Aggregation Of Intuitionistic Fuzzy Information And Its Applications In Decision Making

In this dissertation, we will give some extensions and generalizations of Xu’s in-tuitionistic fuzzy aggregation operators. We will also propose some new intuitionistic fuzzy prioritized aggregation operators for aggregating intuitionistic fuzzy informa-tion:intuitionistic fuzzy prioritized "and" operator and intuitionistic fuzzy prioritized "or" operator. We shall develop some new (weighted) cosine similarity measures between intuitionistic fuzzy sets and we show that the proposed (weighted) cosine similarity measures are more flexible in the process of decision making. We will in-vestigate intuitionistic fuzzy relations from new viewpoints. Relatedness measures of intuitionistic fuzzy set are investigated, these relatedness measures of intuitionis-tic fuzzy sets are applied for medical diagnosis. We will investigate the intuitionistic fuzzy equivalence relations from new viewpoints. We will see that unlike the chain structure of cut relations of fuzzy equivalence relations, there are two different struc-tures about the a-cut relations of intuitionistic fuzzy equivalence relations. We will investigate the chain structure and the partially ordered structure of the a-cut relations of intuitionistic fuzzy equivalence relations.In chapter1, we give some preliminaries. We give some basic concepts such as intuitionistic fuzzy sets, intuitionistic fuzzy values and also give some related opera-tions. We investigate some ranking methods for intuitionistic fuzzy values. We also introduce Xu’s intuitionistic fuzzy aggregation operators.In chapter2, we will introduce a family of extended intuitionistic fuzzy ag-gregation operators:E-IFWAN,ω, E-IFOWAH,ω, E-IFHAN,ω’ω, E-IFWGN,ω, E-IFOWGN,ω, and E-IFHGN,ω’ω. It is disclosed that Xu’s intuitionistic fuzzy aggre-gation operators IFWA, IFOWA, IFHA, IFWG, IFOWG and IFHG are special cases (i.e. when N is the standard IF negator) of the corresponding extended intuitionistic fuzzy aggregation operators. We will also define intuitionistic fuzzy weight vector and give some related operation laws, then, we introduce several kinds of intuition- istic fuzzy aggregation operators with respect to intuitionistic fuzzy weight vector(s). These operators are generalization of Xu’s intuitionistic fuzzy aggregation operators.In chapter3, we will propose some new intuitionistic fuzzy prioritized aggre-gation operators for aggregating intuitionistic fuzzy information:intuitionistic fuzzy prioritized "and" operator and intuitionistic fuzzy prioritized "or" operator. According to Yager’s prioritized aggregation operators, the importance weight of a lower priority attribute is based on its satisfaction to the higher priority attributes, and the impor-tance weights of the attributes are real numbers. It is different with Yager’s prioritized aggregation operators, the importance weights of the attributes are intuitionistic fuzzy values.In chapter4, we investigate the molds and orders of intuitionistic fuzzy values. We develop a new (weighted) cosine similarity measure between intuitionistic fuzzy sets and we show that the proposed (weighted) cosine similarity measure is more flex-ible in the process of decision making. The projection method was first proposed by Wang(1999). We will give a new projection formula for intuitionistic fuzzy multiple attribute decision making.In chapter5, we investigate intuitionistic fuzzy relations, intuitionistic fuzzy sim-ilarity relations, intuitionistic fuzzy equivalence relations and some properties. At the same time we give applications of intuitionistic fuzzy equivalence relations to clus-tering method. We investigate some relatedness measures of intuitionistic fuzzy sets. These relatedness measures of intuitionistic fuzzy sets are applied for medical diag-nosis.