Group Decision Making Methods Based On Interval Fuzzy Information And Their Applications

Decision-making is a universal and important behavior,ranging from individual job selection and house purchase,to organizational evaluation and corporate investment,to technology research and national policy making.Due to the complexity and variability of decision-making environment,the uncertainty of objects and the ambiguity of human cognition,group wisdom is more comprehensive and objective than individual wisdom.Then,group decision making method based on interval fuzzy information has become an important branch of decision-making.In recent research,there are many methods for group decision making(GDM)on interval values,but still three limitations exist.Firstly,whether in estimating missing values or improving the consistency of preference relations,the traditional methods do not take the risk attitude of decision maker(DM)into account.Secondly,the interval values are often assumed to be uniformly distributed,and this ideal distribution state does not match the actual decision-making situation.Thirdly,in partial methods of Interval GDM,the aggregated group decision matrix is directly obtained by maximizing the group consensus,while the accurate values of the DMs' weights are ignored.Aiming at the above shortcomings,this paper mainly foucus on following three studies.(1)This paper discusses single-person decision making method for incomplete IMPR.Firstly,the concept of risk attitude and its necessity are proposed.And the acceptably multiplicative consistency is defined by introducing the risk attitude into the multiplicative consistency index.Secondly,a multi-objective linear programming model for solving the most pessimistic and most optimistic IMPR is constructed.This model is able to estimate missing values while retaining as much original information as possible and guaranting the acceptably consistency of IMPR.Based on the triangle distribution of interval values,a stochastic programming model is established to derive the priority weights.Then,a distance minimization mathematical model is built to obtain the priority vector and scheme ranking.Finally,the applicability and reliability of the single-person decision-making method of incomplete IMPR are illustrated through a case study of a new sharing economy development plan selection.(2)This paper investigates the GDM with incomplete IMPRs.Firstly,a new consistency index of IMPR is defined.By minimizing the consistency index,the missing values in an incomplete IMPR can be estimated.Subsequently,considering the risk attitude of DM,two optimization models are constructed to obtain the most pessimistic acceptably multiplicative consistent IMPR and the most optimistic acceptably multiplicative consistent IMPR,respectively.For GDM with incomplete IMPRs,to reach maximum group support degree,a 0-1 mixed integer programming model is established to determine the DMs' weights.After taking the category information of the individual intervals and collective intervals into consideration,the adjusted DMs' weights are defined.Then,the individual IMPRs are integrated into the collective IMPR.Based on the triangular distribution of interval,a stochastic programming model is built to derive the priority weights from an acceptably multiplicative consistent IMPR.The ranking order of alternatives is generated by the collective IMPR.Finally,an example of marine pollution emergency plan selection is demonstrated to illustrate the validity and applicability of the proposed methods.(3)This paper proposes an Interval multi-criteria GDM method based on improved TOPSIS.Firstly,the Euclidean distance formula and the normalization bias between [1/9,9] interval values are defined.Taking the maximum deviation as the goal,a single-objective optimization model is constructed to obtain the optimal single-person criteria weight.Based on the new Euclidean distance formula,the DMs' weights are calculated.The median,width and score of the interval value including risk attitude are defined.Subsequently,the overall positive and negative ideal solutions are found from the ideal solutions of the most pessimistic and optimistic risk attitudes.Then,the closeness and the ranking of alternatives are obtained by the improved TOPSIS method.Finally,the feasibility of this method is illustrated by an example of ancient building fire protection plan selection.