Entropy Models And Their Application In The Multi-attribute Decision Making Based On Fuzzy Information

Due to the complexity of the real world, various decision making problems in real world is full of different kinds of uncertainties, where the uncertain information can mainly be expressed as interval fuzzy numbers, triangular fuzzy numbers or trapezoidal fuzzy numbers, intuitionistic fuzzy numbers, and interval intuitionistic fuzzy numbers et al. Actually, these uncertain information can reflect the basic aspects of real things, however, they also bring us the complexity of real decision making problems in some extent, therefore, research on how to obtain some reasonable decision methods based on these different types of uncertain information is an important content.Since N.Wiener and C.E.Shannon created the information theory and defined the information entropy as the uncertainty of signals of signal source in the communication process, the entropy has been a best measure to measure the uncertainties, and has been widely used in the fields of natural science and social science. However, as the particularity of entropy and the complexity of different types of uncertain information, it comes to be a new trend in decision making theory and entropy theory for the application of entropy theory in the fields of uncertain decision making. And in this paper, we have a try about the mentioned problem that can be summarized as follows:(1) In this paper, the mentioned types of uncertain information's entropy theory, methods and their applications are discussed based on the introductions of these uncertain information, and some new approaches to deal with uncertain decision making problems is provide.(2) Some new computing methods and comparing possibility degree of intuitionistic fuzzy numbers are defined on the basis of the differences and relations among vague sets, intuitionistic fuzzy sets and interval valued intuitionistic fuzzy sets. Combined with the entropy theory and relative entropy theory, a new method for dealing with multi-attribute group decision making under intuitionistic fuzzy information is proposed, which also extend the applying fields of entropy. (3) The intuitionistic fuzzy order of interval fuzzy numbers is proposed on the basis of the characteristic of interval fuzzy numbers and intuitionistic fuzzy numbers, therefore, a new comparing method of interval numbers is introduced. Consider existence knowledge about information entropy, a new uncertain decision making method based on interval valued fuzzy information and intuitionistic fuzzy entropy is proposed. The numerical example of this method shows its feasibility and effectively.