Research Of Multiple Attribute Decision Making Based On Intuitionistic Multiplicative Information

Multiple-attribute decision making is an important branch of the modern decision science. Its theories and methods are applied widely in many fields. Due to the increasing complexity of the socio-economic environment and the lack of knowledge or data about the problem domain, decision makers often use the intuitionistic multiplicative preference relation to express their preference information about the alternatives or criteria. In this paper, we study the multiple attribute decision making based on intuitionistic multiplicative information. The detailed arrangement stands out as follows:1. In this paper, some new operational laws of intuitionistic multiplicative numbers(IMNs) are defined, which can guarantee the closedness of operation. Some aggregation operators are proposed based on these operational laws, including intuitionistic multiplicative weighted averaging(IMWA) operator and intuitionistic multiplicative weighted geometric(IMWG) operator. Then, desirable properties of aggregation operators are also expatiated detailedly. Finally, a group decision making method is presented based on intuitionistic multiplicative preference relation, and the solution process of this decision making method is shown in detail through a numerical example.2. Interval-valued intuitionistic multiplicative set is presented, which is regarded as extension to intuitionistic multiplicative set. Interval-valued intuitionistic multiplicative number is defined for convenience of expression; the operational laws of interval-valued intuitionistic multiplicative numbers are given. The score function and accuracy function of interval-valued intuitionistic multiplicative numbers are defined, and based on these two functions, a method for ranking interval-valued intuitionistic multiplicative numbers is presented. Interval-valued intuitionistic multiplicative weighted averaging(IIMWA) operator and interval-valued intuitionistic multiplicative weighted geometric(IIMWG) operator are proposed. Furthermore, a method of multiple attribute decision making with preference information in the form of interval-valued intuitionistic multiplicative number is proposed, and a numerical example is used to illustrate the proposed method.