Intuitionistic Fuzzy Multiple Attribute Complex-Large Group Decision Making Method Based On Prospect Theory

The existing multi-attribute decision making methods are mostly established on the basis of expected utility theory, but the defects of its descriptive function under uncertain conditions makes utility measure based on which can not correctly reflect the values and preferences of the human; then, the biased utility measure of a decision analysis will lead to incorrect decisions. And in real life, due to the complexity of the decision problem itself, the limited knowledge of the decision-makers, that fuzzy of the evaluation of things, as well as the high cost and other constraints needed to obtain accurate information, decision-making information is often difficult or impossible to represent with exact numbers. This requires people to re-examine the existing theories, methods and techniques, and to make a scientific and reasonable criticism and improvement by combining with the changes.For multi-attribute decision making problems under uncertainty, we study on multiple attribute complex-large group decision making method based on intuitionistic trapezoidal fuzzy information from the perspective of prospect Theory, and introduce the prospect theory into the analysis framework for multi-attribute decision-making. On one hand, prospect theory’s utility function is value judgments based on reference points, compared with the expected utility theory, more practical and more accurately to describe and explain the decision-choice behavior of decision makers under uncertainty. Taking into account the decision analysis is a priscrible discipline based on descriptive research and normative research paradigm, in order to make the intuitionistic trapezoidal fuzzy multiple attribute complex-large group decision making model more guiding value in reality, this paper introduces the idea of prospect theory into the multi-attribute decision model and build decision-making model based on the prospect value information of attributes. On the other hand, as for the vagueness and uncertainty of decision-making information, decision-makers are willing to give their decision-making information with the form of linguistic information or fuzzy information. Intuitionistic trapezoidal fuzzy numbers provide an idea to solve the problem of fuzzy multiple attribute group decision-making. Research work and the results are as follows:First, this paper establishs a prospect value determination method based on prospect theory and intuitionistic trapezoidal fuzzy numbers and extende prospect theory to the intuitionistic trapezoidal fuzzy environment. Further, the case of multiple reference points is taken into account. In view of the advantages of evidence theory in handling uncertainty information, this paper uses evidence theory to integrate prospect value under multi-reference points, and proposes a prospect value determination method based on mRP and DS-TrIF-IOWA operator.Second, this paper proposes a optimal selection method for multi-attribute decision making based on associated information and prospect theory. Taking into account prospect theory instead of the expected utility theory being more in line with the actual human decision-making mode, this paper use the proposed prospect value determination method based on prospect theory and intuitionistic trapezoidal fuzzy numbers to compute single attribute value in the multi-attribute decision-making. On the other hand, taking into account the interactive characteristics among the attributes in the reality of decision-making, this paper introduces the Choquet integral to solve the uncertain decision problem with attributes interrelated. This paper proposes several Intuitionistic trapezoidal fuzzy aggregation operators based on Choquet integral such as the TrIC, ITrIC, TrICD, and ITrICD operator, and the nature of the operators are discussed. On the basis of these concepts, this paper proposes comprehensive prospect value method based on TrIF-Choquet operator and intuitionistic trapezoidal fuzzy TOPSIS method based on TrIF-Choquet distance operator.Again, this paper proposes the group clustering algorithm based on ITrIFC TrIF-OWAD operator. By introducing the idea of prospect theory, this clustering algorithm take intuitionistic trapezoidal fuzzy prospect value matrix as basis information. Considering the properties of the interaction between information and programs sort position in the cluster analyzes, in the construction of similarity matrix, ITrIFC and TrIF-OWAD operator are used to assemble the relevant information for decision-making,and based on the similarity matrix, large group clustering algorithm are establised.On this basis, we propose intuitionistic fuzzy multiple attribute complex-large group decision making consistency analysis and consistency correction automatic algorithm. Taking into account the existence of the possibility of sub-groups of clusters or "Union" in large groups within groups, this paper first use the proposed large group clustering algorithm to cluster the large groups, and design cluster consistency index and group consistency index based on group clustering results, and then establish group consistency analysis method based on large group clustering algorithm. As for modification of the evaluation information, taking into account the respect of the original decision-makers evaluate information, this paper establishs consistency correction approach based clustering of large groups. Taking into account the time and cost constraints as well as the impact of herd behavior, complex-Large group decision making consistency correction automatic algorithm is proposed. According to this algorithm computer program are established; example analysis shows that the algorithm has strong maneuverability and practicability.Then, we propose the complex large group intuitionistic trapezoidal fuzzy prospect value matrix assembly method. Based on the proposed intuitionistic fuzzy multiple attribute complex-large group decision making consistency analysis and consistency correction automatic algorithm, taking into account the similar characteristics among individual prospect value matrix in each sub-group, this paper determine the weights of decision-makers based on intuitionistic trapezoidal fuzzy distance, individual decision-making information and the preferences of cluster virtual central figure; secondly; build cluster consensus intuitionistic trapezoidal fuzzy prospect value matrix; and based on cluster consensus intuitionistic trapezoidal fuzzy prospect value matrix, build lager group consensus intuitionistic trapezoidal fuzzy prospect value matrix by using weight information between clusters. This group assembly method can be better to reduce the loss of information, as much as possible to retain the original information of the decision-makers.Finally, we propose a intuitionistic trapezoidal fuzzy multiple attribute complex-large group decision making model based on prospect theory (MRP-TRIFPV-MAGDM). As for the decision-making process, the proposed model integrates the single attribute’s prospect value determination method, group consistency analysis and consistency correction, lager group consensus intuitionistic trapezoidal fuzzy prospect value matrix and program selection, and provides support for the development of decision support systems. On the research paradigm, the model combined with the normative paradigm and descriptive research paradigm. We consider the utility measure based on multiple reference points, the associated information between attributes, complex characteristics of decision makers, and based on utility measure,construct a intuitionistic trapezoidal fuzzy multiple attribute complex-large group decision making model. Then the proposed intuitionistic trapezoidal fuzzy multiple attribute complex-large group decision making model is more valueable in practice. The practicality and operability of the model has been proven by applying the proposed mRP-TrIFPV-MAGDM model into evaluation of two types of products.