Two Kinds Of Interval Fuzzy Set Theories And Their Applications On Group Decision Making

In recent years,Fuzzy theory has played an increasingly important role on decision-making problems,among which the research on uncertain information is one of its hot spots.On the basis of reading and studying the existing literature,this paper mainly discusses two kinds of multi-attribute group decision making problems represented by interval type fuzzy sets.The specific works are as follows:1.Based on the related properties and concepts of interval type-2 fuzzy sets and inter-val type-2 fuzzy sets introduced,a new interval type-2 fuzzy expectation formula is defined.According to the three uncertainties of interval type-2 fuzzy sets,a new relative cross-entropy of interval type-2 fuzzy sets is defined.Then the distance formula between two IT2FSs is proposed.Based on the distance formula,the entropy of IT2FSs is defined,and it meets the requirement of four axioms with the entropy rule,this paper proposes a decision method based on total probability entropy.Assuming that the expert weights are known in group decision making,the optimal attribute weights are solved by the optimized linear model construct-ed,and the attribute values of each scheme are aggregated by using IT20WA operator.The scheme plans are ranked by using the expected results equation of IT2FSs defined so as to get the optimal scheme.2.Based on ?-cut sets,fuzzy factor and interval factor of interval type-2 fuzzy sets are proposed.Then,based on these two factors,cross-entropy and entropy formulas of IT2FSs are proposed to measure the fuzzy information and mutual information between IT2FSs.In addition,based on the IT2FSs cross entropy formula and the total probability formula,the IT2FSs total probability cross entropy formula is proposed to measure the relative uncertainty between IT2FSs.Next,an utility function of IT2FSs is proposed to compare the good or bad relationships between IT2FSs.Finally,an optimal linear programming model based on IT2FSs entropy,total probability cross entropy and utility function is established to solve the optimal scheme problem on multi-attribute group decision-making.3.The basic properties and operations of interval picture fuzzy sets are studied.The interval weighted arithmetic mean operator is proposed and its properties are discussed.Then the score function of interval picture set is used to measure the merits of interval picture fuzzy numbers.The cross entropy of interval picture fuzzy set is used to measure the difference be-tween two IvPFSs.A new sorting formula based on positive ideal solution is proposed to select the optimal scheme on decision making,the defined cross entropy and sorting formula are used to solve the attribute weights on the multi-attribute group decision making problems.The expert weights is given by the similarity formula.Finally,a new multi-attribute group decision making method is proposed and applied to the multi-attribute group decision making problems.