Study On Several Problems Of Decision-making Model Under Comlex Enviroments

Decision-making is always based on the preference relations of decision makers over alternatives.Due to the complexity and uncertainty of practical decision problems and the diversity of decision environment,it is reasonable to use fuzzy numbers to express decision information.By considering the rational behavior of the decision maker,it is very important to study the consistency of preference relations in the decision-making model.Second,due to the uncertain nature of fuzzy decision-making information,it describes the flexibility of decision-maker's opinions,and it is an important issue worth studying on how to quantify the flexibility.Third,the weights of alternatives in fuzzy decision-making process are often expressed as fuzzy numbers.is still worth studying on how to deal with the uncertainty of fuzzy numbers to make the final ranking reasonable.In this thesis,the above-mentioned problems are studied.The main research work and novelty are given as follows:(1)Based on the concept of approximate consistency,the generalized consistency index has been defined to quantify the inconsistency degree of triangular fuzzy multiplicative reciprocal matrices.Moreover,its properties are studied and the acceptable consistency is also discussed.It is expatiated quantitatively that triangular fuzzy multiplicative reciprocal matrices are the softened version of consistent multiplicative reciprocal matrices.Second,using the consistency index as an order-inducing variable,the generalized aggregation operator is proposed and the group decision making model is established.Finally,the advantages and novelty of the constructed index and group decision making model are demonstrated by numerical examples.(2)Based on the scale [1/s,s],a new method for calculating the flexibility degree of fuzzy numbers is proposed.With the confidence level and multiplicative reciprocal property,the new flexibility degree formulae of interval numbers,triangular and trapezoidal fuzzy numbers are constructed.The effect of the centroids of triangular and trapezoidal fuzzy numbers on the flexibility degrees is also taken into account.In addition,by simulating the situation that there is a leader in group decision making,the flexibility degree-driven aggregation operator and consensus model of group decision making has been proposed.Based on numerical examples,the influence of flexibility degree and confidence levels on the final results is analyzed.(3)Based on the probability theory,the combined effect of the prossibilistic mean value and variance or standard deviation on the ranking of the generalized fuzzy numbers is considered.The axiomatic properties of the ranking method are further studied.Some comparisons are analyzed by carrying out lots of numerical examples.The obtained results show that the proposed new ranking method is feasible.In summary,under fuzzy environments,the group decision making models are established by proposing consistency index and flexibility degree of fuzzy numbers.A new method has been given to rank the generalized fuzzy numbers.The decision theory and methods have developed in a complex environment.