| The scope of study and application of mathematics has extended from accuracy into fuzzy since Prof. Zadeh established fuzzy sets theory in 1965. Because an intuitionistic fuzzy sets, which is introduced by Atanassov in 1983, processes the information of membership and non-membership, it provides more choices for the attribute description of an object and has stonger ability to express uncertainty than Zadeh's fuzzy sets. It gains extensive attention from the academic circles and the circles of engineering and technology. This dissertation will study the problems of multiattribute fuzzy decision-making and fuzzy reasoning by means of intuitionistic fuzzy sets and will establish a series of methods for solving above problems. The main results, obtained in this dissertation, may be summarized as follows:1. Chapter 2 mainly discusses intuitionistic fuzzy implication operators. First, the Co-D-P conditions of fuzzy complication operators(FCO) and their relationship are discussed. Further, the expressions of 32 FCOs are given. The FCOs'situation of satisfying the Co-D-P conditions is listed. Finally, the expressions of 32 intuitionistic fuzzy implication operators(IFIO) are presented according to the definition of fuzzy implication operators, fuzzy coimplication operators and aggregation operators. Its'situation of satisfying the properties, which are in common use, is disscussed in details.2. In chapter 3, several methods of intuitionistic fuzzy reasoning are considered. In recent years, it is because the intuitionistic fuzzy sets can effectively solve the uncertainty problem that intuitionistic fuzzy reasoning is followed with interest. Firstly, the constructive theory of intuitionistic fuzzy t-norms and t-conorms by t-norms and t-conorms on interval [0,1] is given. Then the reasonableness of intuitionistic compositional rule of inference (ICRI) is verified. Secondly, the inclusion degree and similarity measures of intuitionistic fuzzy sets are defined and their computing formulae are established by means of fuzzy implication operators. Then a method of intuitionistic fuzzy reasoning based on inclusion degree and similarity measure is proposed. The process of reasoning is illustrated with an example. Finally, an intuitionistic fuzzy reasoning method based on intuitionistic fuzzy production rules is proposed. In order to use the method for reasoning, two intuitionistic fuzzy matching functions, one is based on similarity measure and the other is based on similarity and dissimilarity measures, are given. Theefficiency of the two functions is illustrated by comparing with the ordinary matching function.3. Chapter 4 mainly discusses several methods and applications of intuitionistic multi-attribute fuzzy decision-making. Firstly, possible degree of intuitionistic fuzzy sets is defined. On the basis of it, a method on ordering for intuitionistic fuzzy sets is given. Secondly, the intuitionistic multiattribute fuzzy decision-making methods based on possible degree under two conditions: attribute weighting is known and attribute weighting is absolutely unknown,are discussed. Then,three intuitionistic multiattribute fuzzy decision-making methods with only partial attribute weighting information are proposed" they are optimal model of single object, intuitionistic multiattribute fuzzy decision-making method based on dissimilarity measure and possible degree and intuitionistic multiattribute fuzzy decision-making method on the basis of score function. Finally, an intuitionistic multiattribute fuzzy decision-making method based on intuitionistic fuzzy reasoning is put forward. By this method, decision-making information is turned into intuitionistic reasoning process. Thus, the method makes decision-making process simpler and makes its realization on computer easier. Every method is illustrated by examples in this part. |
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