Interval-valued Intuitionistic Normal Fuzzy Aggregation Operators And Their Application To Multiple Attribute Decision Making

The domestic and foreign scholars have studied on fuzzy multiple attribute decision making (FMADM) type of the triangular fuzzy numbers, trapezoidal fuzzy numbers and intuitionistic fuzzy numbers. But in real life a lot of phenomena follow Gaussian distributions. The real decision making information can be more objectively reflected with normal fuzzy numbers. Although some scholars has put forward the concept of normal fuzzy numbers, but it has not been reported to describe the multiple attribute decision making information with interval-valued intuitionistic normal fuzzy numbers (IVINFNS). The thorough and comprehensive studies on IVINFNS both enrich FMADM theory and provide the scientific theory for solving complex problems. It improves the validity and feasibility of decision-making.Firstly, the author presents the background and the current research situation and the relevant theoretical knowledge of IVINFNS.Secondly, some kinds of aggregation operators are preliminary researched which include IVINFN weighted arithmetic average (IVINFN-WAA) operator, IVINFN ordered weighted arithmetic average (IVINFN-OWA) operator, IVINFN hybrid weighted arithmetic average (IVINFN-HWA) operator, IVINFN weighted geometric average (IVINFN-WGA) operator, IVINFN ordered weighted geometric average operator (IVINFN-OWGA), IVINFN hybrid weighted geometric average (IVINFN-HWGA) operator. The properties of the operators are discussed.Finally, for FMADM, in which the attribute weight information is known and the attribute value information is IVINFNS, the score function and accurate function of IVINFNS are put forward based on mean and standard deviation which are used for ranking IVINFNS. An ensample is illustrated to show the method is feasible and effective. Aiming at FMADM, in which the attribute weight information is unknown and the attribute value information is IVINFNS, we define the distance of IVINFNS and calculated weight with maximum deviation. The example is given to show the method is feasible and effective.