Group Decision Making Method Based On Incomplete Probabilistic Linguistic Preference Relation

This thesis discusses how to derive the ranking vector from the incomplete PLPR mainly in the following three aspects.Firstly,a algorithm is designed to derive the ranking vector of the complete PLPR,which could also improve the consistency.Secondly,a model which could simultaneously calculate the ranking vector,incomplete elements and consistency index is given to the incomplete product PLPR under the restriction of optimal consistency.A definition of the consistency index is composed to ensure that the ranking vectors are consistent.The definition,which is composed of the deviation values obtained by the minimum deviation algorithm,could detect the degree of consistency.When the consistency index is greater than the consistency threshold,the iterative optimization algorithm proposed in this paper is used to modify the probabilistic language term set with the largest deviation.Iterate until PLPR is consistent,thus the consistent ranking vector is obtained.Theoretically,a theorem could be used to prove that the corrected deviation of PLPR is zero,and the consistency of PLPR is improved.Thirdly,we design an algorithm to derive the incomplete elements and the ranking vector of the PLPR under the condition of the known elements in the incomplete additive PLPR.When the number of alternatives is large,it is very difficult to derive ranking vectors from probabilistic linguistic preference relations.In order to accurately describe the preference of experts and facilitate the operation of decision-making institutions,we introduce the conception of probabilistic hesitant fuzzy preference relation(PPR).According to the demand,two kinds of conversion functions are designed to convert PLPR to PPR,which can be divided into the following two cases: For the complete PPR,the expectation matrix of PPR is obtained by using the expectation operator,and the equation system composed of expectation value and ranking vectors is used for the expectation matrix,which is transformed into a characteristic problem to calculate the ranking vectors;For incomplete PPR,firstly,adding the incomplete element,and then using the perfect PPR to export the ranking vectors.Each algorithm gives the validity and accuracy of the methods.