Research On OWA Operator Based On Elliptic Distribution And Decision-making Method Of Hesitant Fuzzy Information

The complex and changeable uncertain decision making environment and the limited cognitive level of the decision-makers bring more opportunities and challenges to the research of multi-attribute decision making methods.In this paper,the decision making methods based on OWA operator,hesitant fuzzy information,probabilistic hesitant fuzzy information and probabilistic interval-valued hesitant fuzzy information are studied deeply and systematically.The main work is as follows:(1)The OWA operator decision making method based on elliptical distribution is studied.The dual OWA operator and the dual weighted OWA operator are defined using the quantifier functions.The basic properties of two kinds of operators are studied in detail.Based on the elliptical distribution widely existed in probability and statistics,several effective and practical methods for determining the attribute weights of OWA operators are proposed,and some excellent properties of the methods are discussed in detail.(2)In the hesitant fuzzy information environment,a decision making method of hesitant fuzzy distance measure based on the membership deviation weighting is proposed.In order to solve the problem that the number of membership in two hesitant fuzzy elements is not equal,an element complement scheme is proposed which can fully consider the hesitant psychology of the decision-makers with different preferences.According to the deviation of membership between the two hesitation fuzzy elements in the hesitant fuzzy set,the weight coefficient of each complement scheme is defined when measuring the distance,and they are applied to five new improved hesitant fuzzy distances.For the first time,some limit forms of several improved generalized hesitant fuzzy distances with which parameter ? is zero and infinity are given.Finally,combined with financial product investment problems,a case analysis is carried out through multi-source data given by experts in the different fields.(3)In the hesitant fuzzy information environment,a decision making method of hesitant fuzzy Lance distance measure of dimension reduction based on exponential entropy weighting is proposed.Aiming at the unequal number of membership numbers in two hesitant fuzzy elements,a new dimension reduction scheme of the hesitant fuzzy element is introduced.Several hesitant fuzzy Lance distance measures are proposed to overcome the influence of the extreme data on the decision making results.Aiming at the condition that the attribute weight information is completely unknown,the hesitant fuzzy exponential entropy is constructed by using the actual data information,and the information entropy minimization criterion is used to determine the attribute weight.Finally,a case study is carried out based on the practical medical diagnosis problems.(4)In the probabilistic hesitant fuzzy environment,taking into account the decision-maker's limited rationality and attitude to risk,a probabilistic hesitant fuzzy TOP SIS emergency decision making model based on the cumulative prospect theory is proposed.Aiming at the problem of missing probabilistic information in the probabilistic hesitant fuzzy element,a new complement scheme is proposed.Because the mean value is a typical central trend measure in descriptive statistics and has excellent mathematical properties,the new scheme uses the weighted mean value of the original data information to supplement the elements and retains the original data information to a certain extent.Then,several probabilistic hesitant fuzzy Lance distance measure are proposed.The value functions based on the probabilistic hesitation fuzzy Lance distance are defined.In view of the fact that the attribute weights are completely unknown,the probabilistic hesitant fuzzy exponential entropy is constructed by using the actual data,and the attribute weights of the different prospect states are obtained.Aiming at the problem that attribute weights of the different prospect states have the different effects on the cumulative prospect value,the expression of the cumulative prospect value is improved.Finally,combined with the improved closeness coefficient of the TOPSIS method,a case study on the emergency decision making of the sudden outbreak epidemic respiratory disease is carried out.(5)In the probabilistic interval-valued hesitant fuzzy information environment,in order to fully mine the inherent laws of the original data and comprehensively analyze the relationship between the different attributes,a grey correlation projection VIKOR model based on probabilistic interval-valued hesitant fuzzy Lance distance is proposed.Aiming at the problem of missing probabilistic information in the probabilistic interval-valued hesitant fuzzy element,a scheme to complement the missing information is proposed.Then,several probabilistic interval-valued hesitant fuzzy Lance distance measure are proposed.The distance from each scheme to the positive and negative ideal solution is calculated by using the probabilistic interval-valued hesitant fuzzy Lance distance.Aiming at the attribute weights of some known prior information,a nonlinear optimization model of maximum satisfaction based on the probabilistic interval-valued hesitant fuzzy Lance distance is proposed by combining the two aspects of the scheme and the attribute.The attribute weights are determined by the model.The grey system theory,which has great advantages in dealing with "small sample" and "poor information" uncertainty problems,is effectively integrated into the VIKOR method.Finally,a case study on the evaluation of service quality of the different airlines is given.