Research On Multi-attribute Decision-making Method Based On Probabilistic Linguistic Information

Probabilistic linguistic term sets(PLTSs),as a new expanded form of fuzzy set for describing qualitative information,mainly contain two parts of information: multiple linguistic evaluation values and their corresponding probability values.In this thesis,based on PLTSs,some theoretical methods and applications in the field of multiattribute decision making are investigated.The main contributions can be summarized as follows.(1)The comparison method between PLTSs is investigated,and a probabilistic linguistic comparison formula based on the new probability degree is defined.The comparison method between two PLTSs plays an important role in the decision-making process.In order to make up for the defects of comparison method with PLTSs proposed by Feng et al.,this thesis proposes a new comparison method based on the idea of probability degree.Meanwhile,some properties of the method are analyzed and proved.The method not only makes up for the deficiency of the existing methods,but also considers the applicability of the possible degree formula when PLTS is reduced to linguistic term set.(2)The consistency and the solution state of the probabilistic linguistic BWM model is studied.From the original probabilistic linguistic decision information,the preference strength between attributes is mined,and a fuzzy complementary possibility degree matrix on the scale of [0,1] is constructed.Then,combining the classic BWM idea with the possibility degree matrix,two optimization models are constructed to obtain the optimal attribute weights.Finally,the consistency of the preference matrix and the state of the model solution are analyzed and summarized.(3)The problem of determining the weight of attributes characterized by probabilistic linguistic information,where the correlation between attributes exists,is studied.Because there may be some correlation between different attributes,it is important to consider correlation conflicts between attributes when calculating attribute weights.A probabilistic linguistic CRITIC(PL-CRITIC)method for objective attribute weights is proposed.In the PL-CRITIC method,the correlation coefficients between attributes are used to express the differences between the same attributes in different alternatives.Based on the correlation coefficient between attributes and the standard deviation value of each attribute,the amount of information contained in the attribute is characterized to obtain the objective attribute weights.(4)A probabilistic linguistic multi-attribute decision problem based on Wasserstein distance is studied.Firstly,a new Wasserstein-based distance measure is proposed in order to compensate for the shortcomings of existing probabilistic linguistic distance measures.Secondly,it is shown that the proposed distance measure satisfies the conditions of the axiomatic definition of distance,especially including the property of triangular inequality.Finally,by integrating Wasserstein distance measure into the probabilistic linguistic TODIM method,a new behavioral multi-attribute decisionmaking method is proposed to evaluate the potential of sustainable rural tourism.(5)The probabilistic linguistic multi-attribute decision problem that considers individual disappointment emotion is studied.Firstly,a subjective utility function for probabilistic linguistic preferences is defined based on probability distributions and classical utility functions.Secondly,new individual consistency and non-consistency indicators are defined based on disappointment theory.An optimization model for determining attribute weights is established based on the idea of LINMAP,and the comprehensive perceived utility values of the alternatives are calculated for ranking.Finally,applying the method to the selection of the Internet partner company shows that the proposed method is reasonable and effective.(6)The multi-attribute group decision-making problem with incomplete probabilistic linguistic information is studied.Firstly,in order to obtain the missing probabilistic information and linguistic terminology information simultaneously,a discrete mathematical planning model and a mixed integer planning model are developed based on the group consensus variance.Secondly,the group evaluation information is obtained by integrating experts' opinions using the aggregation operator,and coefficients of variation of alternatives are obtained based on the expected value and the weighted variance value so that the alternatives can be ranked and selected.Finally,the effectiveness of the proposed method in this thesis is verified by a numerical example of selecting a brand car,and the comparative analysis shows the advantages and rationality of the proposed method.The above research enriches the methods and applications of multi-attribute decision-making based on probabilistic linguistic information and makes up for some of the shortcomings of existing research,which provides certain methodological support for the solution of actual multi-attribute decision-making problems under the uncertainty and vagueness environments.