalbe decision, they face many challenges to influence their decisions, e.g. the complexity and the dynamics of decision environment, the limitation of knowledge of the decision makers and so on. In recent years, with the rapid development and application of information technologies and computer science, it provides a new idea to solve these types of uncertainty and complex problems for decision makers. As a new method to solve uncertainty decision problems, decision-theoretic rough sets consider the influence of decision risk to the result based on Bayesian decision process. It can serve to help the decision-making.In the viewpoint of the practical semantics, we introduce the fuzzy uncertainty formation into the decision-theoretic rough set model. On the one hand, it extends the application ranges of decision-theoretic rough sets. On the other hand, it also provides a new solution for determining the value of loss function presented in decision-theoretic rough sets. In the light of the research results exsited in the available decision theory and rough set theory, this paper chooses four typical fuzzy formations to individually discuss the models and decision-making methods based on decision-theoretic rough sets, including interval-valued, triangular fuzzy number, linguistic variable and hesitant fuzzy number.Firstly, considering the values of losses used in decision-theoretic eough sets with intervals, we propose a basic model of interval-valued decision-theoretic rough sets. In the frame of interval-valued decision-theoretic rough sets, we focus on deriving decision rules with the aid of the two conventional methods, i.e., a certain ranking method and a degree of possibility ranking method, respectively. Following the above analysis, we further propose an optimization method for interval-valued decision-theoretic rough sets. By the comparsion study of experimental analysis, the criteria for choosing a suitable analysis method to interval-valued decision-theoretic rough sets are generated.Secondly, considering the values of losses used in decision-theoretic eough sets with triangular fuzzy numbes, we propose a basic model of triangular fuzzy decision-theroetic rough sets. Ranking the expected loss with triangular fuzzy number is analyzed and decision rules are derived. With the aid of multiple attribute group decision making, we further design an algorithm to determine the values of losses used in triangular fuzzy decision-theroetic rough sets. It can promote the applications of triangular fuzzy decision-theroetic rough sets. Meanwhile, we optimize the scales of the linguistic variables with the use of particle swarm optimization, which evolves the negotiation process of experts and produces higher values of consistency.Thirdly, we introduce the linguistic variable into decision-theoretic rough sets. Considering the two elements of conditional probability and loss function used in decision-theoretic rough sets, a series of novel models are constructed under their different value types. It can enrich the research contents of original decision-theoretic rough sets. For convenience of application, we determine the values of the two elements used in decision-theoretic rough sets with the aid of multi-attribute group decision making and design an adaptive algorithm.Finally, considering the new expression of evaluation information of hesitant fuzzy number, we introduce hesitant fuzzy number into decision-theoretic rough sets and explore its decision mechanism. In order to solve the resource allocation problems in the decision procedure, we design the associated risks of alternatives and multi-objective0-1integer programming to solve it according to the practical semantics. It greatly promotes the applications of decision-theoretic rough sets in the area of management decision.The topic of this paper is on the decision-theoretic rough sets. We introduce the fuzzy uncertainty formation into decision-theoretic rough sets and focus on discussing the loss function. Under the fuzzy environment, we study some decision-making methods based on decision-theoretic rough sets. It not only extends the application range of decision-theoretic rough sets, but also provides a new direction for decision analysis in the rough set theory.