Multiple Criteria Decision Making Theories And Methods Based On Probabilistic Linguistic Term Sets

Due to the complexity of problems and the limitation of decision makers' cognition,there exists uncertainty and hesitation when human beings consider the problems.The probabilistic linguistic term set is a linguistic information model,which can accurately model the evaluation information of decision makers.It can not only express the hesitant information but also reflect the weight information assigned to different linguistic terms.Analyzing and solving multiple criteria decision making(MCDM)problems based on the probabilistic linguistic information has become a popular research hotspot.Nevertheless,multiple criteria decision making theories and methods based on probabilistic linguistic term sets still show some deficiencies:1)The current research results have never reported the quantification method of the hesitation and uncertainty of probabilistic linguistic term sets;2)There are incomparable defects in the outranking results among alternatives that are obtained by the multiple criteria decision making methods based on the outranking theory;3)The current research results have not yet reported the robustness analysis and effectiveness analysis of the multiple criteria decision making method based on the utility theory.(1)To process probabilistic linguistic term sets in a reasonable way,the probabilistic linguistic ELECTRE ? method has been proposed and applied to solve the cloud service selection problem.First of all,the multiple correlation coefficient analysis is introduced to determine the weights of criteria and an adjustment algorithm is proposed to derive the weight information of decision makers.Then,a novel comparison method based on score function and information entropy has put forward to determine the probabilistic linguistic accordance set,probabilistic linguistic discordance set,as well as probabilistic linguistic indifference set.Finally,the outranking results of alternatives are determined by setting the threshold and improving the outranking level judgement method.The real example shows that the proposed method can better deal with the cloud service selection problem than the existing studies.(2)To improve the decision results of the traditional TOPSIS and VIKOR decision making methods,the probabilisitic linguistic TOPSIS and probabilistic linguistic VIKOR methods are proposed and then applied for solving the network security service selection problem.To this end,a novel score function based on concentration is put forward so as to compare the superiority-inferiorty of probabilistic linguistic term sets.Afterwards,a novel generalized hybrid weighted distance based on probability splitting algorithm is put forward for measuring the difference between probabilistic linguistic term sets.Then,the novel probabilistic linguistic TOPSIS and probabilistic linguistic VIKOR methods based on score function and generalized hybrid weighted distance is put forward and then it is combined with a novel multiplicative analytic hierarchy process for solving the network security service selection problem for mobile edge computing environment.Finally,we conduct the simulation tests of randomly producing 100 probabilistic linguistic decision matrices so as to analyze the proposed decision mathods in terms of minimum violation,total deviation,conformity,and robustness.The simulation testing results show that the minimum violation and total deviation of the proposed probabilistic linguistic TOPSIS and probabilistic linguistic VIKOR methods are smaller than the existing studies,which indicates that the results of the proposed methods are more robust and effective.