Intuitionistic Fuzzy Interaction Aggregation Operators And Their Applications To Multiple Attribute Decision Making

Multiple attribute decision making (MADM) is an important part of modern decision science, which has been widely used in many fields, such as medical diagnosis, pattern recognition, decision support System and so on. Its essence is to rank a set of alternatives and select the optimal scheme through a certain way by the existing decision-making information. The determination of weights of different attributes and information aggregation are two core issues of multiple attribute decision making. Traditional aggregation operator is the weighted arithmetic average (WAA) operator, the ordered weighted arithmetic average (OWAA) operator, the ordered weighted geometric averaging (OWGA) operator and the generalized power operator.As the increasing of the complexity of the decision system and the uncertain factors, the expression of decision-making information is becoming more and more diversified. Fuzzy numbers have become a common form of decision-making information. Intuitionistic fuzzy numbers consider the influence of the degree of membership function, the degree of non-membership and the degree of hesitate at the same time. Thus, it is more flexibility and practicability in dealing with vagueness and fuzzy information.This paper brings the idea of interactions between non-membership function and membership function of different intuitionistic fuzzy sets into the intuitionistic fuzzy environment, develops a series of intuitionistic fuzzy information aggregation operators and applies them to multiple attribute decision making, which provides a good complement to the existing works on IFSs. The main contents are as follows:(1) This paper proposes some new operational laws on intuitionistic fuzzy sets (IFSs) based on probability non-membership (PN) function operator, probability membership (PM) function operator and probability hetergeneous (PH) operator, which are constructed from the probability point of view. The geometric interpretations of these operations are given.(2) A series of intuitionistic fuzzy interaction averaging (IFIA) operators are presented based on the new operational laws for intuitionistic fuzzy sets, including the intuitionistic fuzzy weighted interaction averaging (IFWIA) operator, the intuitionistic fuzzy ordered weighted interaction averaging (IFOWIA) operator, the intuitionistic fuzzy hybrid interaction averaging (IFHIA) operator, the intuitionistic fuzzy weighted geometric interaction averaging(IFWGIA) operator, the intuitionistic fuzzy ordered weighted geometric interaction averaging (IFOWGIA) operator and the intuitionistic fuzzy hybrid geometric interaction averaging (IFHGIA) operator. The concrete expressions of these operators are obtained by derivation and some properties of these operators are investigated.(3) Considering the fuzziness of the human and their different preferences, this paper extends the above works to generalized intuitionistic fuzzy environment and presents a series of generalized intuitionistic fuzzy interaction averaging (GIFIA) operators, including the generalized intuitionistic fuzzy weighted interaction averaging (GIFWIA) operator, the generalized intuitionistic fuzzy ordered weighted interaction averaging (GIFOWIA) operator, the generalized intuitionistic fuzzy hybrid interaction averaging (GIFHIA) operator, the generalized intuitionistic fuzzy weighted geometric interaction averaging (GIFWGIA) operator, the generalized intuitionistic fuzzy ordered weighted geometric interaction averaging (GIFOWGIA) operator and the generalized intuitionistic fuzzy hybrid geometric interaction averaging (GIFHGIA) operator. The concrete expressions of these operators are obtained by derivation and some properties of these operators are investigated. Compared with the previous works, different results may be obtained with the different decision attitudes.(4) This paper applies the above investigations to multiple attribute decision making and presents the method of multiple attribute decision making based on the generalized intuitionistic fuzzy interaction averaging (GIFIA) operators, gives a systematic comparison between the results by this paper and that by the previous works. Finally, we get the score simulation images of different alternatives with different parameters λ and discuss the influence on the decision results with the parameter fluctuates in small scope.