Research On Hybrid Multiple Attribute Group Decision-Making Problem Based On OWA Operator Theory

In many domains such as society,economy and military,there exist massive complex group decision-making problems containing both qualitative attributes and quantitative attributes,which form the hybrid multiple attribute group decision-making problem(HMAGDM).The method for HMAGDM is able to deal with the case where the attributes are precise numbers,interval numbers and fuzzy numbers,which conform to the fuzziness and uncertainty of human,and also reduce unreasonable factor in decision-making by fully utilizing the wisdom of group experts.This paper will propose the method for the hybrid multiple attribute group decision-making problem in which the information about attribute weights is completely unknown and the primary coverage is as follows:(1)We first review the main existing methods for determining OWA operator weights,which obey the principle of maximum-entropy approximately.We next introduce an alternative measure of entropy based distance approach and analyze its desirable properties.Based on the alternative measure of entropy,we propose a linear objective programming(LP)model for determining OWA operator weights,which can ease computation and deal with DMs' vague preference information. Finally,we prove that Xu's normal distribution based method obeys the principle of maximum entropy and propose an argument-dependent approach based on normal distribution,which assigns very low weights to these "false" or "biased" opinions and can relieve the influence of the unfair arguments.(2)Presenting some extended continuous ordered weighted geometric(COWG)operator,such as weighted geometric averaging COWG(WG-COWG),ordered weighted geometric averaging COWG(OWG-COWG)operators and induced weighted geometric averaging COWG(I-COWG) operator.We next study their desirable properties.We then develop an approach to solving group decision-making(GDM)with interval multiplicative preference relations by the application of I-COWG operator,which can improve the consistency degree of group experts.(3)Proposing the model for hybrid multiple attribute decision-making(HMAGDM).For transforming the hybrid judgment matrix to the standardized judgment matrix,we turn interval numbers and fuzzy numbers into precise numbers by continuous ordered weighted averaging (COWA)operator,fuzzy maximizing operator and fuzzy minimizing operator.(4)This paper studies the multi-attribute decision-making problems in which attribute assessments and attribute weight are given in the forms of fuzzy linguistic assessments.We propose a fuzzy language multi-attribute method to obtain experts' synthetic evaluation value.Then we turn trapezoidal fuzzy numbers into precise numbers by COWA operator and get the weights of group experts directly.Finally,an illustrative example is given to demonstrate the feasibility and practicability of the proposed method.Then,we integrate the standardized judgment matrix of group experts by HOWA operator according the group experts' weights and the DM's optimistic degree.(5)A model with adjustability is proposed to seek objective weight based on the entropy of attributes,which is able to adjust the difference degree of the attribute weights by the system parameterρ.Then subjective weight and objective weight are integrated into general weight linearly by trade-off coefficientβ,which can reflect both subjective factors and objective factors.Finally,the basic flow of HMAGDM is given and a numerical example for choosing suppliers is given to illustrate the developed method.