The Study Of Bipolar-valued Fuzzy Set And Its Application

For descripting and resolving uncertainty and fuzziness in practical prob-lems, probability theory, fuzzy set theory, rough set theory, soft set theory have attracted widely attention by many scholars which has been got many theo-retical results and applied in financial and medical fields extensively. However, mostly theoretical results are in static status. But information is changing as time goes on, so dynamic bipolar-valued fuzzy soft sets, method of determining the weight of time and bipolar-valued rough model based on dominance rela-tion are investigated in this paper. The thesis mainly includes the following works:(1) The development of fuzzy set, soft set, bipolar-valued fuzzy set and theoretical results of intuitionsitic fuzzy set that taking time into it are intro-duced. Then, current state of rough set models in the domestic and foreign are reviewed.(2) After summarizing the concepts of fuzzy set, soft set, bipolar-valued fuzzy set, and discussing the reality situation that decision making information changing with time, the concept of dynamic bipolar-valued fuzzy soft set is defined, relative operations and properties are discussed, too. The influence of time on decision making questions are investigated from two different fields, and these changes are transform into weight which applied to decision making. So, the best decision is made with aggregation operators which the dynamic bipolar-value fuzzy soft sets have been aggregated into collective fuzzy soft set and level soft set theory. At last, several examples are given.(3) Based on the theories of the dominance relation rough set model and interval-valued information systems, the bipolar-valued information system is put forward, taking dominance relation into bipolar-valued information sys-tem and a new king of multi-attributes decision making is provide. Taking into account granular computing theory and attribute types, we extend single granulation to two-granulation rough set and define a new dominance degree formula. By calculating the whole dominance degree with aggregation thought and ranking them, the best choice can be made.