Multi-attribute Group Decision-making Methods Based On Linguistic Interval-valued Spherical Fuzzy Set

In real life,multi-attribute group decision-making problems are the important part of decision theory in which we choose the best one from the set of finite alternatives based on the collective information.Most decision-making problems are in an uncertain environment,and it is difficult to use quantitative information for evaluation.People are often more accustomed to using natural linguistic terms to evaluate.As an extension of a new type of fuzzy set,spherical fuzzy set is represented by four functions of the membership,non-membership,hesitation and waiver degree,which can more accurately describe the evaluation information and more close to real life.In order to better deal with the uncertain information in the decision-making process,this thesis proposes the multi-attribute decision-making method based on linguistic interval-valued spherical fuzzy set.The main research work is as follows:(1)In order to deal with the uncertainty problem described by linguistic values,the linguistic interval-valued spherical fuzzy set is proposed,where the membership,non-membership,hesitation and waiver degree are represented by linguistic interval-valued terms,improving the preference freedom of decision-makers.On this basis,the basic operations and properties of the linguistic interval-valued spherical fuzzy set are discussed to better deal with decision information in the linguistic interval-valued spherical fuzzy environment.(2)A multi-attribute group decision-making model based on the linguistic interval-valued spherical fuzzy environment is proposed.In order to deal with the information fusion problem in the linguistic interval-valued spherical fuzzy environment,the linguistic interval-valued spherical fuzzy power weighted average operator and the linguistic interval-valued spherical fuzzy power average operator are proposed to aggregate the evaluation information of different experts.Considering the evaluation information of multiple experts,the similarity between linguistic interval-valued spherical fuzzy numbers is used to determine attribute weights,effectively solving the problem of assigning attribute weights in decision-making problems.Based on the proposed operator,a multi-attribute group decision-making model is established to deal with group decision-making problems in the linguistic interval-valued spherical fuzzy environment,improving the limitations of traditional spherical fuzzy set.(3)To deal with the dynamic decision-making problem in the linguistic interval-valued spherical fuzzy environment,a dynamic multi-attribute group decision-making model based on the linguistic interval-valued spherical fuzzy environment is proposed.The dynamic linguistic interval-valued spherical fuzzy weighted average operator is proposed for time weighting,which aggregates nonlinear evaluation information and makes the decision result more realistic.Based on the dynamic linguistic interval-valued spherical fuzzy weighted average operator,a dynamic linguistic interval-valued spherical fuzzy TOPSIS decision-making model is proposed.Finally,an example of selecting the best land contractor shows the rationality and effectiveness of the model.