Linguistic Multi-attribute Decision Making Method With Decision Makers’ Risk Preferences And Its Use In Low-carbon Tourism

There widely exist multi-attribute decision making problems in many fields such as real life,enterprise operation and management,industrial engineering,travel services and so on,multi-attribute decision making is an important part of modern decision science.Multi-attribute decision making problem is a problem that how to evaluate,rank and prioritize alternatives.Due to the fuzziness and complexity of decision making problems,decision makers tend to use linguistic terms to represent evaluation values over each alternative with respect to different attributes,namely,linguistic multi-attribute decision making.In linguistic multi-attribute decision making,decision makers usually have risk preferences which reflect their expectations and requirements on semantic values of linguistic terms.Therefore,the study of linguistic multi-attribute decision making methods based on decision makers’ risk preferences will enrich theories and methods of multi-attribute decision making.With the rapid development of social economy,the global carbon emissions has been increasing.In order to balance economic development with reduction of carbon emissions,low-carbon economy has attracted increasingly great attention from all walks of life,and it is an inevitable trend that the world economy transforms into low-carbon economy.Tourism is an important component of economic development,and then low-carbon tourism is a positive reaction to low-carbon economy.Thus,it is particularly important to make reasonable decisions in the actual promotion and construction of low-carbon tourism.Low-carbon tourism destination selection,low-carbon tourism destination demonstration area construction and low-carbon supplier selection generally involve many decision makers evaluating alternatives,so it is of theoretical and practical significance to study the application of linguistic multi-attribute group decision making methods based on decision makers’ risk preferences in low-carbon tourism.This paper makes a deep research on linguistic multi-attribute decision making and linguistic multi-attribute group decision making problems based on decision makers’ risk preferences,and the main research contents include the following points:(1)For linguistic multi-attribute decision making problems based on decision makers’ risk preferences,a generalized linguistic term set based on triangular fuzzy semantic information is defined.In order to capture and measure the decision maker’s risk preference,the Sigmoid function is expanded,and then the triangular fuzzy membership function with risk preference parameters is established.Based on the expected semantic information of linguistic terms given by the decision maker and the distance between two triangular fuzzy numbers,a nonlinear programming minimization model for solving risk preference parameters is constructed,and then the optimal generalized linguistic term set is obtained.For the case that the weight information is known,a linguistic multi-attribute decision making method based on decision makers’ risk preferences is proposed.(2)For the linguistic multi-attribute group decision making problems based on decision makers’ risk preferences,in order to determine the group risk preference,a nonlinear programming minimization model for solving group risk preference parameters is established based on expected semantic information given by individual decision makers and the distance between two triangular fuzzy numbers,and then the optimal group generalized linguistic term set is obtained.For the situation that attribute weight information is incomplete,individual triangular fuzzy decision matrices are aggregated into a group triangular fuzzy decision matrix by utilizing a triangular fuzzy aggregation operator,a linear programming maximization model for solving attribute weights is given based on the idea of the maximization of the score of each alternative’s group collective evaluation value,and then a linguistic multi-attribute group decision making method based on decision makers’ risk preferences and incomplete attribute weights is presented.(3)For linguistic multi-attribute group decision making problems that attribute and decision makers weights are all incomplete,firstly,a nonlinear programming model for solving decision makers weights is established based on the idea of the minimum sum of the distance between each element in the group decision matrix and the corresponding element in the individual one,the above model is combined with the linear programming maximization model for solving attribute weights proposed in(2),and then a quadratic linear programming maximization model is established to determine attribute weights,a linguistic multi-attribute group decision making method about incomplete weight information is given subsequently.For linguistic multi-attribute group decision making problems that decision makers weights are partly known,based on the principle that the sum of the distance between group overall evaluation values and individual one is the minimum,a nonlinear programming minimization model for solving decision makers weights is established by utilizing the distance between two triangular fuzzy numbers,and then a linguistic multi-attribute group decision making method that the weight information is partly known is proposed.(4)Considering decision makers’ risk preference,a linguistic multi-attribute decision making method when the weight information is known and three linguistic multiattribute group decision making methods under the situations of incomplete attribute weights,incomplete attribute and decision makers weights and incomplete decision makers weights proposed in this paper are respectively applied to problems of low-carbon tourism company emergency plan selection,low-carbon tourism destination selection,low-carbon tourism destination demonstration area construction and low-carbon supplier selection.