Research On Multi-Attribute Decision-Making Method Based On Spherical Fuzzy Theory

The essence of multi-attribute decision-making is to sort multiple alternatives and select the best one through a certain decision method according to the given decision information.It is mainly composed of two parts,namely,obtaining attribute information and gathering decision information in a certain way,and sorting and selecting the best alternatives.The core idea of individuals,enterprises and governments is to maximize their own benefits when facing different alternatives and make decisions.In the classic multi-attribute decision-making process,the attribute information of each alternative is usually given by the decision experts in the form of accurate statistics.However,with the deepening and complexity of the decision-making problem and the inherent fuzziness of the decision-maker’s thinking,the fuzziness and uncertainty of the information are difficult to be expressed by accurate statistics.Spherical fuzzy set is one of the comparatively advanced tools to describe fuzzy attribute information for present.It allows decision makers to have a larger scale to represent membership,nonmembership and hesitation with nonlinear relationship,which can express decision information more accurately and objectively,with a broad application prospect.Therefore,based on the spherical fuzzy set theory,this paper studies the multi-attribute decision-making method based on the spherical fuzzy theory.The main work of this paper includes the following aspects.1.For the multi-attribute decision-making problem in which attribute information is represented by spherical fuzzy numbers,a spherical fuzzy TOPSIS method based on improved score function is proposed.First of all,in order to solve the defects of the existing scoring function,such as the need for secondary comparison,the violation of the nonlinear relationship of the three elements of the spherical fuzzy number,and the inconsistency with the objective facts in practical application,a scoring function of conformity psychology is proposed.This paper proves the properties of the new score function,and proves its effectiveness and superiority by comparing the calculation example with the existing score functions.Then,the positive and negative ideal solutions are determined by improving the score function,and the distance between the alternatives and the positive and negative ideal solutions is calculated respectively,and the relative closeness between the alternatives and the positive and negative ideal solutions is obtained to sort the alternatives and select the best one.Finally,the spherical fuzzy TOPSIS method based on the improved score function is applied to an example of printer selection,and the effectiveness and superiority of the improved score function and decision method are verified by comparing the simulation data with the existing decision methods.2.For the multi-attribute decision making problem in which the attribute weight is partially known and the attribute information is represented by spherical fuzzy numbers,a spherical fuzzy TOPSIS method based on comprehensive similarity is proposed.First,considering that the attribute weights of the existing spherical fuzzy multi-attribute decision-making problems are all spherical fuzzy numbers given by the decision-makers,which are highly subjective,a method for obtaining objective attribute weights by using a comprehensive similarity programming model is proposed.In addition,the subjective weighted decision matrix and the objective weighted decision matrix are obtained through the subjective attribute weight in the form of spherical fuzzy number and the objective attribute weight in the form of real number.By using the method of linear adjustment,the subjective and objective weighted decision matrix is obtained,which effectively avoids the influence of different subjective and objective preferences of decision makers on the decision results.Then,determine the positive and negative ideal solutions through the score function,calculate the distance between the alternatives and the positive and negative ideal solutions respectively,and obtain the relative closeness between the alternatives and the positive and negative ideal solutions respectively,followed by sorting the options to select the best one.Finally,the spherical fuzzy TOPSIS method based on the weight of comprehensive similarity is applied to the example of hospital site selection,and the effectiveness and superiority of the proposed decision-making method is verified by comparing with the existing methods.3.For the multi-attribute decision making problem in which attribute information is represented by spherical fuzzy numbers,this paper proposes a multi-attribute decision making method based on spherical fuzzy entropy Einstein aggregation operator.First,information entropy is taken as a part of the weight,and Einstein operation is introduced.For the intersection of spherical fuzzy numbers,Einstein product is used to replace the basic algebraic product;For the union of spherical fuzzy numbers,the Einstein weighted average operator of spherical fuzzy entropy and the Einstein ordered weighted average operator of spherical fuzzy entropy are proposed through replacing basic algebraic sum with Einstein sum,with their basic properties discussed.Then,the comprehensive attribute values of the alternatives are obtained through the spherical fuzzy entropy Einstein aggregation operator.After that,the score function value of the comprehensive attribute value is obtained by de-fuzzing the comprehensive attribute value through the score function,and the alternatives are sorted by the score function value to select the best one.Finally,the multi-attribute decision-making method based on the spherical fuzzy entropy Einstein aggregation operator is applied to the example of best teacher selection,and the effectiveness and superiority of the proposed decisionmaking method is verified by comparing with the existing methods.