Hesitant Fuzzy Set And Picture Fuzzy Set With Their Application Research

There are variety of uncertain problems in the real world. Some of them can not be dealt effectively with the existing tools, such as probability theory,fuzzy sets, interval mathematics and so on. In order to cope with the practical needs, Torra, Cuong and Pawlak proposed hesitant fuzzy sets, Picture fuzzy sets and rough sets respectively. All of them are new tools to deal with uncertain phenomenon. A hesitant fuzzy set can be regarded as a generalization of a fuzzy set, which allows each member has a plurality of memberships. As a result, it is appropriate to describe the state of hesitation when it is difficult to make decisions.Picture fuzzy sets can also be viewed as a generalization of fuzzy sets, each of their members is described by four values in [0,1], corresponding to four kinds of attitudes of decision makers: yes, neutrality, against and abstained. As a result,it depicts the voting vividly. The rough set is based on the equivalence relation to generate division, then it approximates any given set by the upper and lower approximation operators. Compared with the fuzzy set, hesitant fuzzy sets and Picture fuzzy sets can carry more information. So they can be more fully describe the object, and facilitate the decision maker to make more rational judgments.The research on hesitant fuzzy set mainly includes similarity measures, distances,aggregation operators and their application in multiple attribute decision making.Meanwhile, Picture fuzzy sets have just been proposed, so there is no related research yet.Although the studies of hesitant fuzzy sets and rough sets have made many achievements, there are still many aspects need further development and improvement. For the Picture fuzzy set, the reclamation of the space is larger. Based on the previous results, we continue to discuss the theory and application of hesitant fuzzy sets, Picture fuzzy sets and rough sets. The detailed arrangement of this dissertation stands out as follows:(1) Study on some dual hesitant fuzzy aggregation operators and their application in multiple decision making. In order to capture the hidden relationships among various attributes, we introduce the Choquet integral operator into the dual hesitant fuzzy set and construct a dual hesitant fuzzy Choquet operator(DHFCOA). We further extend the DHFCOA to the generalized dual hesitant fuzzy Choquet average order operator(GDHFCOA), then study on the corresponding properties of the operator. Furthermore, we discuss the relations between the new operators and existing operators. Based on GDHFCOA, we propose a new method to solve multiple attribute decision making problems. After the parameter is introduced, decision becomes more flexible and decision makers can select the appropriate parameters to meet their different needs.(2) Study on some hesitant triangular fuzzy aggregation operators and their application in multiple attribute decision making. In real decision problems, data are often not independent, but related to each other. Therefore, we combine the Bonferroni operator and the Choquet integral operator to construct some new hesitate triangular fuzzy operators, such as the hesitant triangular fuzzy weighted Bonferroni operator, the hesitant triangular fuzzy weighted geometric Bonferroni operator, the hesitant triangular fuzzy Choquet weighted Bonferroni operator and so on. We discuss the properties of these new operators and their relationships.Using the proposed operators, we propose a method for multiple attribute decision making. Then we give an example to verify its effectiveness and compare it with the existing methods.(3) Study on Picture fuzzy sets. From the viewpoint of probability, we define the basic operations of Picture fuzzy elements and then construct some Picture fuzzy aggregation operators containing Picture fuzzy weighted average operators,Picture fuzzy weighted geometric operators and Picture fuzzy hybrid operators.Next, we discuss the properties and relations of these operators and propose a method for multiple attribute decision making. We also give an illustrative example to show the practicality and superiority of the method.(4) Research on incremental attribute reduction algorithm of rough sets. For dynamic changes of the object set, we establish incremental formulas to update entropies. Then we put forward a new algorithm for incremental reduction.